The Bas-Relief Ambiguity

@inproceedings { 284,
title = {The Bas-Relief Ambiguity},
booktitle = {International Journal of Computer Vision (IJCV)},
volume = {35},
year = {1999},
pages = {33-44},
abstract = {When an unknown object with Lambertian reflectance is viewed orthographically, there is an implicit ambiguity in determining its 3-d structure: we show that the object{\textquoteright}s visible surface is indistinguishable from a {\textquotedblleft}generalized bas-relief{\textquotedblright} transformation of the object{\textquoteright}s geometry, and a corresponding transformation on the object{\textquoteright}s albedo. For each image of the object illuminated by an arbitrary number of distant light sources, there exists an identical image of the transformed object illuminated by similarly
transformed light sources. This result holds both for the illuminated regions of the object as well as those in cast and attached shadows. Furthermore, neither small motion of the object, nor of the viewer will resolve the ambiguity in determining the flattening (or scaling) of the object{\textquoteright}s surface. Implications of this ambiguity on structure recovery and shape representation are discussed.},
keywords = {Variable Illumination, Shadows, Shape Ambiguity, Object Representation, Object Recognition},
author = {Peter N. Belhumeur and David Kriegman and Alan Yuille}
}