Kriegman Research Group

Several methods have been proposed to estimate the structure and motion of polyhedral objects or 3D curved objects with surface markings. The key observation here is that one can track viewpoint independent features over a sequence of images and thereby extract structure and motion information out of it. These methods will not work when dealing with curved objects that are devoid of surface markings or texture. There also exist other methods that determine the structure of textureless 3D curved objects given the camera motion.

We have attempted to use a viewpoint-invariant representation of curved objects using viewpoint dependent features like bitangents, inflection points and parallel tangent points. A brief description of the proposed algorithm follows. For more information, please check [6].

Let us imagine a situation where a 3D object (curved) remains stationary and a camera moves around it taking snap shots. The camera projection model can be either orthographic or scaled orthographic. We extract invariants from each of the snap shots and as explained previously, build an invariant curve representation . From intersection points of the invariant curves, we can determine 2 distinct viewpoints that have mutually visible feature points. We'll call these points stereo frontier points. Stereo frontier points determine the angular velocity of the moving camera frame. Once the camera angular velocity is determined, the epipolar plane and subsequently the infinitesimal frontier points are determined. Infinitesimal points are simply points on the occluding contour that are visible in consecutive images. Finally, the epipolar constraints and the motion of frontier points together are used to determine translation of the camera frame origin and the 3D structure of the object.

At this point in time, we have implemented the stucture and motion algorithm on a synthetic object and its image sequence. The scene in question is a non-symmetric combination of 4 spheres shown at the top of this page. The structure and motion that were extracted are shown in 2 views below. We are presently, trying the algorithm out on real images.

xy-view of estimated structure and motion (click on picture for better resolution)

xz-view of estimated structure and motion (click on picture for better resolution)

• [6] B. Vijayakumar, D. Kriegman and J. Ponce. "Structure and Motion of Curved 3D Objects from Monocular Silhouettes.". In Proceedings of the Conference on Computer Vision and Pattern Recognition. June 1996.