The conceptual component of this work is about "reference surfaces(Formula Presented) which are the analogous to reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.
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We are grateful for the comments of the anonymous reviewers and the comments of Azriel Rosenfeld and Tomaso Poggio on previous drafts of this paper. Also thanks to David Beymer for providing some of the images used for our experiments, and to Long Quan for providing the code we used for recovering epipoles. This work was done at the Center of Biological and Computational Learning at M.I.T. A. Shashua was supported by a McDonnell-Pew postdoctoral fellowship from the Department of Brain and Cognitive Sciences. S. Toelg was supported by a postdoctoral fellowship from the Deutsche Forschungsgemeinschaft.