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\342\200\242 \342\200\242 \342\200\242 \342\200\242 Alternate Slides <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> \342\200\242 \342\200\242 \342\200\242 \342\200\242 \342\200\242 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style angle="45" offset="4" radius="6"/> </styles> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style angle="45" offset="4" radius="6"/> </styles> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> <body visibility="visible" location="157 419" size="709 217" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st0.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="center" font-ligatures="none" tab-stops="L 96" font-size="54" font-name="Futura-Medium">Tracking Multiple Mouse Contours (without Too Many Samples)</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="center" tab-stops="L 96" font-size="36" font-name="Futura-Medium">Kristin Branson and Serge Belongie</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="center" tab-stops="L 96" font-size="36" font-name="Futura-Medium">{kbranson,sjb}@cs.ucsd.edu</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="center" tab-stops="L 96" font-size="36" font-name="Futura-Medium">Dept. of Computer Science</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="center" tab-stops="L 96" font-size="36" font-name="Futura-Medium">U.C. San Diego</content> </bullet> </bullets> <background-fill-style byte-size="864" fill-type="image" image-data="darkbluebg.pdf" image-scale="scale-to-fit"/> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[[My name is Kristin Branson. I’m a student at UC San Diego, and] I will be talking about our research on tracking the contours of multiple mice. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="55 118" size="913 155" vertical-alignment="tracks-master"/> <plugin transformation="1 0 0 1 152 311.667" opacity="1"> <plugin-data> <plugin:movie height="284" key="root" width="720" src="rawvideo.mov"/> <string key="CPVersion">1.0</string> <string key="MIMEType">video/quicktime</string> </plugin-data> <styles> <shadow-style opacity="0" radius="0"/> </styles> </plugin> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8372" size="60 45" file="thumbs/st1.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">problem</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We need to track three identical mice from video of a side view of their cage. </content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[The problem we are trying to solve is to determine the locations and positions of three identical mice from video of a side view of their cage. Here is the raw video we used in our experiments. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 349" size="824 319" vertical-alignment="tracks-master"/> <image byte-size="308766" display-name="contour_raw01819_1.png" transformation="0.626389 0 0 0.626389 301 142" lock-aspect-ratio="true" image-data="contour_raw01819_1.png" natural-size="720 283"/> <g id="g-2" transformation="1 0 0 1 340.05 221"> <shape stroke-color="0.901961 0 0.117647" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.729496 -0.510799 0.209498 0.299196 340.05 272.08" stroke-width="3"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> <shape stroke-color="1 0.8 0.0117647" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.931194 -0.214984 0.080416 0.34832 389.88 264.498" stroke-width="3"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> <shape stroke-color="0.270588 0 0.792157" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="-0.55655 -0.321324 0.203841 -0.353064 707.271 310.439" stroke-width="3"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> </g> <g id="g-1" transformation="1 0 0 1 382 256"> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.105 0 0 0.0999996 382 256"> <styles> <fill-style fill-type="color" fill-color="0.901961 0 0.117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.105 0 0 0.0999996 435 266"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.105 0 0 0.0999996 685 272"> <styles> <fill-style fill-type="color" fill-color="0.270588 0 0.792157"/> </styles> </shape> </g> <image byte-size="310682" display-name="contours01819_1.png" id="image-1" transformation="0.628294 0 0 0.628294 300 141.257" lock-aspect-ratio="true" image-data="contours01819_1.png" natural-size="721 284"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st2.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">what is tracking?</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We want to find the position of each mouse in each frame. </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The more detailed information we can collect, the better.</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-1"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-2"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="image-1"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Our goal is to find the position of each mouse in each frame. At minimum, the position of the mouse is just its location, but we would like to collect more detailed information, like the size of each mouse and the angle of each mouse. Even better would be to fit detailed models of the mice to the image. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="147 525" size="853 176" vertical-alignment="tracks-master"/> <textbox grow-horizontally="true" size="253 28" transformation="1 0 0 1 160.2 454.85"> <content font-color="1 1 1" paragraph-spacing="-2" paragraph-alignment="left" tab-stops="L 0 L 72 L 144" font-size="24" paragraph-line-spacing="0.6" font-name="ArialMT">Mouse Vivarium Room</content> </textbox> <image byte-size="15593" display-name="Image-1" transformation="1.66809 0 0 1.66809 97 150" lock-aspect-ratio="true" image-data="Slide%204%20racks.jpg" natural-size="235 176"> <styles> <dash-style pattern="solid"/> </styles> </image> <shape stroke-color="1 1 1" path="M 0 0 L 41.9147 100 L 100 100 L 5.22928 3.71517 L 0 0 Z M 0 0" transformation="6.22 0 0 0.8 304.5 313.25" stroke-width="1"> <styles> <fill-style fill-type="color" fill-color="0.410201 0.503843 0.784768 0.25"/> <dash-style pattern="solid"/> </styles> </shape> <shape stroke-color="1 1 1" path="M 5.03018 98.9305 L 100 0.534759 L 41.8109 0 L 0 100 L 5.03018 98.9305 Z M 5.03018 98.9305" transformation="6.22 0 0 0.94 304.75 195.125" stroke-width="1"> <styles> <fill-style fill-type="color" fill-color="0.410201 0.503843 0.784768 0.25"/> <dash-style pattern="solid"/> </styles> </shape> <shape stroke-color="1 1 1" path="M 100 100 L 100 0 L 0 2.63158 L 0 86.8421 L 100 100 Z M 100 100" transformation="0.32 0 0 0.28 303.875 288.75" stroke-width="2"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> <image byte-size="853380" display-name="Image-2" transformation="0.496203 0 0 0.496203 568.375 197" lock-aspect-ratio="true" image-data="mouse0500.tiff" natural-size="720 395"> <styles> <dash-style pattern="solid"/> </styles> </image> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8362" size="60 45" file="thumbs/st21.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">motivation</content> </bullet> <bullet level="1" spacing="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">A vivarium houses thousands of cages of mice.</content> </bullet> <bullet level="1" spacing="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Manual, close monitoring of each mouse is impossible.</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[So why are we interested in tracking mice? This research was inspired by the “smart vivarium” project at UCSD. A vivarium is a lab that houses thousands of cages of mice for medical research purposes. At UCSD alone, there are about 100,000 mice used for medical research, while there are only about 100 people caring for the mice. Because of this manual, close monitoring of each mouse is impossible. The smart vivarium project is therefore exploring automated algorithms for monitoring mouse behavior. We would like our algorithm to work with the equipment in existing vivaria. This cage is a cage standard in most vivaria. An overhead view is prevented by the feeder at the top of the cage, so we have been working with side view data. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="89 285" size="846 450" vertical-alignment="tracks-master"/> <image byte-size="853380" display-name="Image-4" transformation="0.397222 0 0 0.397222 30 156" lock-aspect-ratio="true" image-data="mouse0500.tiff" natural-size="720 395"> <styles> <dash-style pattern="solid"/> </styles> </image> <line tail="28 314" stroke-color="0.410201 0.503843 0.784768" head="401 260" stroke-width="4"/> <line tail="30 154" stroke-color="0.410201 0.503843 0.784768" head="403 260" stroke-width="4"/> <line tail="315 312" stroke-color="0.410201 0.503843 0.784768" head="402 261" stroke-width="4"/> <line tail="315 155" stroke-color="0.410201 0.503843 0.784768" head="403 261" stroke-width="4"/> <shape path="M 85.3553 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font-name="Futura-Medium">Behavior Analysis Algorithm</content> </textbox> <g transformation="1 0 0 1 399 169"> <shape path="M 0 0 L 100 0 L 100 100 L 0 100 Z M 0 0" transformation="1.21 0 0 0.73 430 169" stroke-color="0.410201 0.503843 0.784768"> <styles> <fill-style fill-type="color" fill-color="0.410201 0.503843 0.784768 0.5"/> <dash-style pattern="solid"/> <shadow-style opacity="0.75" angle="45" offset="6" radius="10"/> </styles> </shape> <textbox size="123 64" transformation="1 0 0 1 429 173"> <content font-color="g1" paragraph-alignment="center" tab-stops="L 84" font-size="24" font-name="Futura-Medium">Tracking Algorithm</content> </textbox> <line tail="399 259" stroke-color="0.410201 0.503843 0.784768" head="428 206" stroke-width="4"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 L 3 1.5 Z M 0 0" match-point="3 1.5"/> </styles> </line> <line tail="553 207" stroke-color="0.410201 0.503843 0.784768" head="605 207" stroke-width="4"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 L 3 1.5 Z M 0 0" match-point="3 1.5"/> </styles> </line> </g> <shape path="M 0 0 L 100 0 L 100 100 L 0 100 Z M 0 0" transformation="1.55 0 0 1.68 780 145" stroke-color="1 0.8 0.0117647"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647 0.5"/> <dash-style pattern="solid"/> <shadow-style opacity="0.75" angle="45" offset="6" radius="10"/> </styles> </shape> <textbox size="156 160" transformation="1 0 0 1 779 149"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="24" font-name="Futura-Medium">Activity: Eating Scratching Drinking Sleeping</content> </textbox> <line tail="727 229" stroke-color="0.410201 0.503843 0.784768" head="779 229" stroke-width="4"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 L 3 1.5 Z M 0 0" match-point="3 1.5"/> </styles> </line> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st3.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">motivation</content> </bullet> <bullet level="1" spacing="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Automated behavior analysis will allow for:</content> </bullet> <bullet level="2" spacing="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Improved animal care.</content> </bullet> <bullet level="2" spacing="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">More detailed and exact data collection.</content> </bullet> <bullet level="1" spacing="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[An algorithm that tracks individual mice is a necessity for automated behavior analysis. ]]> </content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[With an automated algorithm providing close monitoring of the mice, we will be able to improve animal care, for example by identifying sick mice earlier to prevent the spread of disease. We will also be able to collect more detailed and exact data, from which new medical results can be extracted. The positions of the mice are valuable cues for activity recognition (for example, if we know that a mouse’s mouth is near the water bottle, it is very probable that it is drinking, or if a mouse has not moved for a while, it is probably sleeping). In addition, as the mice are visually identical, collecting individual behavior data requires tracking their identities. For behavior analysis, the more detailed information we can get about the positions of the mice, the better. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 317" size="824 314" vertical-alignment="top"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st10.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">unique difficulties</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Tracking multiple mice is difficult because</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 317" size="824 314" vertical-alignment="top"/> <plugin transformation="1 0 0 1 374 115" opacity="1"> <plugin-data> <plugin:movie height="185" key="root" width="276" src="erratic_motion%2002.mov"/> <string key="CPVersion">1.0</string> <string key="MIMEType">video/quicktime</string> </plugin-data> <styles> <shadow-style opacity="0" radius="0"/> </styles> </plugin> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st11.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">unique difficulties</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Tracking multiple mice is difficult because</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Their motion is erratic. </content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Their motion is erratic and unconstrained. Thus, it is difficult to constrain the positions of the mice in the current frame from their positions in the previous frame. This means we have to search a large space. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 317" size="824 314" vertical-alignment="top"/> <g transformation="1 0 0 1 200 139.5"> <image natural-size="108 227" display-name="pasted.tiff" byte-size="79312" transformation="0.651982 0 0 0.651982 200 139.5" lock-aspect-ratio="true" image-data="pasted.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> <image natural-size="129 106" display-name="pasted.tiff" byte-size="41232" transformation="1.39623 0 0 1.39623 643.5 140" lock-aspect-ratio="true" image-data="pasted1.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> <image natural-size="179 79" display-name="pasted.tiff" byte-size="45650" transformation="1 0 0 1 270.5 208.5" lock-aspect-ratio="true" image-data="pasted2.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> <image natural-size="108 88" display-name="pasted.tiff" byte-size="30690" transformation="0.840909 0 0 0.840909 353.591 140" lock-aspect-ratio="true" image-data="pasted3.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> <image natural-size="103 148" display-name="pasted.tiff" byte-size="51796" transformation="1 0 0 1 441.5 140" lock-aspect-ratio="true" image-data="pasted4.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> <image natural-size="104 87" display-name="pasted.tiff" byte-size="28346" transformation="1 0 0 1 541 139.5" lock-aspect-ratio="true" image-data="pasted5.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> <image natural-size="168 87" display-name="pasted.tiff" byte-size="47856" transformation="0.767857 0 0 0.767857 541 220.696" lock-aspect-ratio="true" image-data="pasted6.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> <image natural-size="83 79" display-name="pasted.tiff" byte-size="20864" transformation="1 0 0 1 270.5 139.5" lock-aspect-ratio="true" image-data="pasted7.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st12.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">unique difficulties</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Tracking multiple mice is difficult because</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Their motion is erratic. </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">They are unconstained and deformable.</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 317" size="824 314" vertical-alignment="top"/> <image byte-size="79785" display-name="Image-6" transformation="1.26597 0 0 1.26603 200 140" lock-aspect-ratio="true" image-data="image2.png" natural-size="493 117"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st13.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">unique difficulties</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Tracking multiple mice is difficult because</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Their motion is erratic. </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">They are unconstained and deformable.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">They are prone to severe occlusions.</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 317" size="824 314" vertical-alignment="top"/> <image byte-size="81566" display-name="Image-5" transformation="1.25635 0 0 1.25641 202 140" lock-aspect-ratio="true" image-data="image.png" natural-size="493 117"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st14.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">unique difficulties</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Tracking multiple mice is difficult because</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Their motion is erratic. </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">They are unconstained and deformable.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">They are prone to severe occlusions.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">They are visually indistinguishable.</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 317" size="824 314" vertical-alignment="top"/> <image byte-size="49528" display-name="pasted.tiff" transformation="1.86082 0 0 1.86082 331 139" lock-aspect-ratio="true" image-data="pasted9.tiff" natural-size="194 80"/> <g id="g-3" transformation="1 0 0 1 121.5 139"> <image byte-size="139536" display-name="pasted.tiff" transformation="1.192 0 0 1.192 121.5 139.5" lock-aspect-ratio="true" image-data="pasted10.tiff" natural-size="335 125"/> <image byte-size="6889" display-name="cannyedge3.png" transformation="0.526502 0 0 0.526502 523 139" lock-aspect-ratio="true" image-data="cannyedge3.png" natural-size="720 283"/> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8088" size="60 45" file="thumbs/st101.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">unique difficulties</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Tracking multiple mice is difficult because</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Their motion is erratic. </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">They are unconstained and deformable.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">They are prone to severe occlusions.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">They are visually indistinguishable.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">This is a real-world problem.</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-3"> <property name="animationType" value="1"/> </build> </events> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 357" size="824 342" vertical-alignment="top"/> <image byte-size="79785" display-name="Image-6" transformation="1.26597 0 0 1.26603 200 140" lock-aspect-ratio="true" image-data="image2.png" natural-size="493 117"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st121.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">occlusions</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The mice often occlude one another severely.</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 357" size="824 342" vertical-alignment="top"/> <image byte-size="64092" display-name="dependenttrackers1.png" transformation="1 0 0 1 363 141" lock-aspect-ratio="true" image-data="dependenttrackers1.png" natural-size="298 145"/> <image byte-size="65688" display-name="dependenttrackers2.png" id="image-2" transformation="1 0 0 1 363 141" lock-aspect-ratio="true" image-data="dependenttrackers2.png" natural-size="298 145"/> <image byte-size="64855" display-name="dependenttrackers3.png" id="image-3" transformation="1 0 0 1 363 141" lock-aspect-ratio="true" image-data="dependenttrackers3.png" natural-size="298 145"/> <image byte-size="65615" display-name="dependenttrackers4.png" id="image-4" transformation="1 0 0 1 363 141" lock-aspect-ratio="true" image-data="dependenttrackers4.png" natural-size="298 145"/> <image byte-size="64081" display-name="dependenttrackers5.png" id="image-5" transformation="1 0 0 1 363 141" lock-aspect-ratio="true" image-data="dependenttrackers5.png" natural-size="298 145"/> <image byte-size="62460" display-name="dependenttrackers6.png" id="image-6" transformation="1 0 0 1 363 141" lock-aspect-ratio="true" image-data="dependenttrackers6.png" natural-size="298 145"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st131.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">occlusions</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The mice often occlude one another severely.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Independent trackers might follow same mouse.</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="image-2"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="image-3"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="image-4"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="image-5"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="image-6"> <property name="animationType" value="1"/> </build> </events> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 357" size="824 342" vertical-alignment="top"/> <image byte-size="62460" display-name="dependenttrackers6.png" transformation="1 0 0 1 363 141" lock-aspect-ratio="true" image-data="dependenttrackers6.png" natural-size="298 145"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st141.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">occlusions</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The mice often occlude one another severely.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Independent trackers might follow the same mouse.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[Explicit multitarget algorithms search a space whose size increases exponentially with the number of objects.]]> </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 238" size="824 450" vertical-alignment="tracks-master"/> <image byte-size="124537" display-name="Image-65" transformation="0.905729 0 0 0.905729 348.5 113.125" lock-aspect-ratio="true" image-data="background_0.png" stroke-width="1" natural-size="360 240"> <styles> <dash-style pattern="solid"/> </styles> </image> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st5.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">simplifications</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We benefit from a number of simplifying assumptions:</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We have a closed environment.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The global illumination does not change.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The camera does not move.</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[There are several simplifying assumptions we can make for our application. First, we have a closed environment -- the number of mice will remain constant. Second, the global illumination does not change, as our vivaria are indoors. Third, the camera is static, which we can exploit with background modeling. