Unique Shape Reconstruction Using Interreflections

概要

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We discuss the uniqueness of 3-D shape reconstruction of a polyhedron from a single shading image. First, we analytically show that multiple convex (and concave) shape solutions usually exist for a simple polyhedron if interreflections are not considered. Then we propose a new approach to uniquely determine the concave shape solution using interreflections as a contraint. A example, in which two convex and two concave shapes were obtained from a single shaded image for a trihedral corner, has been given by Horn. However, how many solutions exist for a general polyhedron wasn't described. We analytically show that multiple convex (and concave) shape solutions usually exist for a pyramid using a reflectance map, if interreflection distribution is not considered. However, if interreflection distribution is used as a constraint that limits the shape solution for a concave polyhedron, the polyhedral shape can be uniquely determined. Interreflections, which were considered to be deleterious in conventional approaches, are used as a constraint to determine the shape solution in our approach.
社団法人電子情報通信学会の論文
1998-03-25