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Any Pair Of 2d Curves Is Consistent With A 3d Symmetric Interpretation., Tadamasa Sawada, Yunfeng Li, Zygmunt Pizlo

Department of Psychological Sciences Faculty Publications

Symmetry has been shown to be a very effective a priori constraint in solving a 3D shape recovery problem. Symmetry is useful in 3D recovery because it is a form of redundancy. There are, however, some fundamental limits to the effectiveness of symmetry. Specifically, given two arbitrary curves in a single 2D image, one can always find a 3D mirror-symmetric interpretation of these curves under quite general assumptions. The symmetric interpretation is unique under a perspective projection and there is a one parameter family of symmetric interpretations under an orthographic projection. We formally state and prove this observation for the …