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 218" size="824 403" vertical-alignment="tracks-master"/> <image byte-size="879520" display-name="pasted.tiff" transformation="0.529316 0 0 0.529316 112 155.5" lock-aspect-ratio="true" image-data="pasted8.tiff" natural-size="1566 307"/> <g id="g-4" transformation="1 0 0 1 148.339 229"> <shape stroke-color="0.901961 0 0.117647" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.696609 -0.487771 0.17661 0.252227 148.339 278.777" stroke-width="3"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647 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0.117647" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.696609 -0.487771 0.17661 0.252227 561.339 277.777" stroke-width="3"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> <shape stroke-color="1 0.8 0.0117647" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.831831 -0.192044 0.0732459 0.317263 607.492 268.478" stroke-width="3"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> <shape stroke-color="0.270588 0 0.792157" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="-0.548873 -0.316892 0.187287 -0.324391 903.271 310.439" stroke-width="3"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st15.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">previous work</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Two popular algorithms</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Track multiple blobs</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-4"> <property name="animationType" value="1"/> </build> </events> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> <g transformation="1 0 0 1 76 148"> <image byte-size="308766" display-name="contour_raw01819_1.png" transformation="0.626389 0 0 0.626389 525 148" lock-aspect-ratio="true" image-data="contour_raw01819_1.png" natural-size="720 283"/> <image byte-size="35095" display-name="contourI01819_1.png" transformation="0.624133 0 0 0.624133 76 148" lock-aspect-ratio="true" image-data="contourI01819_1.png" natural-size="721 284"/> </g> <g id="g-5" transformation="1 0 0 1 74 147"> <image byte-size="310682" display-name="contours01819_1.png" transformation="0.628294 0 0 0.628294 524 147.257" lock-aspect-ratio="true" image-data="contours01819_1.png" natural-size="721 284"/> <image byte-size="36029" display-name="contourI_labeled01819_1.png" transformation="0.62552 0 0 0.62552 74 147" lock-aspect-ratio="true" image-data="contourI_labeled01819_1.png" natural-size="721 284"/> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st16.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">previous work</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Two popular algorithms</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Track multiple blobs</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Track individual contours</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-5"> <property name="animationType" value="1"/> </build> </events> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st17.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">previous work</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Blob tracking does not work because:</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">It does not return detailed information.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">It cannot track mouse identities.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Contour tracking does not work because:</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Tuning hyperparameters is difficult.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The search space is too large and complex.</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 138" size="824 543" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st18.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">contributions</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We combine blob and contour cues to</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Efficiently track contours.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Explicitly address the data association problem.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We reduce the contour search space by</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Using blob tracking to localize the contour search.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Doing most of the search independently for each mouse. </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We achieve good results on a challenging real-world data set. </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 128" size="824 565" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st19.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">overview</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Previous work:</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Tracking assumptions</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Blob tracking</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Contour tracking</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Combined blob-contour model.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Search algorithms:</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Standard search.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Localizing the search space.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Searching independently. </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Results</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Future work</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Our approach to solving this real world problem focuses on feature selection, which I discuss first. Precisely defining the feature selection defines our problem mathematically as a criterion to optimize. I will discuss our approximation algorithm for optimizing this criterion. Then, I will show some preliminary results, and discuss our future work. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="755 235" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 172" size="824 140" vertical-alignment="tracks-master"/> <image byte-size="2643" display-name="bayesianfiltering_t.pdf" transformation="1 0 0 1 426 208" lock-aspect-ratio="true" image-data="bayesianfiltering_t.pdf" natural-size="20 24"/> <image byte-size="7591" display-name="bayesianfiltering_filteringdistr.pdf" transformation="1 0 0 1 336 247" lock-aspect-ratio="true" image-data="bayesianfiltering_filteringdistr.pdf" natural-size="146 38"/> <image byte-size="9092" display-name="pasted.tiff" transformation="0.635033 0 0 0.635033 49.6154 338" lock-aspect-ratio="true" image-data="pasted21.tiff" natural-size="736 143"/> <textbox size="44 47" transformation="1.19249e-08 1 -1 1.19249e-08 790.5 558.5"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="3890" display-name="bayesianfiltering_xt.pdf" transformation="1 0 0 1 264 437" lock-aspect-ratio="true" image-data="bayesianfiltering_xt.pdf" natural-size="38 23"/> <g transformation="1 0 0 1 623 302"> <line tail="624 303.008" head="626 747.993" stroke-color="g1"/> <line tail="623 302" head="667 302" stroke-color="g1"/> <line tail="625 747" head="669 747" stroke-color="g1"/> </g> <g transformation="1 0 0 1 833 302"> <line tail="878 303.008" head="876 747.993" stroke-color="g1"/> <line tail="879 302" head="835 302" stroke-color="g1"/> <line tail="877 747" head="833 747" stroke-color="g1"/> </g> <line tail="387 283" head="387 336" stroke-color="g1"> <styles> <line-tail-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <line tail="442 283" head="442 313.017" stroke-color="g1"> <styles> 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image-data="goal_y1.pdf" natural-size="36 25"/> <image byte-size="3904" display-name="goal_yt.pdf" transformation="1 0 0 1 733 402" lock-aspect-ratio="true" image-data="goal_yt.pdf" natural-size="36 25"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st7.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">goal</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">At each frame , we want to estimate prop-erties of .</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Mathematically, we can describe our goal as estimating the state of the mice, which we always represent as x at frame t, given the observations, which we represent as y, at frames 1 through t. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="4974" display-name="bayesianfiltering_y1throught.pdf" transformation="1 0 0 1 461 458" lock-aspect-ratio="true" image-data="bayesianfiltering_y1throught.pdf" natural-size="58 25"/> <image byte-size="3890" display-name="bayesianfiltering_xt.pdf" transformation="1 0 0 1 341 459" lock-aspect-ratio="true" image-data="bayesianfiltering_xt.pdf" natural-size="38 23"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st8.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">system model</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We assume a model of the relationship between <span font-name="TimesNewRomanPS-ItalicMT"> <![CDATA[ ]]> </span> and .</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[In order to estimate the state given the observation, we must define the relationship between the state and the observation. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 340" size="824 98" vertical-alignment="tracks-master"/> <image byte-size="9156" display-name="bayesianfiltering_recursivedecomp1.pdf" id="image-7" transformation="1 0 0 1 132 447" 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stroke-color="0.580067 0.586735 0.586735" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.75 0 0 0.75 673 256.5" stroke-width="5"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> <shape stroke-color="0.580067 0.586735 0.586735" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.75 0 0 0.75 675 126.5" stroke-width="5"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st1011.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">markov assumption</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We model our system as a HMM.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We can rewrite the posterior recursively as:</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-6"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-7"> <property name="animationType" value="1"/> </build> <build type="apple:appear" duration="1" target-id="image-7"> <property name="animationType" value="2"/> </build> <build type="apple:appear" duration="1" target-id="image-8"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="image-9"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-8"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[We model our system as a hidden Markov model, a common assumption in tracking. The graphical model for a hidden Markov model is shown. In an HMM, we assume the state at each frame includes all important information about the past, so the state at frame t+1 is independent of all previous information given the state at frame t. We also assume that the observation is defined by the state, so the observation at frame t is independent of all information given the state at time t. Because of these independence assumptions, we can rewrite the posterior as the observation likelihood p(y | x) times the probability of the state given the observations at frames 1 through t-1 over a constant. The state at time t given the observations at times 1 through t-1 can be rewritten as this integral over the previous state. This is a recursive definition of the posterior filtering distribution, defined in terms of the observation likelihood and the transition distribution. Thus, if we define models of the observation likelihood and the transition distribution, we will define the relationship between the state and the observations. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st9.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="72" font-name="Futura-Medium">observation likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">In this work, we combine two existing observation likelihood models.</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[I’ll first discuss the observation likelihood, which we create by combining two existing observation likelihood models. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 139" size="824 329" vertical-alignment="tracks-master"/> <image byte-size="879520" display-name="pasted.tiff" transformation="0.529316 0 0 0.529316 112 435.5" lock-aspect-ratio="true" image-data="pasted8.tiff" natural-size="1566 307"/> <image byte-size="9310" display-name="loglikratio.pdf" transformation="1 0 0 1 215 603" lock-aspect-ratio="true" image-data="loglikratio.pdf" natural-size="177 60"/> <g id="g-9" transformation="1 0 0 1 148.339 509"> <shape stroke-color="0.901961 0 0.117647" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 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65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.831831 -0.192044 0.0732459 0.317263 607.492 548.478" stroke-width="3"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> <shape stroke-color="0.270588 0 0.792157" path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="-0.548873 -0.316892 0.187287 -0.324391 903.271 590.439" stroke-width="3"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> </styles> </shape> <g transformation="1 0 0 1 173 601"> <shape path="M 0 0 L 100 0 L 100 100 L 0 100 Z M 0 0" transformation="2.94 0 0 0.8 173 601"> <styles> <fill-style fill-type="color" fill-color="0.163351 0.190525 0.321429"/> </styles> </shape> <textbox grow-horizontally="true" size="116 32" transformation="1 0 0 1 262 609"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="24" font-name="Futura-Medium">Ellipse fits</content> </textbox> </g> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st10111.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">blob likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The Bayesian Multiple Blob (BraMBLe) tracker:</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Finds <span font-name="TimesNewRomanPS-ItalicMT">K</span> “blobs” of pixels that look like the foreground and not like the background.</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-9"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[The first is the Bayesian multiple blob likelihood model, abbreviated BraMBLe, which tries to find K blobs of pixels that look like the foreground and not like the background. Here we show the log ratio of the probability of a pixel given that it is foreground over the probability of a pixel given that it is background. Here is an example fit in which the blobs are ellipses. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 444" size="824 300" vertical-alignment="tracks-master"/> <image byte-size="9092" display-name="pasted.tiff" transformation="0.594273 0 0 0.594273 55.615 121.253" lock-aspect-ratio="true" image-data="pasted21.tiff" natural-size="736 143"/> <image byte-size="2732" display-name="state_combinedtracker.pdf" transformation="1 0 0 1 261 222" lock-aspect-ratio="true" image-data="state_combinedtracker.pdf" natural-size="26 18"/> <image byte-size="308766" display-name="contour_raw01819_1.png" transformation="0.5 0 0 0.5 565 93" lock-aspect-ratio="true" image-data="contour_raw01819_1.png" natural-size="720 283"/> <g id="g-11" transformation="1 0 0 1 299 268"> <image byte-size="1464" display-name="ellipsefit.png" transformation="0.5 0 0 0.5 299 268" lock-aspect-ratio="true" image-data="ellipsefit.png" natural-size="720 283"/> <textbox grow-horizontally="true" size="133 32" transformation="1 0 0 1 668 316"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="24" font-name="Futura-Medium">foreground</content> </textbox> <textbox grow-horizontally="true" size="141 32" transformation="1 0 0 1 664 276"> <content font-color="0 0 0" paragraph-alignment="left" tab-stops="L 84" font-size="24" font-name="Futura-Medium">background</content> </textbox> <line tail="663 333" head="611 377" stroke-color="0.410201 0.503843 0.784768"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 L 3 1.5 Z M 0 0" match-point="3 1.5"/> </styles> </line> <line tail="663 292" head="611 336" stroke-color="0.410201 0.503843 0.784768"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 L 3 1.5 Z M 0 0" match-point="3 1.5"/> </styles> </line> <image byte-size="6168" display-name="bloblikelihood_label.pdf" 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image-data="bloblikelihood_pixellik.pdf" natural-size="187 39"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7928" size="60 45" file="thumbs/st161.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">blob likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given a hypothesized state <span font-name="TimesNewRomanPS-ItalicMT">x</span> and image <span font-name="TimesNewRomanPS-ItalicMT">y</span> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Label all grid points as foreground or background.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Assume</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> are GMMs learned from training data.</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-10"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-11"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Here are some details on how to compute the likelihood of the blob observation given the state. Given a state x and image y, we first look at pixel patches on grid points. From the state, we label all grid points as either foreground or background. Here is an example of the labels we would give for the state shown. We make the assumption that the pixel patches are conditionally independent, that is that the probability of the blob observation given the state is the product over all the grid points of the likelihood of the pixel patch at the grid point given the label of the grid point. We model the probability of a pixel patch given the label of the pixel patch as Gaussian mixture models that are learned from training data. There is a common model of the foreground for all grid points, and a different model of background for each grid point. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 171" size="824 85" vertical-alignment="tracks-master"/> <g id="g-13" transformation="1 0 0 1 194.5 280.31"> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.295 0 0 0.295 194.5 289" stroke-color="0.410201 0.503843 0.784768"> <styles> <fill-style fill-type="color" fill-color="0.410201 0.503843 0.784768"/> <dash-style pattern="none"/> </styles> </shape> <textbox size="745 46" transformation="1 0 0 1 203 281"> <content font-color="g1" tab-stops="L 28 L 56 L 84 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<content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">BraMBLe’s strengths and weaknesses:</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-12"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-13"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-14"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-15"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-16"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-17"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-18"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-19"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-20"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-21"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[The multiple blob likelihood has several strengths and weaknesses. First, we feel that it handles multiple targets naturally. Second, the blob object model is easy to define and needs only five parameters per mouse. Most importantly, we found that the multiple blob likelihood was smooth -- this fit gets a relatively low likelihood, while this fit has a higher likelihood, this fit has an even higher likelihood, ... Because of this, even if the fit is suboptimal at a frame, our tracker will not completely drift from its target because the suboptimal fit has a higher score than a less optimal fit. One of the weaknesses of the blob likelihood is that the exact fit which optimizes the blob criterion may not be what we would consider the best fit. This is because mice, in general, are not precisely elliptical. A more detailed and mouse-specific model is necessary for a precise fit. A major weakness of the blob likelihood is that it often lacks signal during and occlusion. For instance, in this occlusion, the true fit and this incorrect fit are indistinguishable given just the blob cue. Experimentally, we found that BraMBLe actually behaved even worse than giving more or less equal scores to each of these. Because of the independence assumption made, one of these fits might get a score that is orders of magnitude better than the other, based solely on how the ellipses fit. Thus, the BraMBLe tracker will make a greedy decision at this ambiguous frame, which may lead to identities being switched during an occlusion. Because of the lack of signal during occlusions, we also felt that a more detailed model was necessary. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 233" size="824 204" vertical-alignment="tracks-master"/> <g transformation="1 0 0 1 62 422"> <image byte-size="308766" display-name="contour_raw01819_1.png" transformation="0.626389 0 0 0.626389 511 422" lock-aspect-ratio="true" image-data="contour_raw01819_1.png" natural-size="720 283"/> <image byte-size="35095" display-name="contourI01819_1.png" transformation="0.624133 0 0 0.624133 62 422" lock-aspect-ratio="true" image-data="contourI01819_1.png" natural-size="721 284"/> </g> <g id="g-22" transformation="1 0 0 1 60 421"> <image byte-size="310682" display-name="contours01819_1.png" transformation="0.628294 0 0 0.628294 510 421.257" lock-aspect-ratio="true" image-data="contours01819_1.png" natural-size="721 284"/> <image byte-size="36029" display-name="contourI_labeled01819_1.png" transformation="0.62552 0 0 0.62552 60 421" lock-aspect-ratio="true" image-data="contourI_labeled01819_1.png" natural-size="721 284"/> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st151.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">contour likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Contour trackers:</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Fit a contour to image edges.</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-22"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[So, we looked at contour trackers, which try to fit contours to edges in the image. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="124 257" size="837 252" vertical-alignment="tracks-master"/> <image byte-size="2732" display-name="state_combinedtracker.pdf" transformation="1 0 0 1 292 241" lock-aspect-ratio="true" image-data="state_combinedtracker.pdf" natural-size="26 18"/> <image byte-size="308766" display-name="contour_raw01819_1.png" transformation="0.5 0 0 0.5 565 93" lock-aspect-ratio="true" image-data="contour_raw01819_1.png" natural-size="720 283"/> <textbox grow-horizontally="true" size="33 42" transformation="1 0 0 1 727.5 227"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="TimesNewRomanPS-ItalicMT">y</content> </textbox> <image byte-size="3114" display-name="examplecontour1.png" transformation="0.576037 0 0 0.576037 155 113" lock-aspect-ratio="true" image-data="examplecontour1.png" natural-size="434 343"/> <image byte-size="4078" display-name="examplecontourmeaslines1.png" id="image-10" transformation="0.576037 0 0 0.576037 155 114" lock-aspect-ratio="true" image-data="examplecontourmeaslines1.png" natural-size="434 342"/> <image byte-size="6893" display-name="examplecontourintersections.png" id="image-11" transformation="0.733138 0 0 0.733138 155 107" lock-aspect-ratio="true" image-data="examplecontourintersections.png" natural-size="341 285"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8152" size="60 45" file="thumbs/st181.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">contour likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given a hypothesized state <span font-name="TimesNewRomanPS-ItalicMT">x</span> and image <span font-name="TimesNewRomanPS-ItalicMT">y</span> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Edges are detected along measurement lines.</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="image-10"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="image-11"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Here are some details on how to compute the contour likelihood for a hypothesized state x of one mouse and an observed image y. First, we are going to limit our observations to a small number of short measurement lines that are centered on and normal to the contour defined by x. We then detect edges in the image along these measurement lines. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="124 257" size="837 303" vertical-alignment="tracks-master"/> <image byte-size="2732" display-name="state_combinedtracker.pdf" transformation="1 0 0 1 292 241" lock-aspect-ratio="true" image-data="state_combinedtracker.pdf" natural-size="26 18"/> <image byte-size="3114" display-name="examplecontour1.png" transformation="0.576037 0 0 0.576037 155 113" lock-aspect-ratio="true" image-data="examplecontour1.png" natural-size="434 343"/> <image byte-size="4078" display-name="examplecontourmeaslines1.png" transformation="0.576037 0 0 0.576037 155 114" lock-aspect-ratio="true" image-data="examplecontourmeaslines1.png" natural-size="434 342"/> <image byte-size="6893" display-name="examplecontourintersections.png" transformation="0.733138 0 0 0.733138 155 108" lock-aspect-ratio="true" image-data="examplecontourintersections.png" natural-size="341 285"/> <g transformation="1 0 0 1 545 124"> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 688 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 841 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> </g> <image byte-size="9440" display-name="image-106.pdf" transformation="1 0 0 1 334 435" lock-aspect-ratio="true" image-data="image-106.pdf" natural-size="385 48"/> <image byte-size="6991" display-name="image-107.pdf" transformation="1 0 0 1 620 149" lock-aspect-ratio="true" image-data="image-107.pdf" natural-size="219 38"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8150" size="60 45" file="thumbs/st1611.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">contour likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given a hypothesized state <span font-name="TimesNewRomanPS-ItalicMT">x</span> and image <span font-name="TimesNewRomanPS-ItalicMT">y</span> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Edges are detected along measurement lines.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Assume </content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Let us denote by y_{km} where edges are detected along measurement line m of mouse k. For example, if we detect edges 1 inward from the center and 3 outward from the center, then y_{km} would be the set {-1,3}. We make the assumption that all measurement line observations are conditionally independent given the state. For this approximation to hold, there cannot be too many measurement lines, and they must not be very long. The likelihood of the observation at measurement line m of mouse k given the state x is the same for all x. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="124 257" size="837 400" vertical-alignment="tracks-master"/> <image byte-size="2732" display-name="state_combinedtracker.pdf" transformation="1 0 0 1 292 241" lock-aspect-ratio="true" image-data="state_combinedtracker.pdf" natural-size="26 18"/> <image byte-size="3114" display-name="examplecontour1.png" transformation="0.576037 0 0 0.576037 155 113" lock-aspect-ratio="true" image-data="examplecontour1.png" natural-size="434 343"/> <image byte-size="4078" display-name="examplecontourmeaslines1.png" transformation="0.576037 0 0 0.576037 155 114" lock-aspect-ratio="true" image-data="examplecontourmeaslines1.png" natural-size="434 342"/> <image byte-size="6893" display-name="examplecontourintersections.png" transformation="0.733138 0 0 0.733138 155 108" lock-aspect-ratio="true" image-data="examplecontourintersections.png" natural-size="341 285"/> <g transformation="1 0 0 1 545 124"> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 688 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 841 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> </g> <image byte-size="9440" display-name="image-106.pdf" transformation="1 0 0 1 334 435" lock-aspect-ratio="true" image-data="image-106.pdf" natural-size="385 48"/> <image byte-size="6991" display-name="image-107.pdf" transformation="1 0 0 1 620 88" lock-aspect-ratio="true" image-data="image-107.pdf" natural-size="219 38"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8150" size="60 45" file="thumbs/st171.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">contour likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given a hypothesized state <span font-name="TimesNewRomanPS-ItalicMT">x</span> and image <span font-name="TimesNewRomanPS-ItalicMT">y</span> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Edges are detected along measurement lines.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Assume </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">At most one detection is the intersection.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">All other detections are clutter.</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[We assume that at most one edge detection is the true intersection between the contour and the measurement line, while all other edge detections are from clutter. I say at most one because we also include the possibility that the intersection is not detected at all. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="124 257" size="837 400" vertical-alignment="tracks-master"/> <image byte-size="2732" display-name="state_combinedtracker.pdf" transformation="1 0 0 1 292 241" lock-aspect-ratio="true" image-data="state_combinedtracker.pdf" natural-size="26 18"/> <image byte-size="3114" display-name="examplecontour1.png" transformation="0.576037 0 0 0.576037 155 113" lock-aspect-ratio="true" image-data="examplecontour1.png" natural-size="434 343"/> <image byte-size="4078" display-name="examplecontourmeaslines1.png" transformation="0.576037 0 0 0.576037 155 114" lock-aspect-ratio="true" image-data="examplecontourmeaslines1.png" natural-size="434 342"/> <image byte-size="6893" display-name="examplecontourintersections.png" transformation="0.733138 0 0 0.733138 155 108" lock-aspect-ratio="true" image-data="examplecontourintersections.png" natural-size="341 285"/> <g transformation="1 0 0 1 545 124"> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 688 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 841 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> </g> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 688 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 841 124"> <styles> <fill-style fill-type="color" fill-color="0.901961 0 0.117647"/> </styles> </shape> <textbox grow-horizontally="true" size="110 47" transformation="1 0 0 1 817 188"> <content font-color="0.901961 0 0.117647" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">clutter</content> </textbox> <textbox grow-horizontally="true" size="269 47" transformation="1 0 0 1 533 188"> <content font-color="1 0.8 0.0117647" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">true intersection</content> </textbox> <line tail="700 194" head="700 155" stroke-color="1 0.8 0.0117647"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <line tail="852 194" head="852 155" stroke-color="0.901961 0 0.117647"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <image byte-size="7659" display-name="contourlikelihood_term1.pdf" transformation="1 0 0 1 528 231" lock-aspect-ratio="true" image-data="contourlikelihood_term1.pdf" natural-size="404 38"/> <image byte-size="6991" display-name="image-107.pdf" transformation="1 0 0 1 620 88" lock-aspect-ratio="true" image-data="image-107.pdf" natural-size="219 38"/> <image byte-size="9440" display-name="image-106.pdf" transformation="1 0 0 1 334 435" lock-aspect-ratio="true" image-data="image-106.pdf" natural-size="385 48"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8150" size="60 45" file="thumbs/st1811.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">contour likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given a hypothesized state <span font-name="TimesNewRomanPS-ItalicMT">x</span> and image <span font-name="TimesNewRomanPS-ItalicMT">y</span> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Edges are detected along measurement lines.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Assume </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">At most one detection is the intersection.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">All other detections are clutter.</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[So for the measurement line observation where edges are detected at -1 and 3, there are three possibilities. The first possibility is that the -1 detection is the true intersection and the 3 detection is from clutter. This is a joint event in which the intersection between the measurement line and the contour is detected, the intersection is detected at -1. there is one clutter detection, and the clutter is detected at 3. We model the probability that the intersection is detected as a constant P_D. As our state x hypothesizes that the intersection occurs at the center of the measurement line, we assume that the location of the intersection detection is Gaussian around 0 with a constant standard deviation. We assume that clutter detections are uniformly distributed along the meaurement line. Finally, we assume that the number of clutter detections follows a Poisson distribution. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="124 257" size="837 400" vertical-alignment="tracks-master"/> <image byte-size="2732" display-name="state_combinedtracker.pdf" transformation="1 0 0 1 292 241" lock-aspect-ratio="true" image-data="state_combinedtracker.pdf" natural-size="26 18"/> <image byte-size="3114" display-name="examplecontour1.png" transformation="0.576037 0 0 0.576037 155 113" lock-aspect-ratio="true" image-data="examplecontour1.png" natural-size="434 343"/> <image byte-size="4078" display-name="examplecontourmeaslines1.png" transformation="0.576037 0 0 0.576037 155 114" lock-aspect-ratio="true" image-data="examplecontourmeaslines1.png" natural-size="434 342"/> <image byte-size="6893" display-name="examplecontourintersections.png" transformation="0.733138 0 0 0.733138 155 108" lock-aspect-ratio="true" image-data="examplecontourintersections.png" natural-size="341 285"/> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 688 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 841 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 841 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 688 124"> <styles> <fill-style fill-type="color" fill-color="0.901961 0 0.117647"/> </styles> </shape> <textbox grow-horizontally="true" size="110 47" transformation="1 0 0 1 817 188"> <content font-color="0.901961 0 0.117647" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">clutter</content> </textbox> <textbox grow-horizontally="true" size="269 47" transformation="1 0 0 1 533 188"> <content font-color="1 0.8 0.0117647" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">true intersection</content> </textbox> <line tail="700 194" head="829 148" stroke-color="1 0.8 0.0117647"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <line tail="852 194" head="715 147" stroke-color="0.901961 0 0.117647"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <image byte-size="7659" display-name="contourlikelihood_term2.pdf" transformation="1 0 0 1 528 231" lock-aspect-ratio="true" image-data="contourlikelihood_term2.pdf" natural-size="404 38"/> <image byte-size="6991" display-name="image-107.pdf" transformation="1 0 0 1 620 88" lock-aspect-ratio="true" image-data="image-107.pdf" natural-size="219 38"/> <image byte-size="9440" display-name="image-106.pdf" transformation="1 0 0 1 334 435" lock-aspect-ratio="true" image-data="image-106.pdf" natural-size="385 48"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8150" size="60 45" file="thumbs/st191.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">contour likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given a hypothesized state <span font-name="TimesNewRomanPS-ItalicMT">x</span> and image <span font-name="TimesNewRomanPS-ItalicMT">y</span> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Edges are detected along measurement lines.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Assume </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">At most one detection is the intersection.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">All other detections are clutter.</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[The second possibility is that the true intersection is detected at 3 while clutter is detected at -1. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="124 257" size="837 400" vertical-alignment="tracks-master"/> <image byte-size="2732" display-name="state_combinedtracker.pdf" transformation="1 0 0 1 292 241" lock-aspect-ratio="true" image-data="state_combinedtracker.pdf" natural-size="26 18"/> <image byte-size="3114" display-name="examplecontour1.png" transformation="0.576037 0 0 0.576037 155 113" lock-aspect-ratio="true" image-data="examplecontour1.png" natural-size="434 343"/> <image byte-size="4078" display-name="examplecontourmeaslines1.png" transformation="0.576037 0 0 0.576037 155 114" lock-aspect-ratio="true" image-data="examplecontourmeaslines1.png" natural-size="434 342"/> <image byte-size="6893" display-name="examplecontourintersections.png" transformation="0.733138 0 0 0.733138 155 108" lock-aspect-ratio="true" image-data="examplecontourintersections.png" natural-size="341 285"/> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 688 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 841 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 688 124"> <styles> <fill-style fill-type="color" fill-color="0.901961 0 0.117647"/> </styles> </shape> <textbox grow-horizontally="true" size="110 47" transformation="1 0 0 1 817 188"> <content font-color="0.901961 0 0.117647" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">clutter</content> </textbox> <textbox grow-horizontally="true" size="110 47" transformation="1 0 0 1 644 188"> <content font-color="0.901961 0 0.117647" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">clutter</content> </textbox> <line tail="700 194" head="700 155" stroke-color="0.901961 0 0.117647"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <line tail="852 194" head="852 155" stroke-color="0.901961 0 0.117647"> <styles> <line-head-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 841 124"> <styles> <fill-style fill-type="color" fill-color="0.901961 0 0.117647"/> </styles> </shape> <image byte-size="7644" display-name="contourlikelihood_term3.pdf" transformation="1 0 0 1 450 231" lock-aspect-ratio="true" image-data="contourlikelihood_term3.pdf" natural-size="560 38"/> <image byte-size="6991" display-name="image-107.pdf" transformation="1 0 0 1 620 88" lock-aspect-ratio="true" image-data="image-107.pdf" natural-size="219 38"/> <image byte-size="9440" display-name="image-106.pdf" transformation="1 0 0 1 334 435" lock-aspect-ratio="true" image-data="image-106.pdf" natural-size="385 48"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8150" size="60 45" file="thumbs/st20.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">contour likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given a hypothesized state <span font-name="TimesNewRomanPS-ItalicMT">x</span> and image <span font-name="TimesNewRomanPS-ItalicMT">y</span> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Edges are detected along measurement lines.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Assume </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">At most one detection is the intersection.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">All other detections are clutter.</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[And the third possibility is that the intersection is not detected and both of the detections are clutter. The likelihood of the measurement line observation is the sum of the likelihood of each of these possibilities. Here is the general form for this likelihood. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="124 257" size="837 450" vertical-alignment="tracks-master"/> <image byte-size="2732" display-name="state_combinedtracker.pdf" transformation="1 0 0 1 292 241" lock-aspect-ratio="true" image-data="state_combinedtracker.pdf" natural-size="26 18"/> <image byte-size="3114" display-name="examplecontour1.png" transformation="0.576037 0 0 0.576037 155 113" lock-aspect-ratio="true" image-data="examplecontour1.png" natural-size="434 343"/> <image byte-size="4078" display-name="examplecontourmeaslines1.png" transformation="0.576037 0 0 0.576037 155 114" lock-aspect-ratio="true" image-data="examplecontourmeaslines1.png" natural-size="434 342"/> <image byte-size="6893" display-name="examplecontourintersections.png" transformation="0.733138 0 0 0.733138 155 108" lock-aspect-ratio="true" image-data="examplecontourintersections.png" natural-size="341 285"/> <g transformation="1 0 0 1 545 124"> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 688 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 841 124"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> </g> <image byte-size="6991" display-name="image-107.pdf" transformation="1 0 0 1 620 149" lock-aspect-ratio="true" image-data="image-107.pdf" natural-size="219 38"/> <image byte-size="9440" display-name="image-106.pdf" transformation="1 0 0 1 334 435" lock-aspect-ratio="true" image-data="image-106.pdf" natural-size="385 48"/> <image byte-size="10448" display-name="image-108.pdf" transformation="1 0 0 1 201 581" lock-aspect-ratio="true" image-data="image-108.pdf" natural-size="615 43"/> <image byte-size="12859" display-name="image-109.pdf" transformation="1 0 0 1 310 634" lock-aspect-ratio="true" image-data="image-109.pdf" natural-size="657 50"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8150" size="60 45" file="thumbs/st211.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">contour likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given a hypothesized state <span font-name="TimesNewRomanPS-ItalicMT">x</span> and image <span font-name="TimesNewRomanPS-ItalicMT">y</span> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Edges are detected along measurement lines.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Assume </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">At most one detection is the intersection.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">All other detections are clutter.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="95 93" size="836 204" vertical-alignment="tracks-master"/> <g id="g-23" transformation="1 0 0 1 188.5 297"> <g transformation="1 0 0 1 188.5 297"> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.295 0 0 0.295 188.5 305" stroke-color="0.410201 0.503843 0.784768"/> <textbox size="745 46" transformation="1 0 0 1 197 297"> <content font-color="g1" tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="12" font-name="Helvetica"> <![CDATA[ ]]> <span font-size="36" font-name="Futura-Medium" font-ligatures="none">More complex model.</span> </content> </textbox> </g> <g transformation="1 0 0 1 621 305.428"> <shape path="M 0 0 L 100 0 L 100 100 L 0 100 Z M 0 0" transformation="1 0 0 1 727 364"> <styles> <fill-style fill-type="color" fill-color="0.0833798 0.112817 0.214286"/> </styles> </shape> <image byte-size="9038" display-name="pasted.tiff" transformation="0.569588 0 0 0.569588 666 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image-data="smaj_featureselection.pdf" natural-size="18 12"/> <image byte-size="2648" display-name="smin_featureselection.pdf" transformation="1 0 0 1 773 417" lock-aspect-ratio="true" image-data="smin_featureselection.pdf" natural-size="16 18"/> <line tail="771 391" stroke-color="1 0.8 0.0117647" head="843 391" stroke-width="3"> <styles> <dash-style pattern="3 3"/> </styles> </line> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.0900003 0 0 0.0900003 763 386"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <image byte-size="2579" display-name="angle_featureselection.pdf" transformation="1 0 0 1 798 368" lock-aspect-ratio="true" image-data="angle_featureselection.pdf" natural-size="17 18"/> <image byte-size="4872" 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font-name="Futura-Medium">Contour tracking’s strengths and weaknesses:</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-23"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-24"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-25"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-26"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-27"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-28"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-29"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-30"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Blob and contour tracking have complementing strengths and weaknesses. While the blob likelihood had a natural multiple target form, the extension of contour tracking to multiple targets is less natural and requires many parameters that are difficult to set, at least for our application. The model required for contour tracking is much more difficult to define, and requires more parameters. The biggest drawback we found is that the contour tracker is relatively fragile -- the likelihood does not give a reliable ranking for fits very far from the true mouse state. For example, this fit, which is not far from the true fit, gets a lower score than this worse fit. Contour tracking has the advantage that, if the optimal fit is found, it is very precise, assuming that the contour model is powerful enough. In addition, contour tracking has signal during occlusions in which blob tracking does not. This signal is from both the silhouette of the occlusion and the boundary between the mice. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" id="body-1" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st221.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">edge detection</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We found that standard edge detection algorithms did not work well on our data.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[The boundary detection algorithm used by the Berkeley Segmentation Engine worked well.]]> </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[The BSE incorporates a texture gradient, which is robust to the types of cluttter present. ]]> </content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" delivery="1" target-id="body-1"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Here is a bit of an implementation detail that we thought might be interesting. We found that standard edge detection algorithms based solely on image gradient did not work well. In fact, the only algorithm we tried that gave us good results was the boundary detection algorithm used by the Berkeley segmentation engine. The BSE computes the posterior probability of an edge based on the brightness, texture, and color gradient using a classifier trained on 12,000 manually labeled images. We credit BSE's superior performance in part to the texture gradient, which is robust to the types of clutter described.]]> </notes> </slide> <slide master-slide-id="master-slide-4"> <drawables> <plugin transformation="1 0 0 1 252.333 68" opacity="1"> <plugin-data> <plugin:movie height="632" key="root" width="519" src="edgedetection_dv.mov"/> <string key="CPVersion">1.0</string> <string key="MIMEType">video/quicktime</string> </plugin-data> <styles> <shadow-style opacity="0" radius="0"/> </styles> </plugin> <textbox grow-horizontally="true" size="116 47" transformation="1 0 0 1 811 360"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">Canny</content> </textbox> <textbox grow-horizontally="true" size="73 47" transformation="1 0 0 1 832 583"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">BSE</content> </textbox> <title visibility="hidden" vertical-alignment="tracks-master"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7856" size="60 45" file="thumbs/st24.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="64" font-name="Futura-Medium"/> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Here we show the output of the Canny edge detection algorithm, which is either 1 or 0, and the probability returned by the BSE, which ranges between 0 and 1. I am showing the results in three channels so that we can see the weakly detected edges between the mice. Note the large amount of clutter detections in the bedding by Canny, and the lack of signal during occlusion for the Canny detection. Note also that, for the BSE, the clutter detections have similar strength to the detections of boundaries between mice. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 259" size="824 450" vertical-alignment="tracks-master"/> <image byte-size="6785" display-name="image-100.pdf" transformation="1 0 0 1 714 420" lock-aspect-ratio="true" image-data="image-100.pdf" natural-size="168 38"/> <image byte-size="35095" display-name="contourI01819_1.png" transformation="0.836338 0 0 0.836338 210 113.48" lock-aspect-ratio="true" image-data="contourI01819_1.png" natural-size="721 284"/> <image byte-size="6785" display-name="image-100.pdf" transformation="1 0 0 1 428 365" lock-aspect-ratio="true" image-data="image-100.pdf" natural-size="168 38"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st241.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">soft edges</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The BSE returns the probability .</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Clutter edges often have a higher probability than true edges during occlusions.</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[The BSE returns a probability, the posterior probabilty of an edge given a patch of pixels. Often, clutter edges have a higher probability than the edges between mice during occlusions. Thus, any threshold we choose will either result in detecting clutter or missing edges in occlusions. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 376" size="824 292" vertical-alignment="tracks-master"/> <image byte-size="13427" display-name="image-101.pdf" transformation="1 0 0 1 262 601" lock-aspect-ratio="true" image-data="image-101.pdf" natural-size="500 91"/> <line tail="545 135" stroke-color="0 1 1" head="915.992 136" stroke-width="5"/> <line tail="116 135" stroke-color="0 1 1" head="486.992 136" stroke-width="5"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 288 124"> <styles> <fill-style 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47" transformation="-4.37114e-08 1 -1 -4.37114e-08 766.5 323.5"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2746" display-name="image-102.pdf" transformation="1 0 0 1 286 170" lock-aspect-ratio="true" image-data="image-102.pdf" natural-size="25 25"/> <image byte-size="2744" display-name="image-103.pdf" transformation="1 0 0 1 719 421" lock-aspect-ratio="true" image-data="image-103.pdf" natural-size="22 18"/> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 719 159"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.21 0 0 0.21 634 195"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st261.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">soft edges</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We generalize the contour likelihood to input edge probabilities.</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[Because of this, we generalized the existing contour likelihood model to input edge probabilities. Our measurement line observation y is actually a sequence of probabilities, the probability that an edge is detected at each point along the measurement line. From these probabilities, we compute the probability of each possible hard measurement line observation: we compute the probability that there are no edges detected, that there is one edge detected in the center, etc, and sum up the likelihood for each of these cases. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st2211.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">combined tracker</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[We efficiently combine blob and contour tracking to accentuate the strengths of each.]]> </content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[As I was saying a few slides ago, blob and contour tracking have complementing strengths. Most notably, blob tracking is robust and easier to optimize, while there is contour signal available during occlusions. 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</styles> </line> <image byte-size="2681" display-name="smaj_featureselection.pdf" transformation="1 0 0 1 548 199" lock-aspect-ratio="true" image-data="smaj_featureselection.pdf" natural-size="18 12"/> <image byte-size="2648" display-name="smin_featureselection.pdf" transformation="1 0 0 1 523 276" lock-aspect-ratio="true" image-data="smin_featureselection.pdf" natural-size="16 18"/> <line tail="521 250" stroke-color="1 0.8 0.0117647" head="593 250" stroke-width="3"> <styles> <dash-style pattern="3 3"/> </styles> </line> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.0900003 0 0 0.0900003 513 245"> <styles> <fill-style fill-type="color" fill-color="1 0.8 0.0117647"/> </styles> </shape> <image byte-size="2579" display-name="angle_featureselection.pdf" transformation="1 0 0 1 548 227" lock-aspect-ratio="true" image-data="angle_featureselection.pdf" natural-size="17 18"/> </g> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7178" size="60 45" file="thumbs/st231.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">blob-contour state</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[We represent a mouse as any affine transformation of any template in a set and its velocity.]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">A mouse blob is the ellipse defined by the affine transformation.</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="image-12"> <property name="animationType" value="2"/> </build> <build type="apple:dissolve" duration="1" target-id="image-13"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-31"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-32"> <property name="animationType" value="1"/> </build> </events> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[To represent a mouse, we first constructed by hand a set of 12 contour templates, shown here. I created this set by arbitrarily choosing 12 images in which I thought the mice had unique 2D shapes, outlining the mice, and fitting a B-spline to the outline. An individual mouse is represented by choosing one of these 12 templates and applying any affine transformation to it. A mouse blob is the ellipse that is defined by applying this affine transformation to the unit circle. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="10484" display-name="image-1.pdf" transformation="1 0 0 1 275 323" lock-aspect-ratio="true" image-data="image-1.pdf" natural-size="504 48"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st2411.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">model dynamics</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Each mouse moves independently:</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[We assume independent Gaussian transition distributions for each continuous parameter.]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[The probability of a template depends on if the template is the same and if the template direction is the same.]]> </content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[We assume that each mouse moves independently, so we can factorize the probability that the K mice are in a certain state at time t given their state at time t-1 as the product over all K mice of the probability that mouse k is in a certain state at time t given the state of mouse k at time t-1. We make standard, simple assumptions for the individual mouse transition distributions. Basically, we assume that all continuous parameters follow Gaussian distributions. The only discrete parameter is which contour template we are applying the affine transformation to. The probability that the template does not change is highest. Second highest is the probability of all templates facing the same direction as the previous template. Lowest is the probability of all templates facing the opposite direction. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 160" size="824 103" vertical-alignment="tracks-master"/> <image byte-size="7051" display-name="indepobs_combinedtracker.pdf" transformation="1 0 0 1 361 245" lock-aspect-ratio="true" image-data="indepobs_combinedtracker.pdf" natural-size="425 38"/> <image byte-size="29596" display-name="pasted.tiff" transformation="0.556328 0 0 0.556328 66.5 351" lock-aspect-ratio="true" image-data="pasted20.tiff" natural-size="719 284"/> <image byte-size="35095" display-name="contourI01819_1.png" transformation="0.554785 0 0 0.554785 569 351" lock-aspect-ratio="true" image-data="contourI01819_1.png" natural-size="721 284"/> <image byte-size="9092" display-name="pasted.tiff" transformation="0.86014 0 0 0.86014 194.615 575" lock-aspect-ratio="true" image-data="pasted21.tiff" natural-size="736 143"/> <line tail="413 283" head="413 351" stroke-color="g1"> <styles> <line-head-style is-filled="false"/> <line-tail-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <line tail="730 282" head="730 350" stroke-color="0.705882 0.752941 0.894118"> <styles> <dash-style pattern="1 1"/> <line-tail-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <line tail="496 282" head="494.2 570.989" stroke-color="0.410201 0.503843 0.784768"> <styles> <line-tail-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <line tail="616 281" head="616 305" stroke-color="g1"> <styles> <line-tail-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <line tail="616 304" head="414.025 304" stroke-color="g1"> <styles> <line-tail-style is-filled="false"/> </styles> </line> <line tail="729 316" head="459.018 315" stroke-color="0.705882 0.752941 0.894118"> <styles> <dash-style pattern="1 1"/> </styles> </line> <line tail="458 282" head="458 315.015" stroke-color="0.705882 0.752941 0.894118"> <styles> <dash-style pattern="1 1"/> <line-tail-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <line tail="652.987 329" head="495.025 330" stroke-color="0.410201 0.503843 0.784768"/> <line tail="652 281" head="652 329" stroke-color="0.410201 0.503843 0.784768"> <styles> <line-tail-style is-filled="true" path="M 0 0 L 3 6 L 6 0 Z M 0 0" match-point="3 0.1"/> </styles> </line> <image byte-size="3847" display-name="contourobs_combinedtracker.pdf" transformation="1 0 0 1 750 517" lock-aspect-ratio="true" image-data="contourobs_combinedtracker.pdf" natural-size="37 25"/> <image byte-size="3891" display-name="blobobs_combinedtracker.pdf" transformation="1 0 0 1 247 517" lock-aspect-ratio="true" image-data="blobobs_combinedtracker.pdf" natural-size="39 25"/> <image byte-size="2732" display-name="state_combinedtracker.pdf" transformation="1 0 0 1 498 706" lock-aspect-ratio="true" image-data="state_combinedtracker.pdf" natural-size="26 18"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st251.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">independence</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We assume conditional independence:</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[How do we combine the blob and contour likelihoods? We do this in the simplest way possible -- by making an independence assumption. We assume that the blob and contour observations are conditionally independent given the state. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="8201" display-name="bayesianfiltering_transdistr.pdf" transformation="1 0 0 1 271 402" lock-aspect-ratio="true" image-data="bayesianfiltering_transdistr.pdf" natural-size="162 38"/> <image byte-size="7591" display-name="bayesianfiltering_filteringdistr.pdf" transformation="1 0 0 1 570 449" lock-aspect-ratio="true" image-data="bayesianfiltering_filteringdistr.pdf" natural-size="146 38"/> <image byte-size="6526" display-name="bayesianfiltering_obslik.pdf" transformation="1 0 0 1 758 353" lock-aspect-ratio="true" image-data="bayesianfiltering_obslik.pdf" natural-size="123 38"/> <image byte-size="7591" display-name="bayesianfiltering_filteringdistr.pdf" transformation="1 0 0 1 728 498" lock-aspect-ratio="true" image-data="bayesianfiltering_filteringdistr.pdf" natural-size="146 38"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st2611.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">system model</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We have described the models of and .</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">These implicitly define .</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">How do we compute statistics of ?</content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[I have now described the blob and contour observation model and the model dynamics. Because of the HMM assumptions, this implicitly defines the posterior filtering distribution, the distribution of the state at time t given the observation images at times 1 through t. Now, I discuss how we compute properties, e.g. the mean, of the filtering distribution. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 320" size="824 450" vertical-alignment="tracks-master"/> <image byte-size="8201" display-name="bayesianfiltering_transdistr.pdf" transformation="1 0 0 1 732 408" lock-aspect-ratio="true" image-data="bayesianfiltering_transdistr.pdf" natural-size="162 38"/> <image byte-size="6526" display-name="bayesianfiltering_obslik.pdf" transformation="1 0 0 1 525 408" lock-aspect-ratio="true" image-data="bayesianfiltering_obslik.pdf" natural-size="123 38"/> <image byte-size="7591" display-name="bayesianfiltering_filteringdistr.pdf" transformation="1 0 0 1 707 459" lock-aspect-ratio="true" image-data="bayesianfiltering_filteringdistr.pdf" natural-size="146 38"/> <image byte-size="7591" display-name="bayesianfiltering_filteringdistr.pdf" transformation="1 0 0 1 266 648" lock-aspect-ratio="true" image-data="bayesianfiltering_filteringdistr.pdf" natural-size="146 38"/> <image byte-size="3364" display-name="pasted.pdf" transformation="0.815217 0 0 0.815217 175.5 134" lock-aspect-ratio="true" image-data="pasted.pdf" natural-size="408.5 184"/> <image byte-size="3258" display-name="pasted.pdf" transformation="0.371287 0 0 0.371287 551 134" lock-aspect-ratio="true" image-data="pasted1.pdf" natural-size="799.5 404"/> <image byte-size="7591" display-name="bayesianfiltering_filteringdistr.pdf" transformation="1 0 0 1 269 314" lock-aspect-ratio="true" image-data="bayesianfiltering_filteringdistr.pdf" natural-size="146 38"/> <image byte-size="8720" display-name="particlefiltering_approx.pdf" transformation="1 0 0 1 564 280" lock-aspect-ratio="true" image-data="particlefiltering_approx.pdf" natural-size="270 106"/> <image byte-size="2574" display-name="particlefiltering_approx2.pdf" transformation="1 0 0 1 495 324" lock-aspect-ratio="true" image-data="particlefiltering_approx2.pdf" natural-size="34 18"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st112.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">particle filtering</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[For general forms of and , we cannot analytically compute . ]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We approximate the distribution by a set of weighted samples.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Particle filtering iteratively generates samples from . </content> </bullet> </bullets> <notes font-name="LucidaGrande" font-size="18"> <![CDATA[For general forms of the observation likelihood and the transition distribution, we cannot analytically compute the form of the filtering distribution. Instead, we approximate the distribution by a set of weighted samples. So, if this is our true distribution, we might approximate it by samples at these locations with these weights. The approximation is more accurate the closer the samples are to being drawn from the true distribution. Particle filtering is an algorithm for iteratively generating samples from the filtering distribution. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="top"/> <image byte-size="10436" display-name="image-110.pdf" transformation="1 0 0 1 242 267" lock-aspect-ratio="true" image-data="image-110.pdf" natural-size="540 52"/> <image byte-size="9503" display-name="image-111.pdf" transformation="1 0 0 1 293 359" lock-aspect-ratio="true" image-data="image-111.pdf" natural-size="437 49"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st46.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">particle filtering</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">At each iteration t, particle filtering inputs</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">and outputs</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="808 120" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="top"/> <image byte-size="8183" display-name="image-113.pdf" transformation="1 0 0 1 389 316" lock-aspect-ratio="true" image-data="image-113.pdf" natural-size="246 49"/> <image byte-size="8879" display-name="image-116.pdf" transformation="1 0 0 1 373 389" lock-aspect-ratio="true" image-data="image-116.pdf" natural-size="278 107"/> <image byte-size="7591" display-name="image-117.pdf" transformation="1 0 0 1 702 518" lock-aspect-ratio="true" image-data="image-117.pdf" natural-size="146 38"/> <image byte-size="11121" display-name="image-118.pdf" transformation="1 0 0 1 171 605" lock-aspect-ratio="true" image-data="image-118.pdf" natural-size="682 106"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st47.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">importance sampling</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Each iteration is importance sampling:</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Sample from a proposal distribution</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Weight by </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">To approximate a statistic of , use the sample approximation, e.g.</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="10436" display-name="image-110.pdf" transformation="1 0 0 1 242 312" lock-aspect-ratio="true" image-data="image-110.pdf" natural-size="540 52"/> <image byte-size="9503" display-name="image-111.pdf" transformation="1 0 0 1 293 487" lock-aspect-ratio="true" image-data="image-111.pdf" natural-size="437 49"/> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-3.80289e-08 0.87 -1 -4.37114e-08 562 390"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st33.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">standard filtering</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[Here is how one iteration of the most common form of particle filtering recursively generates particles. We are given a set of weighted particles that approximates the filtering distribution for time t-1, and we want to generate a set of weighted particles to approximate the filtering distribution for time t. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="801 120" vertical-alignment="tracks-master"/> <textbox grow-horizontally="true" size="776 47" transformation="1 0 0 1 91 239"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">0) Given :</content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="304363" display-name="sample01818_max2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_max2.png" natural-size="721 284"/> <image byte-size="304224" display-name="sample01818_max1000.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_max1000.png" natural-size="721 284"/> <image byte-size="304708" display-name="sample01818_max1.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_max1.png" natural-size="721 284"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="7633" display-name="particlefiltering_sample1.pdf" transformation="1 0 0 1 75 467" lock-aspect-ratio="true" image-data="particlefiltering_sample1.pdf" natural-size="190 52"/> <image byte-size="7842" display-name="particlefiltering_sampleN.pdf" transformation="1 0 0 1 747 467" lock-aspect-ratio="true" image-data="particlefiltering_sampleN.pdf" natural-size="192 52"/> <image byte-size="7757" display-name="particlefiltering_sample2.pdf" transformation="1 0 0 1 386 467" lock-aspect-ratio="true" image-data="particlefiltering_sample2.pdf" natural-size="190 52"/> </g> <image byte-size="10584" display-name="image-14.pdf" transformation="1 0 0 1 243 230" lock-aspect-ratio="true" image-data="image-14.pdf" natural-size="605 55"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st49.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">given</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[Here is an illustration of what we are given. We are given a set of samples, where each sample corresponds to the positions of the mice in frame t-1. We are also given the weight of each of these samples. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="809 120" vertical-alignment="tracks-master"/> <textbox size="847 94" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[1) Resample according to the weights to create]]> </content> </textbox> <image byte-size="10584" display-name="image-14.pdf" transformation="1 0 0 1 307 174" lock-aspect-ratio="true" image-data="image-14.pdf" natural-size="605 55"/> <image byte-size="10521" display-name="image-15.pdf" transformation="1 0 0 1 269 274" lock-aspect-ratio="true" image-data="image-15.pdf" natural-size="486 55"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 583" lock-aspect-ratio="true" 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transformation="1 0 0 1 135 707" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted1.pdf" natural-size="70 52"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 618"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> </g> <g transformation="1 0 0 1 -10 335"> <image byte-size="304363" display-name="sample01818_max2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_max2.png" natural-size="721 284"/> <image byte-size="304224" display-name="sample01818_max1000.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_max1000.png" natural-size="721 284"/> <image byte-size="304708" display-name="sample01818_max1.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_max1.png" natural-size="721 284"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="7633" display-name="particlefiltering_sample1.pdf" transformation="1 0 0 1 75 467" lock-aspect-ratio="true" image-data="particlefiltering_sample1.pdf" natural-size="190 52"/> <image byte-size="7842" display-name="particlefiltering_sampleN.pdf" transformation="1 0 0 1 747 467" lock-aspect-ratio="true" image-data="particlefiltering_sampleN.pdf" natural-size="192 52"/> <image byte-size="7757" display-name="particlefiltering_sample2.pdf" transformation="1 0 0 1 386 467" lock-aspect-ratio="true" image-data="particlefiltering_sample2.pdf" natural-size="190 52"/> </g> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 537"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st50.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">resample</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[The first step is to resample the particles according to these weights. So, we choose sample 1 with probability .082, sample 2 with probability .079, and particle N with probability 3 x 10^-11. From this, we create a set of unweighted samples, which I represent as \tilde{x}, that still represent the state at time t-1. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="804 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 184"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[2) From each sample generate to create . ]]> </content> </textbox> <g transformation="1 0 0 1 -10 572"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image 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lock-aspect-ratio="true" image-data="particlefiltering_sampletN.pdf" natural-size="70 49"/> <image byte-size="5137" display-name="particlefiltering_samplet2.pdf" transformation="1 0 0 1 451 707" lock-aspect-ratio="true" image-data="particlefiltering_samplet2.pdf" natural-size="59 49"/> </g> <g transformation="1 0 0 1 -10 335"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_unweighted10.png" natural-size="721 284"/> <image byte-size="303493" display-name="sample01818_unweighted2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_unweighted2.png" natural-size="721 284"/> <image byte-size="303628" display-name="sample01818_unweighted1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_unweighted1.png" natural-size="721 284"/> <image byte-size="7467" display-name="particlefiltering_sampleunweightedN.pdf" transformation="1 0 0 1 808 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweightedN.pdf" natural-size="70 52"/> <image byte-size="7384" display-name="particlefiltering_sampleunweighted2.pdf" transformation="1 0 0 1 446 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted2.pdf" natural-size="70 52"/> <image byte-size="7260" display-name="particlefiltering_sampleunweighted1.pdf" transformation="1 0 0 1 135 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted1.pdf" natural-size="70 52"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> </g> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 537"/> <image byte-size="10070" display-name="image-20.pdf" transformation="1 0 0 1 447 179" lock-aspect-ratio="true" image-data="image-20.pdf" natural-size="448 55"/> <image byte-size="9498" display-name="image-21.pdf" transformation="1 0 0 1 254 226" lock-aspect-ratio="true" image-data="image-21.pdf" natural-size="412 55"/> <image byte-size="10074" display-name="image-22.pdf" transformation="1 0 0 1 248 275" lock-aspect-ratio="true" image-data="image-22.pdf" natural-size="413 55"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7532" size="60 45" file="thumbs/st51.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">predict</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[From each of these samples distributed according to the filtering distribution at time t-1, we generate a sample corresponding to the next frame according to the transition model I discussed briefly before. Note that in the generation of these samples, the current observed image is not used. Here is an illustration of this step. From sample 1 at time t-1, we generate sample 1 at time t using the transition dynamics. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="807 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[3) Weight each sample by to create . ]]> </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 346" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" 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display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 570" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 570" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 617"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="304057" display-name="sample01819_2.png" transformation="0.416089 0 0 0.416089 22 585" lock-aspect-ratio="true" image-data="sample01819_2.png" natural-size="721 284"/> <image byte-size="304241" display-name="sample01819_1.png" transformation="0.416089 0 0 0.416089 693 585" lock-aspect-ratio="true" image-data="sample01819_1.png" natural-size="721 284"/> <image byte-size="6675" display-name="particlefiltering_particlet1.pdf" transformation="1 0 0 1 87 709" lock-aspect-ratio="true" image-data="particlefiltering_particlet1.pdf" natural-size="170 49"/> <image byte-size="6717" display-name="particlefiltering_particlet2.pdf" transformation="1 0 0 1 396 709" lock-aspect-ratio="true" image-data="particlefiltering_particlet2.pdf" natural-size="170 49"/> <image byte-size="6777" display-name="particlefiltering_particletN.pdf" transformation="1 0 0 1 747 709" lock-aspect-ratio="true" image-data="particlefiltering_particletN.pdf" natural-size="192 49"/> <image byte-size="303748" display-name="sample01819_10.png" transformation="0.416089 0 0 0.416089 333 585" lock-aspect-ratio="true" image-data="sample01819_10.png" natural-size="721 284"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7554" size="60 45" file="thumbs/st52.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">update</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[We have so far only incorporated the transition dynamics, we must now incorporate the current observation and the observation likelihood. To do this, we weight each sample by the observation likelihood, which we have modeled as the blob likelihood times the product over all K mice of the contour likelihood. This creates a set of weighted samples which approximates the filtering distribution. Note that each iteration of particle filtering is just importance sampling, where the proposal distribution is the distribution of the state at time t given the images from times 1 through t-1, and the importance weight is the observation likelihood. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st29.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">standard filtering</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Recall: blob tracking is robust and contour tracking is precise.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">The most straightforward application of particle filtering </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Does not accentuate these strengths.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Empirically does not work well.</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[Recall that blob tracking is robust while contour tracking can find a precise fit. This most straightforward application of particle filtering does not accentuate these strengths, and empirically does not work well. ]]> </notes> </slide> <slide id="slide-1" master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 411" size="824 348" vertical-alignment="top"/> <image byte-size="9404" display-name="image-120.pdf" transformation="1 0 0 1 516 559" lock-aspect-ratio="true" image-data="image-120.pdf" natural-size="298 39"/> <image byte-size="8995" display-name="image-119.pdf" transformation="1 0 0 1 739 517" lock-aspect-ratio="true" image-data="image-119.pdf" natural-size="239 39"/> <image byte-size="9406" display-name="image-6.pdf" transformation="1 0 0 1 565 611" lock-aspect-ratio="true" image-data="image-6.pdf" natural-size="298 39"/> <image byte-size="3557" display-name="gaussian2.png" transformation="0.474684 0 0 0.474684 362 144" lock-aspect-ratio="true" image-data="gaussian2.png" natural-size="632 300"/> <image byte-size="8995" display-name="image-119.pdf" transformation="1 0 0 1 222 208" lock-aspect-ratio="true" image-data="image-119.pdf" natural-size="239 39"/> <image byte-size="9404" display-name="image-120.pdf" transformation="1 0 0 1 193 155" lock-aspect-ratio="true" image-data="image-120.pdf" natural-size="298 39"/> <image byte-size="8253" display-name="weightedblob1.png" transformation="0.461267 0 0 0.461267 679.257 262" lock-aspect-ratio="true" image-data="weightedblob1.png" natural-size="721 284"/> <line tail="536 287" stroke-color="0 1 1" head="536 328.601" stroke-width="3"> <styles> <line-head-style is-filled="false"/> <line-tail-style is-filled="true" path="M 0 0 L 3 6 L 6 0 L 3 1.5 Z M 0 0" match-point="3 1.5"/> </styles> </line> <line tail="679 327" stroke-color="0 1 1" head="536 327.1" stroke-width="3"> <styles> <line-tail-style is-filled="false"/> </styles> </line> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8188" size="60 45" file="thumbs/st54.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We use the <span font-color="0 1 1">blob observation</span> to localize the search space for contour tracking.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[Instead of drawing samples from draw samples from .]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[To draw samples from , we perform an iteration of blob particle filtering.]]> </content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[We thus modified the algorithm so that it uses blob tracking to localize the search space for contour tracking. To do this, instead of using the distribution as time t given the observations at times 1 through t-1 as our proposal distribution, we use the state at time t given the images at times 1 through t-1 and the blob observation at time t as our proposal distribution. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 315" size="824 353" vertical-alignment="tracks-master"/> <image byte-size="10584" display-name="image-14.pdf" transformation="1 0 0 1 297 363" lock-aspect-ratio="true" image-data="image-14.pdf" natural-size="605 55"/> <image byte-size="10483" display-name="image-35.pdf" transformation="1 0 0 1 191 463" lock-aspect-ratio="true" image-data="image-35.pdf" natural-size="528 50"/> <image byte-size="9649" display-name="image-27.pdf" transformation="1 0 0 1 192 560" lock-aspect-ratio="true" image-data="image-27.pdf" natural-size="481 55"/> <g transformation="1 0 0 1 -3 114"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 28 125" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 338 125" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 700 125" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -3 114" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 990 114" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 648 161"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="8248" display-name="weightedblobN.png" transformation="0.416089 0 0 0.416089 700 125" lock-aspect-ratio="true" image-data="weightedblobN.png" natural-size="721 284"/> <image byte-size="8031" display-name="weightedblob2.png" transformation="0.416089 0 0 0.416089 338 125" lock-aspect-ratio="true" image-data="weightedblob2.png" natural-size="721 284"/> <image byte-size="8253" display-name="weightedblob1.png" transformation="0.416089 0 0 0.416089 28 126" lock-aspect-ratio="true" image-data="weightedblob1.png" natural-size="721 284"/> <image byte-size="7016" display-name="image-37.pdf" transformation="1 0 0 1 89 249" lock-aspect-ratio="true" image-data="image-37.pdf" natural-size="177 50"/> <image byte-size="7135" display-name="image-38.pdf" transformation="1 0 0 1 399 249" lock-aspect-ratio="true" image-data="image-38.pdf" natural-size="177 50"/> <image byte-size="7201" display-name="image-39.pdf" transformation="1 0 0 1 756 249" lock-aspect-ratio="true" image-data="image-39.pdf" natural-size="188 50"/> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st55.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Perform blob tracking to create</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Perform contour tracking to create</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[To review, this first solution performs one step of blob tracking to narrow down the search space based on the blob observation. It then performs one step of contour tracking to fine tune the fit based on the contour observation. We are thus taking into account the strengths of each algorithm. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 315" size="824 353" vertical-alignment="tracks-master"/> <image byte-size="10584" display-name="image-14.pdf" transformation="1 0 0 1 297 363" lock-aspect-ratio="true" image-data="image-14.pdf" natural-size="605 55"/> <image byte-size="10483" display-name="image-35.pdf" transformation="1 0 0 1 191 463" lock-aspect-ratio="true" image-data="image-35.pdf" natural-size="528 50"/> <image byte-size="9649" display-name="image-27.pdf" transformation="1 0 0 1 192 560" lock-aspect-ratio="true" image-data="image-27.pdf" natural-size="481 55"/> <g transformation="1 0 0 1 -3 113"> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -3 113" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 990 113" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 648 160"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="305399" display-name="blobparticleweightedN.png" transformation="0.416089 0 0 0.416089 700 128" lock-aspect-ratio="true" image-data="blobparticleweightedN.png" natural-size="721 284"/> <image byte-size="304393" display-name="blobparticleweighted2.png" transformation="0.416089 0 0 0.416089 338 128" lock-aspect-ratio="true" image-data="blobparticleweighted2.png" natural-size="721 284"/> <image byte-size="304314" display-name="blobparticleweighted1.png" transformation="0.416089 0 0 0.416089 29 128" lock-aspect-ratio="true" image-data="blobparticleweighted1.png" natural-size="721 284"/> <image byte-size="6675" display-name="particlefiltering_particlet1.pdf" transformation="1 0 0 1 94 252" lock-aspect-ratio="true" image-data="particlefiltering_particlet1.pdf" natural-size="170 49"/> <image byte-size="6717" display-name="particlefiltering_particlet2.pdf" transformation="1 0 0 1 403 252" lock-aspect-ratio="true" image-data="particlefiltering_particlet2.pdf" natural-size="170 49"/> <image byte-size="6777" display-name="particlefiltering_particletN.pdf" transformation="1 0 0 1 754 252" lock-aspect-ratio="true" image-data="particlefiltering_particletN.pdf" natural-size="192 49"/> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st56.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Perform blob tracking to create</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Perform contour tracking to create</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[To review, this first solution performs one step of blob tracking to narrow down the search space based on the blob observation. It then performs one step of contour tracking to fine tune the fit based on the contour observation. We are thus taking into account the strengths of each algorithm. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="10484" display-name="image-1.pdf" transformation="1 0 0 1 308 320" lock-aspect-ratio="true" image-data="image-1.pdf" natural-size="504 48"/> <image byte-size="9495" display-name="image-2.pdf" transformation="1 0 0 1 190 367" lock-aspect-ratio="true" image-data="image-2.pdf" natural-size="396 48"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st341.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Recall: and</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[ ]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Solution #1 </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Does not exploit these independencies.</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Empirically does not work well.</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[Recall, though, that we made some independence assumptions that this algorithm does not take advantage of. First, we assumed that the mice moved independently. Second, we assumed that the contour likelihoods were independent for each mouse. The solution I just presented does not exploit these independencies, and empirically we found that it did not work well. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="100 335" size="824 450" vertical-alignment="tracks-master"/> <image byte-size="9128" display-name="image-4.pdf" transformation="1 0 0 1 173 641" lock-aspect-ratio="true" image-data="image-4.pdf" natural-size="257 38"/> <image byte-size="9406" display-name="image-6.pdf" transformation="1 0 0 1 176 590" lock-aspect-ratio="true" image-data="image-6.pdf" natural-size="298 39"/> <image byte-size="30770" display-name="pasted.tiff" transformation="0.569476 0 0 0.569476 123.619 144" lock-aspect-ratio="true" image-data="pasted22.tiff" natural-size="439 352"/> <image byte-size="2210" display-name="gaussian3.png" transformation="0.45977 0 0 0.45977 474 165" lock-aspect-ratio="true" image-data="gaussian3.png" natural-size="435 343"/> <image byte-size="2210" display-name="gaussian3.png" transformation="0.45977 0 0 0.45977 736 165" lock-aspect-ratio="true" image-data="gaussian3.png" natural-size="435 343"/> <image byte-size="9406" display-name="image-6.pdf" transformation="1 0 0 1 100 364" lock-aspect-ratio="true" image-data="image-6.pdf" natural-size="298 39"/> <image byte-size="8945" display-name="image-121.pdf" transformation="1 0 0 1 446 334" lock-aspect-ratio="true" image-data="image-121.pdf" natural-size="255 38"/> <image byte-size="9069" display-name="image-122.pdf" transformation="1 0 0 1 718 334" lock-aspect-ratio="true" image-data="image-122.pdf" natural-size="255 38"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7804" size="60 45" file="thumbs/st58.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">To exploit the independence assumptions, we sample independently for each mouse.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Instead of drawing samples from</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> we draw samples from</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[To exploit the independence assumptions, we need to do our sampling independently for each mouse. So, instead of using a as our proposal distribution, we use b as our proposal distribution. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 218" size="824 449" vertical-alignment="top"/> <image byte-size="10848" display-name="image-76.pdf" transformation="1 0 0 1 309 315" lock-aspect-ratio="true" image-data="image-76.pdf" natural-size="436 50"/> <image byte-size="8550" display-name="image-83.pdf" transformation="1 0 0 1 348 406" lock-aspect-ratio="true" image-data="image-83.pdf" natural-size="358 67"/> <image byte-size="10686" display-name="image-85.pdf" transformation="1 0 0 1 312 504" lock-aspect-ratio="true" image-data="image-85.pdf" natural-size="429 55"/> <image byte-size="10237" display-name="image-123.pdf" transformation="1 0 0 1 425 556" lock-aspect-ratio="true" image-data="image-123.pdf" natural-size="254 111"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st59.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We perform contour tracking independently for each mouse to create <span font-name="TimesNewRomanPS-ItalicMT">K</span> sets representing</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We sample from each set and concatenate:</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">This creates</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We weight by </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <g transformation="1 0 0 1 130 165"> <image byte-size="10584" display-name="image-14.pdf" transformation="1 0 0 1 286 165" lock-aspect-ratio="true" image-data="image-14.pdf" natural-size="605 55"/> <textbox grow-horizontally="true" size="107 47" transformation="1 0 0 1 173 171"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">Given</content> </textbox> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.33 0 0 0.33 130 177"> <styles> <fill-style fill-type="color" fill-color="0.410201 0.503843 0.784768"/> </styles> </shape> </g> <g id="g-33" transformation="1 0 0 1 130 217"> <image byte-size="10848" display-name="image-76.pdf" transformation="1 0 0 1 408 217" lock-aspect-ratio="true" image-data="image-76.pdf" natural-size="436 50"/> <textbox grow-horizontally="true" size="693 47" transformation="1 0 0 1 173 218"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">Create <span font-name="TimesNewRomanPS-ItalicMT">K</span> sets :</content> </textbox> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.33 0 0 0.33 130 227"/> </g> <g id="g-36" transformation="1 0 0 1 129 459"> <image byte-size="10686" display-name="image-85.pdf" transformation="1 0 0 1 170 505" lock-aspect-ratio="true" image-data="image-85.pdf" natural-size="429 55"/> <textbox grow-horizontally="true" size="607 47" transformation="1 0 0 1 172 459"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">Resample and concatenate to create</content> </textbox> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.33 0 0 0.33 129 465"/> </g> <g id="g-37" transformation="1 0 0 1 129 552"> <image byte-size="9649" display-name="image-92.pdf" transformation="1 0 0 1 486 552" lock-aspect-ratio="true" image-data="image-92.pdf" natural-size="481 55"/> <textbox grow-horizontally="true" size="314 47" transformation="1 0 0 1 172 558"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">Reweight to create</content> </textbox> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.33 0 0 0.33 129 564"/> </g> <g id="g-34" transformation="1 0 0 1 167 269"> <image byte-size="10483" display-name="image-35.pdf" transformation="1 0 0 1 210 311" lock-aspect-ratio="true" image-data="image-35.pdf" natural-size="528 50"/> <textbox grow-horizontally="true" size="522 47" transformation="1 0 0 1 210 269"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">Perform blob tracking to create</content> </textbox> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.33 0 0 0.33 167 275" stroke-color="0.410201 0.503843 0.784768"> <styles> <fill-style fill-type="color" fill-color="0.0833798 0.112817 0.214286"/> <dash-style pattern="solid"/> </styles> </shape> </g> <g id="g-35" transformation="1 0 0 1 166 360"> <image byte-size="10848" display-name="image-76.pdf" transformation="1 0 0 1 215 407" lock-aspect-ratio="true" image-data="image-76.pdf" natural-size="436 50"/> <textbox grow-horizontally="true" size="571 47" transformation="1 0 0 1 207 360"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">Perform contour tracking to create</content> </textbox> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.33 0 0 0.33 166 367" stroke-color="0.410201 0.503843 0.784768"> <styles> <fill-style fill-type="color" fill-color="0.0833798 0.112817 0.214286"/> <dash-style pattern="solid"/> </styles> </shape> </g> <body visibility="hidden" location="100 162" size="824 502" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st60.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 review</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Given</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Create <span font-name="TimesNewRomanPS-ItalicMT" font-ligatures="default">K</span> <span font-ligatures="default"> sets</span> : </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Perform blob tracking to create<span font-color="g0" font-ligatures="default"> <![CDATA[ ]]> </span> </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Generate <span font-name="TimesNewRomanPS-ItalicMT" font-ligatures="default">K</span> <span font-ligatures="default"> sets . </span> </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Perform contour tracking to create</content> </bullet> <bullet level="2" marker-type="none"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Resample and concatenate to create</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Reweight to create</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-33"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-34"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-35"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-36"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-37"> <property name="animationType" value="1"/> </build> </events> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[To review, our second solution has three particle filtering steps. First, we perform blob tracking to generate. Then, we generate the contour state for mouse k from the blob state for all the mice. We then perform an iteration of contour tracking for each mouse independently. We are left with K marginal distributions. We sample from the product of these marginals by sampling from each marginal independently and concatenating. To make our particle set represent the joint distribution, we weight by the joing probability divided by the product of the marginal probability. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="top"/> <image byte-size="17866" display-name="pasted.tiff" transformation="0.560538 0 0 0.560538 412 321" lock-aspect-ratio="true" image-data="pasted23.tiff" natural-size="446 352"/> <image byte-size="30770" display-name="pasted.tiff" transformation="0.569476 0 0 0.569476 108.619 320" lock-aspect-ratio="true" image-data="pasted22.tiff" natural-size="439 352"/> <image byte-size="2210" display-name="gaussian3.png" transformation="0.45977 0 0 0.45977 744 282" lock-aspect-ratio="true" image-data="gaussian3.png" natural-size="435 343"/> <image byte-size="2210" display-name="gaussian3.png" transformation="0.45977 0 0 0.45977 744 494" lock-aspect-ratio="true" image-data="gaussian3.png" natural-size="435 343"/> <image byte-size="9406" display-name="image-6.pdf" transformation="1 0 0 1 388 530" lock-aspect-ratio="true" image-data="image-6.pdf" natural-size="298 39"/> <image byte-size="8945" display-name="image-121.pdf" transformation="1 0 0 1 716 435" lock-aspect-ratio="true" image-data="image-121.pdf" natural-size="255 38"/> <image byte-size="9069" display-name="image-122.pdf" transformation="1 0 0 1 716 653" lock-aspect-ratio="true" image-data="image-122.pdf" natural-size="255 38"/> <image byte-size="8995" display-name="image-125.pdf" transformation="1 0 0 1 114 530" lock-aspect-ratio="true" image-data="image-125.pdf" natural-size="239 39"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7546" size="60 45" file="thumbs/st61.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">comparison</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Each algorithm uses different proposal distributions</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="10848" display-name="image-76.pdf" transformation="1 0 0 1 381 511" lock-aspect-ratio="true" image-data="image-76.pdf" natural-size="436 50"/> <image byte-size="10686" display-name="image-85.pdf" transformation="1 0 0 1 312 609" lock-aspect-ratio="true" image-data="image-85.pdf" natural-size="429 55"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st62.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">summary</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[Modification #1: Localize the contour search by performing blob tracking before contour tracking.]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Modification #2: </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Perform contour tracking independently to generate</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Combining the K sets creates </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st66.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">experiments</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[We evaluated our algorithm on video of three identical mice exploring a cage containing 11 occlusion events.]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Model parameters were set using <span font-color="g1">knowledge of the problem and fine-tuned on </span>a separate video sequence. </content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[We now describe our preliminary experimental results. We evaluated our algorithm on a challenging video sequence of threee identical mice exploring a cage. This video contains 11 occlusion events of varying difficulty. We set all parameters using knowledge of the problem. Some of the less intuitive parameters were fine tuned on a separate video sequence. We then tested on this novel sequence. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <plugin transformation="1 0 0 1 154.333 242" opacity="1"> <plugin-data> <plugin:movie height="284" key="root" width="720" src="tracking_results.mov"/> <string key="CPVersion">1.0</string> <string key="MIMEType">video/quicktime</string> </plugin-data> <styles> <shadow-style opacity="0" radius="0"/> </styles> </plugin> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st67.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">results</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[Here is a video of our results. We are plotting the average affine transformation applied to the contour with the most total weight. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 539" size="824 129" vertical-alignment="tracks-master"/> <plugin transformation="1 0 0 1 264.333 133.833" opacity="1"> <plugin-data> <plugin:movie height="409" key="root" width="496" src="jumpingmouse.mov"/> <string key="CPVersion">1.0</string> <string key="MIMEType">video/quicktime</string> </plugin-data> <styles> <shadow-style opacity="0" radius="0"/> </styles> </plugin> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8362" size="60 45" file="thumbs/st68.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">erratic behavior</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Our algorithm is robust to erratic behavior.</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[These results demonstrate a number of strengths of our algorithm. First, our algorithm is robust to erratic behavior. The mouse in this sequence jumps then falls to the ground. This does not match our model of mouse dynamics well, but our algorithm is robust enough to follow the mouse. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 539" size="824 129" vertical-alignment="tracks-master"/> <plugin transformation="1 0 0 1 310.667 133.667" opacity="1"> <plugin-data> <plugin:movie height="408" key="root" width="402" src="fallingmouse.mov"/> <string key="CPVersion">1.0</string> <string key="MIMEType">video/quicktime</string> </plugin-data> <styles> <shadow-style opacity="0" radius="0"/> </styles> </plugin> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st69.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">erratic behavior</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Our algorithm is robust to erratic behavior.</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[This clip shows a mouse falling from the ceiling. Again, this does not match our motion model well, but we still do not lose the mouse. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 328" size="824 340" vertical-alignment="tracks-master"/> <plugin transformation="1 0 0 1 244.167 203.667" opacity="1"> <plugin-data> <plugin:movie height="202" key="root" width="535" src="crossingmice.mov"/> <string key="CPVersion">1.0</string> <string key="MIMEType">video/quicktime</string> </plugin-data> <styles> <shadow-style opacity="0" radius="0"/> </styles> </plugin> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st70.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">data association</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Two trackers never track the same mouse.</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[Another success of our algorithm is that two trackers never follow the same mouse, even though our contour likelihood is independent for each mouse. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 372" size="824 296" vertical-alignment="tracks-master"/> <image byte-size="28407" display-name="scratchclutter.png" transformation="1 0 0 1 102 142" lock-aspect-ratio="true" image-data="scratchclutter.png" natural-size="394 284"/> <image byte-size="51901" display-name="shadowandtail.png" transformation="1 0 0 1 536 153" lock-aspect-ratio="true" image-data="shadowandtail.png" natural-size="385 262"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st71.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">clutter</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Our algorithm is rarely distracted by background clutter.</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[Our algorithm is rarely distracted by background clutter. This implies that our feature extraction methods and the blob and contour combination provide robust observation likelihoods. One of the most difficult types of clutter are the scratches illuminated in the corners of the cage. We are able to ignore the scratches in this example. We are only distracted by clutter if both the blob and contour observations fail. In this example, the blob likelihood fails because it mistakes shaded bedding for foreground and the contour likelihood is distracted by the mouse tail. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st72.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">occlusions</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[Our algorithm accurately tracks the mice through 7/11 occlusions, and partially through the other 4.]]> </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="115 448" size="824 220" vertical-alignment="tracks-master"/> <image byte-size="42285" display-name="backwardstemplate.png" transformation="1 0 0 1 311 166" lock-aspect-ratio="true" image-data="backwardstemplate.png" natural-size="402 284"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st73.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">failure modes</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[Our tracker occasionally gets stuck in local optima in which the contour fit is facing the wrong direction.]]> </content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande">There are a couple failure modes we are working to address. </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st74.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">failure modes</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Our algorithm fails in 4/11 occlusions.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[This is because our algorithm is heavily biased by BraMBLe, even during occlusions.]]> </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st75.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">summary</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[I have presented a combined blob and contour tracking algorithm that performs well on a difficult video sequence. ]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Our algorithm leverages the strengths of</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">multiple blob tracking</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">contour tracking</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">independence assumptions</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">To accurately track without too many particles.</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st76.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">future work</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We plan on exploring </content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Methods for automatically setting the hyperparameters</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Models of the mouse contour</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Transition distributions</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="114 415" size="824 276" vertical-alignment="tracks-master"/> <image byte-size="314339" display-name="startocclusion.png" transformation="0.416089 0 0 0.416089 92 174" lock-aspect-ratio="true" image-data="startocclusion.png" natural-size="721 284"/> <image byte-size="310206" display-name="endocclusion1.png" transformation="0.277393 0 0 0.277393 487 103" lock-aspect-ratio="true" image-data="endocclusion1.png" natural-size="721 284"/> <image byte-size="310226" display-name="endocclusion2.png" transformation="0.277393 0 0 0.277393 702 102" lock-aspect-ratio="true" image-data="endocclusion2.png" natural-size="721 284"/> <image byte-size="310211" display-name="endocclusion4.png" transformation="0.277393 0 0 0.277393 487 194" lock-aspect-ratio="true" image-data="endocclusion4.png" natural-size="721 284"/> <image byte-size="310202" display-name="endocclusion5.png" transformation="0.277393 0 0 0.277393 702 193" lock-aspect-ratio="true" image-data="endocclusion5.png" natural-size="721 284"/> <image byte-size="310198" display-name="endocclusion6.png" transformation="0.277393 0 0 0.277393 487 285" lock-aspect-ratio="true" image-data="endocclusion6.png" natural-size="721 284"/> <image byte-size="310193" display-name="endocclusion3.png" transformation="0.277393 0 0 0.277393 702 284" lock-aspect-ratio="true" image-data="endocclusion3.png" natural-size="721 284"/> <textbox grow-horizontally="true" size="242 47" transformation="1 0 0 1 121 300"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">occlusion start</content> </textbox> <textbox grow-horizontally="true" size="232 47" transformation="1 0 0 1 576 360"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">occlusion end</content> </textbox> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st77.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">current work</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Tracking is accurate when the mice are not occluding one another. </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"> <![CDATA[At the end of an occlusion, the positions of the mice are known, but the identities might have been switched. ]]> </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-6"> <drawables> <title visibility="tracks-master" location="222 56" size="746 125" vertical-alignment="bottom"/> <textbox grow-horizontally="true" size="634 47" transformation="1 0 0 1 195 360"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">http://vision.ucsd.edu/smart_vivarium</content> </textbox> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st78.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="36" paragraph-line-spacing="-50" font-name="Futura-Medium">thank you for your attention!</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-alignment="center" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="42" font-name="Futura-Medium">Thank you for your attention!</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <body visibility="tracks-master" location="115 121" size="824 450" vertical-alignment="tracks-master"/> <plugin transformation="1 0 0 1 402 146" opacity="1"> <plugin-data> <plugin:movie height="147" key="root" width="220" src="erratic_motion%20021.mov"/> <string key="CPVersion">1.0</string> <string key="MIMEType">video/quicktime</string> </plugin-data> <styles> <shadow-style opacity="0" radius="0"/> </styles> </plugin> <g id="g-38" transformation="1 0 0 1 191.5 370"> <textbox grow-horizontally="true" size="714 46" transformation="1 0 0 1 203 370"> <content tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="12" font-name="Helvetica"> <![CDATA[ ]]> <span font-color="g1" font-size="36" font-name="Futura-Medium" font-ligatures="none">Their motion is unconstrained and erratic.</span> </content> </textbox> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.295 0 0 0.295 191.5 378" 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font-name="Helvetica"> <![CDATA[ ]]> <span font-color="g1" font-size="36" font-name="Futura-Medium" font-ligatures="none">They are deformable 3-D objects.</span> </content> </textbox> <g transformation="1 0 0 1 208 146.5"> <image natural-size="108 227" display-name="pasted.tiff" byte-size="79312" transformation="0.651982 0 0 0.651982 208 146.5" lock-aspect-ratio="true" image-data="pasted.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> <image natural-size="129 106" display-name="pasted.tiff" byte-size="41232" transformation="1.39623 0 0 1.39623 651.5 147" lock-aspect-ratio="true" image-data="pasted1.tiff" stroke-width="3" stroke-color="0.0833798 0.112817 0.214286"> <styles> <dash-style pattern="solid"/> </styles> </image> <image natural-size="179 79" display-name="pasted.tiff" byte-size="45650" transformation="1 0 0 1 278.5 215.5" lock-aspect-ratio="true" image-data="pasted2.tiff" stroke-width="3" 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font-ligatures="none">They are indistinguishable.</span> </content> </textbox> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.295 0 0 0.295 190.5 472" stroke-color="0.410201 0.503843 0.784768"> <styles> <fill-style fill-type="color" fill-color="0.0833798 0.112817 0.214286"/> <dash-style pattern="solid"/> </styles> </shape> </g> <image byte-size="81566" display-name="Image-5" transformation="1.26597 0 0 1.26603 208 146" lock-aspect-ratio="true" image-data="image.png" natural-size="493 117"/> </g> <g id="g-41" transformation="1 0 0 1 189.5 146"> <g transformation="1 0 0 1 189.5 512"> <textbox grow-horizontally="true" size="718 46" transformation="1 0 0 1 201 512"> <content tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="12" font-name="Helvetica"> <![CDATA[ ]]> <span font-color="g1" font-size="36" font-name="Futura-Medium" font-ligatures="none">They have few (if any) trackable features.</span> </content> </textbox> <shape path="M 85.3553 14.6447 C 104.882 34.1709 104.882 65.8291 85.3553 85.3553 C 65.8291 104.882 34.1709 104.882 14.6447 85.3553 C -4.88155 65.8291 -4.88155 34.1709 14.6447 14.6447 C 34.1709 -4.88155 65.8291 -4.88155 85.3553 14.6447 Z M 85.3553 14.6447" transformation="0.295 0 0 0.295 189.5 520" stroke-color="0.410201 0.503843 0.784768"> <styles> <fill-style fill-type="color" fill-color="0.0833798 0.112817 0.214286"/> <dash-style pattern="solid"/> </styles> </shape> </g> <image byte-size="79701" display-name="Image-7" transformation="1.26597 0 0 1.26603 205 146" lock-aspect-ratio="true" image-data="image1.png" natural-size="493 117"/> </g> <g id="g-42" transformation="1 0 0 1 190.5 146"> <g transformation="1 0 0 1 190.5 557"> <textbox grow-horizontally="true" size="717 46" 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font-name="Futura-Medium">X</content> </textbox> <textbox grow-horizontally="true" size="25 32" transformation="1 0 0 1 630 391"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="24" font-name="Futura-Medium">=</content> </textbox> </g> <g id="g-44" transformation="1 0 0 1 522 335"> <image byte-size="1202" display-name="logfilter.png" transformation="0.364964 0 0 0.364964 522 357" lock-aspect-ratio="true" image-data="logfilter.png" natural-size="274 275"/> <image byte-size="9188" display-name="example_h_hsv_log.png" transformation="0.347705 0 0 0.347705 671 335" lock-aspect-ratio="true" image-data="example_h_hsv_log.png" natural-size="719 285"/> <image byte-size="11975" display-name="example_v_hsv_log.png" transformation="0.347705 0 0 0.347705 671 534" lock-aspect-ratio="true" image-data="example_v_hsv_log.png" natural-size="719 285"/> <image byte-size="17633" display-name="example_s_hsv_log.png" transformation="0.347705 0 0 0.347705 671 435" lock-aspect-ratio="true" image-data="example_s_hsv_log.png" natural-size="719 285"/> </g> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8310" size="60 45" file="thumbs/st16111.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">blob likelihood</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Image processing:</content> </bullet> <bullet level="2" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">Apply Gaussian and LoG filters to each channel at each grid point.</content> </bullet> </bullets> <events> <build type="apple:dissolve" duration="1" target-id="g-43"> <property name="animationType" value="1"/> </build> <build type="apple:dissolve" duration="1" target-id="g-44"> <property name="animationType" value="1"/> </build> </events> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox grow-horizontally="true" size="776 47" transformation="1 0 0 1 91 239"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">0) Given :</content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="304363" display-name="sample01818_max2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_max2.png" natural-size="721 284"/> <image byte-size="304224" display-name="sample01818_max1000.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_max1000.png" natural-size="721 284"/> <image byte-size="304708" display-name="sample01818_max1.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_max1.png" natural-size="721 284"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="7633" display-name="particlefiltering_sample1.pdf" transformation="1 0 0 1 75 467" lock-aspect-ratio="true" image-data="particlefiltering_sample1.pdf" natural-size="190 52"/> <image byte-size="7842" display-name="particlefiltering_sampleN.pdf" transformation="1 0 0 1 747 467" lock-aspect-ratio="true" image-data="particlefiltering_sampleN.pdf" natural-size="192 52"/> <image byte-size="7757" display-name="particlefiltering_sample2.pdf" transformation="1 0 0 1 386 467" lock-aspect-ratio="true" image-data="particlefiltering_sample2.pdf" natural-size="190 52"/> </g> <image byte-size="10584" display-name="image-14.pdf" transformation="1 0 0 1 243 230" lock-aspect-ratio="true" image-data="image-14.pdf" natural-size="605 55"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st3311.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step (0)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[Our filtering algorithm is then very similar to standard filtering. We are again given a set of weighted samples representing the filtering distribution at time t-1. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox size="847 94" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[1) Resample according to the weights to create]]> </content> </textbox> <image byte-size="10584" display-name="image-14.pdf" transformation="1 0 0 1 307 174" lock-aspect-ratio="true" image-data="image-14.pdf" natural-size="605 55"/> <image byte-size="10521" display-name="image-15.pdf" transformation="1 0 0 1 269 274" lock-aspect-ratio="true" image-data="image-15.pdf" natural-size="486 55"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 583" lock-aspect-ratio="true" image-data="sample01818_unweighted10.png" natural-size="721 284"/> <image byte-size="303493" display-name="sample01818_unweighted2.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01818_unweighted2.png" natural-size="721 284"/> <image byte-size="303628" display-name="sample01818_unweighted1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01818_unweighted1.png" natural-size="721 284"/> <image byte-size="7467" display-name="particlefiltering_sampleunweightedN.pdf" transformation="1 0 0 1 808 707" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweightedN.pdf" natural-size="70 52"/> <image byte-size="7384" display-name="particlefiltering_sampleunweighted2.pdf" transformation="1 0 0 1 446 707" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted2.pdf" natural-size="70 52"/> <image byte-size="7260" display-name="particlefiltering_sampleunweighted1.pdf" transformation="1 0 0 1 135 707" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted1.pdf" natural-size="70 52"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 618"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> </g> <g transformation="1 0 0 1 -10 335"> <image byte-size="304363" display-name="sample01818_max2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_max2.png" natural-size="721 284"/> <image byte-size="304224" display-name="sample01818_max1000.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_max1000.png" natural-size="721 284"/> <image byte-size="304708" display-name="sample01818_max1.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_max1.png" natural-size="721 284"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="7633" display-name="particlefiltering_sample1.pdf" transformation="1 0 0 1 75 467" lock-aspect-ratio="true" image-data="particlefiltering_sample1.pdf" natural-size="190 52"/> <image byte-size="7842" display-name="particlefiltering_sampleN.pdf" transformation="1 0 0 1 747 467" lock-aspect-ratio="true" image-data="particlefiltering_sampleN.pdf" natural-size="192 52"/> <image byte-size="7757" display-name="particlefiltering_sample2.pdf" transformation="1 0 0 1 386 467" lock-aspect-ratio="true" image-data="particlefiltering_sample2.pdf" natural-size="190 52"/> </g> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 537"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st351.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step (1)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[As before, we resample according to the weights to create an unweighted sample set representing the filtering distribution for the state at time t-1. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[2) From each sample generate to create . ]]> </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_unweighted10.png" natural-size="721 284"/> <image byte-size="303493" display-name="sample01818_unweighted2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_unweighted2.png" natural-size="721 284"/> <image byte-size="303628" display-name="sample01818_unweighted1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_unweighted1.png" natural-size="721 284"/> <image byte-size="7467" display-name="particlefiltering_sampleunweightedN.pdf" transformation="1 0 0 1 808 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweightedN.pdf" natural-size="70 52"/> <image byte-size="7384" display-name="particlefiltering_sampleunweighted2.pdf" transformation="1 0 0 1 446 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted2.pdf" natural-size="70 52"/> <image byte-size="7260" display-name="particlefiltering_sampleunweighted1.pdf" transformation="1 0 0 1 135 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted1.pdf" natural-size="70 52"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> </g> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 537"/> <image byte-size="10070" display-name="image-20.pdf" transformation="1 0 0 1 447 179" lock-aspect-ratio="true" image-data="image-20.pdf" natural-size="448 55"/> <image byte-size="10469" display-name="image-23.pdf" transformation="1 0 0 1 248 274" lock-aspect-ratio="true" image-data="image-23.pdf" natural-size="472 55"/> <image byte-size="10079" display-name="image-24.pdf" transformation="1 0 0 1 252 227" lock-aspect-ratio="true" image-data="image-24.pdf" natural-size="471 55"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 619"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="5095" display-name="particlefiltering_samplet1.pdf" transformation="1 0 0 1 141 707" lock-aspect-ratio="true" image-data="particlefiltering_samplet1.pdf" natural-size="59 49"/> <image byte-size="5196" display-name="particlefiltering_sampletN.pdf" transformation="1 0 0 1 808 707" lock-aspect-ratio="true" image-data="particlefiltering_sampletN.pdf" natural-size="70 49"/> <image byte-size="5137" display-name="particlefiltering_samplet2.pdf" transformation="1 0 0 1 451 707" lock-aspect-ratio="true" image-data="particlefiltering_samplet2.pdf" natural-size="59 49"/> <image byte-size="8175" display-name="blobparticle2.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="blobparticle2.png" natural-size="721 284"/> <image byte-size="8136" display-name="blobparticle1.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="blobparticle1.png" natural-size="721 284"/> <image byte-size="8247" display-name="blobparticleN.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="blobparticleN.png" natural-size="721 284"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st42.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step (2)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[Our prediction step is slightly different. From each sample representing the state at time t-1, we generate a state at time t using the blob observations from the current frame. I will describe how we do this shortly. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[3) Weight each sample by to create . ]]> </content> </textbox> <g transformation="1 0 0 1 -10 570"> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 570" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 570" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 617"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="305399" display-name="blobparticleweightedN.png" transformation="0.416089 0 0 0.416089 693 585" lock-aspect-ratio="true" image-data="blobparticleweightedN.png" natural-size="721 284"/> <image byte-size="304393" display-name="blobparticleweighted2.png" transformation="0.416089 0 0 0.416089 331 585" lock-aspect-ratio="true" image-data="blobparticleweighted2.png" natural-size="721 284"/> <image byte-size="304314" display-name="blobparticleweighted1.png" transformation="0.416089 0 0 0.416089 22 585" lock-aspect-ratio="true" image-data="blobparticleweighted1.png" natural-size="721 284"/> <image byte-size="6675" display-name="particlefiltering_particlet1.pdf" transformation="1 0 0 1 87 709" lock-aspect-ratio="true" image-data="particlefiltering_particlet1.pdf" natural-size="170 49"/> <image byte-size="6717" display-name="particlefiltering_particlet2.pdf" transformation="1 0 0 1 396 709" lock-aspect-ratio="true" image-data="particlefiltering_particlet2.pdf" natural-size="170 49"/> <image byte-size="6777" display-name="particlefiltering_particletN.pdf" transformation="1 0 0 1 747 709" lock-aspect-ratio="true" image-data="particlefiltering_particletN.pdf" natural-size="192 49"/> </g> <g transformation="1 0 0 1 -10 335"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 346" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 382"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="5095" display-name="particlefiltering_samplet1.pdf" transformation="1 0 0 1 141 470" lock-aspect-ratio="true" image-data="particlefiltering_samplet1.pdf" natural-size="59 49"/> <image byte-size="5196" display-name="particlefiltering_sampletN.pdf" transformation="1 0 0 1 808 470" lock-aspect-ratio="true" image-data="particlefiltering_sampletN.pdf" natural-size="70 49"/> <image byte-size="5137" display-name="particlefiltering_samplet2.pdf" transformation="1 0 0 1 451 470" lock-aspect-ratio="true" image-data="particlefiltering_samplet2.pdf" natural-size="59 49"/> <image byte-size="8175" display-name="blobparticle2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="blobparticle2.png" natural-size="721 284"/> <image byte-size="8136" display-name="blobparticle1.png" transformation="0.416089 0 0 0.416089 21 346" lock-aspect-ratio="true" image-data="blobparticle1.png" natural-size="721 284"/> <image byte-size="8247" display-name="blobparticleN.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="blobparticleN.png" natural-size="721 284"/> </g> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 537"/> <image byte-size="10079" display-name="image-25.pdf" transformation="1 0 0 1 481 178" lock-aspect-ratio="true" image-data="image-25.pdf" natural-size="471 55"/> <image byte-size="10381" display-name="image-26.pdf" transformation="1 0 0 1 145 226" lock-aspect-ratio="true" image-data="image-26.pdf" natural-size="374 50"/> <image byte-size="9649" display-name="image-27.pdf" transformation="1 0 0 1 242 274" lock-aspect-ratio="true" image-data="image-27.pdf" natural-size="481 55"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st43.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step (3)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[As before, we weight each sample by the observation likelihood. However, as we have already taken into account the blob observation, we need only weight by the contour likelihood. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="10079" display-name="image-24.pdf" transformation="1 0 0 1 276 464" lock-aspect-ratio="true" image-data="image-24.pdf" natural-size="471 55"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st601.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step 2</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We perform another particle filtering iteration to sample from</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[How do we sample from our new proposal distribution, which takes into account the blob observation? To do this, we perform another particle filtering iteration. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="803 120" vertical-alignment="tracks-master"/> <textbox grow-horizontally="true" size="664 47" transformation="1 0 0 1 91 239"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">a) Given :</content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_unweighted10.png" natural-size="721 284"/> <image byte-size="303493" display-name="sample01818_unweighted2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_unweighted2.png" natural-size="721 284"/> <image byte-size="303628" display-name="sample01818_unweighted1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_unweighted1.png" natural-size="721 284"/> <image byte-size="7467" display-name="particlefiltering_sampleunweightedN.pdf" transformation="1 0 0 1 808 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweightedN.pdf" natural-size="70 52"/> <image byte-size="7384" display-name="particlefiltering_sampleunweighted2.pdf" transformation="1 0 0 1 446 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted2.pdf" natural-size="70 52"/> <image byte-size="7260" display-name="particlefiltering_sampleunweighted1.pdf" transformation="1 0 0 1 135 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted1.pdf" natural-size="70 52"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> </g> <image byte-size="10521" display-name="image-15.pdf" transformation="1 0 0 1 250 235" lock-aspect-ratio="true" image-data="image-15.pdf" natural-size="486 55"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st381.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step (2a)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[At step 1, we produced a set of unweighted particles representing the filtering distribution for the state at time t-1. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="812 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[b) From each sample generate to create . ]]> </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_unweighted10.png" natural-size="721 284"/> <image byte-size="303493" display-name="sample01818_unweighted2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_unweighted2.png" natural-size="721 284"/> <image byte-size="303628" display-name="sample01818_unweighted1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_unweighted1.png" natural-size="721 284"/> <image byte-size="7467" display-name="particlefiltering_sampleunweightedN.pdf" transformation="1 0 0 1 808 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweightedN.pdf" natural-size="70 52"/> <image byte-size="7384" display-name="particlefiltering_sampleunweighted2.pdf" transformation="1 0 0 1 446 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted2.pdf" natural-size="70 52"/> <image byte-size="7260" display-name="particlefiltering_sampleunweighted1.pdf" transformation="1 0 0 1 135 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted1.pdf" natural-size="70 52"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> </g> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 537"/> <image byte-size="10070" display-name="image-20.pdf" transformation="1 0 0 1 447 179" lock-aspect-ratio="true" image-data="image-20.pdf" natural-size="448 55"/> <image byte-size="9617" display-name="image-28.pdf" transformation="1 0 0 1 255 226" lock-aspect-ratio="true" image-data="image-28.pdf" natural-size="363 55"/> <image byte-size="9819" display-name="image-29.pdf" transformation="1 0 0 1 255 273" lock-aspect-ratio="true" image-data="image-29.pdf" natural-size="364 50"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 619"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2688" display-name="priorblobN.png" transformation="0.415512 0 0 0.415512 693 583" lock-aspect-ratio="true" image-data="priorblobN.png" natural-size="722 283"/> <image byte-size="2698" display-name="priorblob2.png" transformation="0.415512 0 0 0.415512 331 584" lock-aspect-ratio="true" image-data="priorblob2.png" natural-size="722 283"/> <image byte-size="2718" display-name="priorblob1.png" transformation="0.416089 0 0 0.416089 21 584" lock-aspect-ratio="true" image-data="priorblob1.png" natural-size="721 283"/> <image byte-size="5178" display-name="image-30.pdf" transformation="1 0 0 1 137 707" lock-aspect-ratio="true" image-data="image-30.pdf" natural-size="68 50"/> <image byte-size="5297" display-name="image-31.pdf" transformation="1 0 0 1 447 707" lock-aspect-ratio="true" image-data="image-31.pdf" natural-size="68 50"/> <image byte-size="5364" display-name="image-32.pdf" transformation="1 0 0 1 809 707" lock-aspect-ratio="true" image-data="image-32.pdf" natural-size="68 50"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7494" size="60 45" file="thumbs/st39.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step (2b)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[From each of these samples, we generate a blob sample according to the assumed model dynamics described before. All of the contour specific parameters are assumed to remain constant. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="812 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[c) Weight each sample by ]]> <div paragraph-alignment="natural">to create . </div> </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 346" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 382"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2688" display-name="priorblobN.png" transformation="0.415512 0 0 0.415512 693 346" lock-aspect-ratio="true" image-data="priorblobN.png" natural-size="722 283"/> <image byte-size="2698" display-name="priorblob2.png" transformation="0.415512 0 0 0.415512 331 347" lock-aspect-ratio="true" image-data="priorblob2.png" natural-size="722 283"/> <image byte-size="2718" display-name="priorblob1.png" transformation="0.416089 0 0 0.416089 21 347" lock-aspect-ratio="true" image-data="priorblob1.png" natural-size="721 283"/> <image byte-size="5178" display-name="image-30.pdf" transformation="1 0 0 1 137 470" lock-aspect-ratio="true" image-data="image-30.pdf" natural-size="68 50"/> <image byte-size="5297" display-name="image-31.pdf" transformation="1 0 0 1 447 470" lock-aspect-ratio="true" image-data="image-31.pdf" natural-size="68 50"/> <image byte-size="5364" display-name="image-32.pdf" transformation="1 0 0 1 809 470" lock-aspect-ratio="true" image-data="image-32.pdf" natural-size="68 50"/> </g> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 537"/> <image byte-size="9617" display-name="image-28.pdf" transformation="1 0 0 1 479 181" lock-aspect-ratio="true" image-data="image-28.pdf" natural-size="363 55"/> <image byte-size="10483" display-name="image-35.pdf" transformation="1 0 0 1 248 274" lock-aspect-ratio="true" image-data="image-35.pdf" natural-size="528 50"/> <image byte-size="8912" display-name="image-36.pdf" transformation="1 0 0 1 145 227" lock-aspect-ratio="true" image-data="image-36.pdf" natural-size="275 50"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 619"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="8248" display-name="weightedblobN.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="weightedblobN.png" natural-size="721 284"/> <image byte-size="8031" display-name="weightedblob2.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="weightedblob2.png" natural-size="721 284"/> <image byte-size="8253" display-name="weightedblob1.png" transformation="0.416089 0 0 0.416089 21 584" lock-aspect-ratio="true" image-data="weightedblob1.png" natural-size="721 284"/> <image byte-size="7016" display-name="image-37.pdf" transformation="1 0 0 1 82 707" lock-aspect-ratio="true" image-data="image-37.pdf" natural-size="177 50"/> <image byte-size="7135" display-name="image-38.pdf" transformation="1 0 0 1 392 707" lock-aspect-ratio="true" image-data="image-38.pdf" natural-size="177 50"/> <image byte-size="7201" display-name="image-39.pdf" transformation="1 0 0 1 749 707" lock-aspect-ratio="true" image-data="image-39.pdf" natural-size="188 50"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7524" size="60 45" file="thumbs/st41.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step (2c)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[In order to incorporate the blob observation, we weight by the blob likelihood. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="812 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[d) Resample according to the weights to create]]> </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 346" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 382"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="8248" display-name="weightedblobN.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="weightedblobN.png" natural-size="721 284"/> <image 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537"/> <image byte-size="10483" display-name="image-35.pdf" transformation="1 0 0 1 300 174" lock-aspect-ratio="true" image-data="image-35.pdf" natural-size="528 50"/> <image byte-size="10627" display-name="image-40.pdf" transformation="1 0 0 1 243 273" lock-aspect-ratio="true" image-data="image-40.pdf" natural-size="423 50"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 619"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="7942" display-name="resampledblobN.png" transformation="0.416089 0 0 0.416089 693 584" lock-aspect-ratio="true" image-data="resampledblobN.png" natural-size="721 284"/> <image byte-size="7942" display-name="resampledblob2.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="resampledblob2.png" natural-size="721 284"/> <image byte-size="7942" display-name="resampledblob1.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="resampledblob1.png" natural-size="721 284"/> <image byte-size="6423" display-name="image-41.pdf" transformation="1 0 0 1 136 707" lock-aspect-ratio="true" image-data="image-41.pdf" natural-size="69 50"/> <image byte-size="6543" display-name="image-42.pdf" transformation="1 0 0 1 446 707" lock-aspect-ratio="true" image-data="image-42.pdf" natural-size="69 50"/> <image byte-size="6609" display-name="image-43.pdf" transformation="1 0 0 1 808 707" lock-aspect-ratio="true" image-data="image-43.pdf" natural-size="69 50"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st411.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step (2d)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande">We then resample according to the weights to create ...</notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="812 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[e) From each sample generate ]]> <div paragraph-alignment="natural">to create . </div> </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 346" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 346" 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537"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 619"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="5095" display-name="particlefiltering_samplet1.pdf" transformation="1 0 0 1 141 707" lock-aspect-ratio="true" image-data="particlefiltering_samplet1.pdf" natural-size="59 49"/> <image byte-size="5196" display-name="particlefiltering_sampletN.pdf" transformation="1 0 0 1 808 707" lock-aspect-ratio="true" image-data="particlefiltering_sampletN.pdf" natural-size="70 49"/> <image byte-size="5137" display-name="particlefiltering_samplet2.pdf" transformation="1 0 0 1 451 707" lock-aspect-ratio="true" image-data="particlefiltering_samplet2.pdf" natural-size="59 49"/> <image byte-size="7838" display-name="priorcontour2.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="priorcontour2.png" natural-size="721 284"/> <image byte-size="7901" display-name="priorcontour1.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="priorcontour1.png" natural-size="721 284"/> <image byte-size="7877" display-name="priorcontourN.png" transformation="0.416089 0 0 0.416089 693 584" lock-aspect-ratio="true" image-data="priorcontourN.png" natural-size="721 284"/> </g> <image byte-size="10188" display-name="image-44.pdf" transformation="1 0 0 1 448 179" lock-aspect-ratio="true" image-data="image-44.pdf" natural-size="386 50"/> <image byte-size="9111" display-name="image-45.pdf" transformation="1 0 0 1 255 229" lock-aspect-ratio="true" image-data="image-45.pdf" natural-size="332 50"/> <image byte-size="10469" display-name="image-23.pdf" transformation="1 0 0 1 248 274" lock-aspect-ratio="true" image-data="image-23.pdf" natural-size="472 55"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st421.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #1 step (2e)</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox grow-horizontally="true" size="776 47" transformation="1 0 0 1 91 239"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">0) Given :</content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="304363" display-name="sample01818_max2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_max2.png" natural-size="721 284"/> <image byte-size="304224" display-name="sample01818_max1000.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_max1000.png" natural-size="721 284"/> <image byte-size="304708" display-name="sample01818_max1.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_max1.png" natural-size="721 284"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="7633" display-name="particlefiltering_sample1.pdf" transformation="1 0 0 1 75 467" lock-aspect-ratio="true" image-data="particlefiltering_sample1.pdf" natural-size="190 52"/> <image byte-size="7842" display-name="particlefiltering_sampleN.pdf" transformation="1 0 0 1 747 467" lock-aspect-ratio="true" image-data="particlefiltering_sampleN.pdf" natural-size="192 52"/> <image byte-size="7757" display-name="particlefiltering_sample2.pdf" transformation="1 0 0 1 386 467" lock-aspect-ratio="true" image-data="particlefiltering_sample2.pdf" natural-size="190 52"/> </g> <image byte-size="10584" display-name="image-14.pdf" transformation="1 0 0 1 243 230" lock-aspect-ratio="true" image-data="image-14.pdf" natural-size="605 55"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st471.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (0)</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox size="847 94" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[1) Resample according to the weights to create]]> </content> </textbox> <image byte-size="10584" display-name="image-14.pdf" transformation="1 0 0 1 307 174" lock-aspect-ratio="true" image-data="image-14.pdf" natural-size="605 55"/> <image byte-size="10521" display-name="image-15.pdf" transformation="1 0 0 1 269 274" lock-aspect-ratio="true" image-data="image-15.pdf" natural-size="486 55"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 583" lock-aspect-ratio="true" image-data="sample01818_unweighted10.png" natural-size="721 284"/> <image byte-size="303493" display-name="sample01818_unweighted2.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01818_unweighted2.png" natural-size="721 284"/> <image byte-size="303628" display-name="sample01818_unweighted1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01818_unweighted1.png" natural-size="721 284"/> <image byte-size="7467" display-name="particlefiltering_sampleunweightedN.pdf" transformation="1 0 0 1 808 707" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweightedN.pdf" natural-size="70 52"/> <image byte-size="7384" display-name="particlefiltering_sampleunweighted2.pdf" transformation="1 0 0 1 446 707" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted2.pdf" natural-size="70 52"/> <image byte-size="7260" display-name="particlefiltering_sampleunweighted1.pdf" transformation="1 0 0 1 135 707" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted1.pdf" natural-size="70 52"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 618"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> </g> <g transformation="1 0 0 1 -10 335"> <image byte-size="304363" display-name="sample01818_max2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_max2.png" natural-size="721 284"/> <image byte-size="304224" display-name="sample01818_max1000.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_max1000.png" natural-size="721 284"/> <image byte-size="304708" display-name="sample01818_max1.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_max1.png" natural-size="721 284"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="7633" display-name="particlefiltering_sample1.pdf" transformation="1 0 0 1 75 467" lock-aspect-ratio="true" image-data="particlefiltering_sample1.pdf" natural-size="190 52"/> <image byte-size="7842" display-name="particlefiltering_sampleN.pdf" transformation="1 0 0 1 747 467" lock-aspect-ratio="true" image-data="particlefiltering_sampleN.pdf" natural-size="192 52"/> <image byte-size="7757" display-name="particlefiltering_sample2.pdf" transformation="1 0 0 1 386 467" lock-aspect-ratio="true" image-data="particlefiltering_sample2.pdf" natural-size="190 52"/> </g> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 537"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st48.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (1)</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[2) From each sample generate to create ]]> <span font-name="TimesNewRomanPS-ItalicMT">K</span> sets . </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_unweighted10.png" natural-size="721 284"/> <image byte-size="303493" display-name="sample01818_unweighted2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_unweighted2.png" natural-size="721 284"/> <image byte-size="303628" display-name="sample01818_unweighted1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_unweighted1.png" natural-size="721 284"/> <image byte-size="7467" display-name="particlefiltering_sampleunweightedN.pdf" transformation="1 0 0 1 808 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweightedN.pdf" natural-size="70 52"/> <image byte-size="7384" display-name="particlefiltering_sampleunweighted2.pdf" transformation="1 0 0 1 446 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted2.pdf" natural-size="70 52"/> <image byte-size="7260" display-name="particlefiltering_sampleunweighted1.pdf" transformation="1 0 0 1 135 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted1.pdf" natural-size="70 52"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" 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lock-aspect-ratio="true" image-data="priorcontour1_1.png" natural-size="721 284"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 228 607.5"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.2069 0 0 2.36842 463 586" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="6271" display-name="priorcontour2000_1.png" transformation="0.277393 0 0 0.277393 269 591.61" lock-aspect-ratio="true" image-data="priorcontour2000_1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.2069 0 0 2.36842 525 586" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="6384" display-name="priorcontour2000_2.png" transformation="0.277393 0 0 0.277393 787 591.61" lock-aspect-ratio="true" image-data="priorcontour2000_2.png" natural-size="721 284"/> <image byte-size="6480" display-name="priorcontour1_2.png" transformation="0.277393 0 0 0.277393 547 591.61" lock-aspect-ratio="true" image-data="priorcontour1_2.png" natural-size="721 284"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 745 607.5"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.2069 0 0 2.36842 980 586" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 484 606.5"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="6118" display-name="image-70.pdf" transformation="1 0 0 1 100 671" lock-aspect-ratio="true" image-data="image-70.pdf" natural-size="59 49"/> <image byte-size="6327" display-name="image-71.pdf" transformation="1 0 0 1 334 671" lock-aspect-ratio="true" image-data="image-71.pdf" natural-size="70 49"/> <image byte-size="6369" display-name="image-72.pdf" transformation="1 0 0 1 852 671" lock-aspect-ratio="true" image-data="image-72.pdf" natural-size="70 49"/> <image byte-size="6242" display-name="image-73.pdf" transformation="1 0 0 1 617 671" lock-aspect-ratio="true" image-data="image-73.pdf" natural-size="59 49"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st491.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (2)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[As our sampling is independent for each mouse, we now have K independent sets of samples which approximate this marginal distribution. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[3) Weight each sample by to create ]]> <span font-name="TimesNewRomanPS-ItalicMT">K</span> sets . </content> </textbox> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 287 507"/> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 802 507"/> <g transformation="1 0 0 1 8 355"> <image byte-size="2759" display-name="leftbrace.pdf" 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size="44 47" transformation="1 0 0 1 484 606.5"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="6918" display-name="image-77.pdf" transformation="1 0 0 1 45 670" lock-aspect-ratio="true" image-data="image-77.pdf" natural-size="170 49"/> <image byte-size="7131" display-name="image-78.pdf" transformation="1 0 0 1 273 670" lock-aspect-ratio="true" image-data="image-78.pdf" natural-size="192 49"/> <image byte-size="7251" display-name="image-79.pdf" transformation="1 0 0 1 791 670" lock-aspect-ratio="true" image-data="image-79.pdf" natural-size="192 50"/> <image byte-size="7191" display-name="image-80.pdf" transformation="1 0 0 1 562 670" lock-aspect-ratio="true" image-data="image-80.pdf" natural-size="170 50"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st501.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (3)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[We then weight each sample in a set by the contour likelihood for that mouse, which results in K particle sets which represent the marginal. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[4) For k = 1,...,K: draw and concatenate: to create ]]> </content> </textbox> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 507"/> <image byte-size="10132" display-name="image-82.pdf" transformation="1 0 0 1 486 175" lock-aspect-ratio="true" image-data="image-82.pdf" natural-size="338 50"/> <image byte-size="8550" display-name="image-83.pdf" transformation="1 0 0 1 318 224" lock-aspect-ratio="true" image-data="image-83.pdf" natural-size="358 67"/> <image byte-size="10686" display-name="image-85.pdf" transformation="1 0 0 1 269 284" lock-aspect-ratio="true" image-data="image-85.pdf" natural-size="429 55"/> <g transformation="1 0 0 1 8 355"> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.2069 0 0 2.36842 8 355" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="306535" display-name="weightcontour2000_2.png" transformation="0.277393 0 0 0.277393 787 360" lock-aspect-ratio="true" image-data="weightcontour2000_2.png" natural-size="721 284"/> <image 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transformation="1.2069 0 0 2.36842 525 355" image-data="leftbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 745 376.5"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.2069 0 0 2.36842 980 355" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 484 375.5"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="6918" display-name="image-77.pdf" transformation="1 0 0 1 45 439" lock-aspect-ratio="true" image-data="image-77.pdf" natural-size="170 49"/> <image byte-size="7131" display-name="image-78.pdf" transformation="1 0 0 1 273 439" lock-aspect-ratio="true" image-data="image-78.pdf" natural-size="192 49"/> <image byte-size="7251" display-name="image-79.pdf" transformation="1 0 0 1 791 439" lock-aspect-ratio="true" image-data="image-79.pdf" natural-size="192 50"/> <image byte-size="7191" display-name="image-80.pdf" transformation="1 0 0 1 562 439" lock-aspect-ratio="true" image-data="image-80.pdf" natural-size="170 50"/> </g> <g transformation="1 0 0 1 -10 572"> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 618"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="301972" display-name="contourunweightedN.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="contourunweightedN.png" natural-size="721 284"/> <image byte-size="302847" display-name="contourunweighted2.png" transformation="0.416089 0 0 0.416089 332 583" lock-aspect-ratio="true" image-data="contourunweighted2.png" natural-size="721 284"/> <image byte-size="301825" display-name="contourunweighted1.png" transformation="0.416089 0 0 0.416089 20 583" lock-aspect-ratio="true" image-data="contourunweighted1.png" natural-size="721 284"/> <image byte-size="5683" display-name="image-86.pdf" transformation="1 0 0 1 123 705" lock-aspect-ratio="true" image-data="image-86.pdf" natural-size="93 55"/> <image byte-size="5802" display-name="image-87.pdf" transformation="1 0 0 1 435 705" lock-aspect-ratio="true" image-data="image-87.pdf" natural-size="93 55"/> <image byte-size="5864" display-name="image-88.pdf" transformation="1 0 0 1 783 705" lock-aspect-ratio="true" image-data="image-88.pdf" natural-size="93 55"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st5111.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (4)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[From each set, we draw one sample according to the weights and concatenate. The concatenation is a draw from the product of the marginal distributions. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[5) Weight each sample by to create ]]> </content> </textbox> <shape path="M 0 33.3 L 0 66.7 L 60 66.7 L 60 100 L 100 50 L 60 0 L 60 33.3 Z M 0 33.3" transformation="-1.44247e-08 0.329999 -0.739999 -3.23464e-08 549 532"/> <image byte-size="10132" display-name="image-82.pdf" transformation="1 0 0 1 486 175" lock-aspect-ratio="true" image-data="image-82.pdf" natural-size="338 50"/> <image byte-size="12296" display-name="image-90.pdf" transformation="1 0 0 1 152 226" lock-aspect-ratio="true" image-data="image-90.pdf" natural-size="700 55"/> <image byte-size="9649" display-name="image-92.pdf" transformation="1 0 0 1 247 278" lock-aspect-ratio="true" image-data="image-92.pdf" natural-size="481 55"/> <g transformation="1 0 0 1 -10 335"> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="301972" display-name="contourunweightedN.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="contourunweightedN.png" natural-size="721 284"/> <image byte-size="302847" display-name="contourunweighted2.png" transformation="0.416089 0 0 0.416089 332 346" lock-aspect-ratio="true" image-data="contourunweighted2.png" natural-size="721 284"/> <image byte-size="301825" display-name="contourunweighted1.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="contourunweighted1.png" natural-size="721 284"/> <image byte-size="5683" display-name="image-86.pdf" transformation="1 0 0 1 123 468" lock-aspect-ratio="true" image-data="image-86.pdf" natural-size="93 55"/> <image byte-size="5802" display-name="image-87.pdf" transformation="1 0 0 1 435 468" lock-aspect-ratio="true" image-data="image-87.pdf" natural-size="93 55"/> <image byte-size="5864" display-name="image-88.pdf" transformation="1 0 0 1 783 468" lock-aspect-ratio="true" image-data="image-88.pdf" natural-size="93 55"/> </g> <g transformation="1 0 0 1 -10 572"> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 618"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <image byte-size="303490" display-name="contourweighted2.png" transformation="0.416089 0 0 0.416089 332 583" lock-aspect-ratio="true" image-data="contourweighted2.png" natural-size="721 284"/> <image byte-size="302610" display-name="contourweighted1.png" transformation="0.416089 0 0 0.416089 20 583" lock-aspect-ratio="true" image-data="contourweighted1.png" natural-size="721 284"/> <image byte-size="302978" display-name="contourweightedN.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="contourweightedN.png" natural-size="721 284"/> <image byte-size="7263" display-name="image-93.pdf" transformation="1 0 0 1 69 705" lock-aspect-ratio="true" image-data="image-93.pdf" natural-size="201 55"/> <image byte-size="7381" display-name="image-94.pdf" transformation="1 0 0 1 381 705" lock-aspect-ratio="true" image-data="image-94.pdf" natural-size="201 55"/> <image byte-size="7449" display-name="image-95.pdf" transformation="1 0 0 1 737 705" lock-aspect-ratio="true" image-data="image-95.pdf" natural-size="212 55"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st521.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (5)</content> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande"> <![CDATA[We are actually interested in representing the joint distribution, not the product of the marginals. To do this, we reweight by the joint probability over the product of the marginal probabilities, which reduces to this form. ]]> </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="11988" display-name="image-68.pdf" transformation="1 0 0 1 321 466" lock-aspect-ratio="true" image-data="image-68.pdf" natural-size="411 55"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st53.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (2)</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium">We perform another particle filtering iteration to sample from</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="g1" paragraph-head-indent="7" paragraph-first-line-indent="7" font-ligatures="none" tab-stops="L 58" font-size="36" font-name="Futura-Medium"/> </bullet> </bullets> <notes tab-stops="L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" font-name="LucidaGrande">Sampling from the marginal is very similar to sampling from the joint. </notes> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="807 120" vertical-alignment="tracks-master"/> <textbox grow-horizontally="true" size="664 47" transformation="1 0 0 1 91 239"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">a) Given :</content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_unweighted10.png" natural-size="721 284"/> <image byte-size="303493" display-name="sample01818_unweighted2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_unweighted2.png" natural-size="721 284"/> <image byte-size="303628" display-name="sample01818_unweighted1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_unweighted1.png" natural-size="721 284"/> <image byte-size="7467" display-name="particlefiltering_sampleunweightedN.pdf" transformation="1 0 0 1 808 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweightedN.pdf" natural-size="70 52"/> <image byte-size="7384" display-name="particlefiltering_sampleunweighted2.pdf" transformation="1 0 0 1 446 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted2.pdf" natural-size="70 52"/> <image byte-size="7260" display-name="particlefiltering_sampleunweighted1.pdf" transformation="1 0 0 1 135 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted1.pdf" natural-size="70 52"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 381"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 335" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 335" image-data="rightbrace.pdf" natural-size="29 38"/> </g> <image byte-size="10521" display-name="image-15.pdf" transformation="1 0 0 1 250 235" lock-aspect-ratio="true" image-data="image-15.pdf" natural-size="486 55"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st541.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (2a)</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="812 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[b) From each sample generate to create . ]]> </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="303512" display-name="sample01818_unweighted10.png" transformation="0.416089 0 0 0.416089 20 346" lock-aspect-ratio="true" image-data="sample01818_unweighted10.png" natural-size="721 284"/> <image byte-size="303493" display-name="sample01818_unweighted2.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01818_unweighted2.png" natural-size="721 284"/> <image byte-size="303628" display-name="sample01818_unweighted1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01818_unweighted1.png" natural-size="721 284"/> <image byte-size="7467" display-name="particlefiltering_sampleunweightedN.pdf" transformation="1 0 0 1 808 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweightedN.pdf" natural-size="70 52"/> <image byte-size="7384" display-name="particlefiltering_sampleunweighted2.pdf" transformation="1 0 0 1 446 470" lock-aspect-ratio="true" image-data="particlefiltering_sampleunweighted2.pdf" natural-size="70 52"/> <image byte-size="7260" 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image-data="image-20.pdf" natural-size="448 55"/> <image byte-size="9617" display-name="image-28.pdf" transformation="1 0 0 1 255 226" lock-aspect-ratio="true" image-data="image-28.pdf" natural-size="363 55"/> <image byte-size="9819" display-name="image-29.pdf" transformation="1 0 0 1 255 273" lock-aspect-ratio="true" image-data="image-29.pdf" natural-size="364 50"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 619"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="2688" display-name="priorblobN.png" transformation="0.415512 0 0 0.415512 693 583" lock-aspect-ratio="true" image-data="priorblobN.png" natural-size="722 283"/> <image byte-size="2698" display-name="priorblob2.png" transformation="0.415512 0 0 0.415512 331 584" lock-aspect-ratio="true" image-data="priorblob2.png" natural-size="722 283"/> <image byte-size="2718" display-name="priorblob1.png" transformation="0.416089 0 0 0.416089 21 584" lock-aspect-ratio="true" image-data="priorblob1.png" natural-size="721 283"/> <image byte-size="5178" display-name="image-30.pdf" transformation="1 0 0 1 137 707" lock-aspect-ratio="true" image-data="image-30.pdf" natural-size="68 50"/> <image byte-size="5297" display-name="image-31.pdf" transformation="1 0 0 1 447 707" lock-aspect-ratio="true" image-data="image-31.pdf" natural-size="68 50"/> <image byte-size="5364" display-name="image-32.pdf" transformation="1 0 0 1 809 707" lock-aspect-ratio="true" image-data="image-32.pdf" natural-size="68 50"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7494" size="60 45" file="thumbs/st551.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (2b)</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="812 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[c) Weight each sample by ]]> <div paragraph-alignment="natural">to create . </div> </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 346" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" 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1 248 274" lock-aspect-ratio="true" image-data="image-35.pdf" natural-size="528 50"/> <image byte-size="8912" display-name="image-36.pdf" transformation="1 0 0 1 145 227" lock-aspect-ratio="true" image-data="image-36.pdf" natural-size="275 50"/> <g transformation="1 0 0 1 -10 572"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 619"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="8248" display-name="weightedblobN.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="weightedblobN.png" natural-size="721 284"/> <image byte-size="8031" display-name="weightedblob2.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="weightedblob2.png" natural-size="721 284"/> <image byte-size="8253" display-name="weightedblob1.png" transformation="0.416089 0 0 0.416089 21 584" lock-aspect-ratio="true" image-data="weightedblob1.png" natural-size="721 284"/> <image byte-size="7016" display-name="image-37.pdf" transformation="1 0 0 1 82 707" lock-aspect-ratio="true" image-data="image-37.pdf" natural-size="177 50"/> <image byte-size="7135" display-name="image-38.pdf" transformation="1 0 0 1 392 707" lock-aspect-ratio="true" image-data="image-38.pdf" natural-size="177 50"/> <image byte-size="7201" display-name="image-39.pdf" transformation="1 0 0 1 749 707" lock-aspect-ratio="true" image-data="image-39.pdf" natural-size="188 50"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="7524" size="60 45" file="thumbs/st561.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (2c)</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="812 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[d) Resample according to the weights to create]]> </content> </textbox> <g transformation="1 0 0 1 -10 335"> <image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 346" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 346" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 346" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 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<image byte-size="2822" display-name="sample01819_prior2.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="sample01819_prior2.png" natural-size="721 284"/> <image byte-size="2960" display-name="sample01819_prior10.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="sample01819_prior10.png" natural-size="721 284"/> <image byte-size="2782" display-name="sample01819_prior1.png" transformation="0.416089 0 0 0.416089 693 583" lock-aspect-ratio="true" image-data="sample01819_prior1.png" natural-size="721 284"/> <image byte-size="2759" display-name="leftbrace.pdf" transformation="1.72414 0 0 3.68421 -10 572" image-data="leftbrace.pdf" natural-size="29 38"/> <image byte-size="2764" display-name="rightbrace.pdf" transformation="1.72414 0 0 3.68421 983 572" image-data="rightbrace.pdf" natural-size="29 38"/> <textbox grow-horizontally="true" size="44 47" transformation="1 0 0 1 641 619"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium">...</content> </textbox> <image byte-size="7942" display-name="resampledblobN.png" transformation="0.416089 0 0 0.416089 693 584" lock-aspect-ratio="true" image-data="resampledblobN.png" natural-size="721 284"/> <image byte-size="7942" display-name="resampledblob2.png" transformation="0.416089 0 0 0.416089 331 583" lock-aspect-ratio="true" image-data="resampledblob2.png" natural-size="721 284"/> <image byte-size="7942" display-name="resampledblob1.png" transformation="0.416089 0 0 0.416089 21 583" lock-aspect-ratio="true" image-data="resampledblob1.png" natural-size="721 284"/> <image byte-size="6423" display-name="image-41.pdf" transformation="1 0 0 1 136 707" lock-aspect-ratio="true" image-data="image-41.pdf" natural-size="69 50"/> <image byte-size="6543" display-name="image-42.pdf" transformation="1 0 0 1 446 707" lock-aspect-ratio="true" image-data="image-42.pdf" natural-size="69 50"/> <image byte-size="6609" display-name="image-43.pdf" transformation="1 0 0 1 808 707" lock-aspect-ratio="true" image-data="image-43.pdf" natural-size="69 50"/> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st57.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (2d)</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="196 -16" size="812 120" vertical-alignment="tracks-master"/> <textbox size="847 141" transformation="1 0 0 1 88 183"> <content font-color="g1" paragraph-alignment="left" tab-stops="L 84" font-size="36" font-name="Futura-Medium"> <![CDATA[e) From each sample generate ]]> <div 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level="0" marker-type="inherited"> <content font-color="1 1 1" paragraph-alignment="left" font-ligatures="none" tab-stops="L 96" font-size="82" font-name="Futura-Medium">solution #2 step (2e)</content> </bullet> </bullets> </slide> </slide-list> <ui-state> <number key="BGShowUIStateRulersVisible">1</number> <number key="BGShowUIStateNotesVisible">0</number> <array key="BGShowUIStateSelectedSlides"> <reference id-ref="slide-1"/> </array> <number key="BGShowUIStateViewLayout">1</number> <array key="BGShowUIStateSelectedDrawables"/> <reference key="BGShowUIStateActiveSlide" id-ref="slide-1"/> <array key="BGShowUIStateSelectedBulletPoints"/> <string key="BGShowUIStateCanvasOrigin">{0, 0}</string> <string key="BGShowUIStateWindowSize">3 121 1271 711 0 0 1280 832 </string> <number key="BGShowUIStateMasterNavigatorHeight">0</number> <string key="BGShowUIStateCanvasZoom">0.750000</string> </ui-state> </presentation>