UNIQUE SHAPE RECONSTRUCTION USING INTERREFLECTIONS

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 polyh edron if interreflections are not considered. Then we propose a new ap proach to uniquely determine the concave shape solution using interref lections as a constraint. A example, in which two convex and two conca ve shapes were obtained from a single shaded image for a trihedral cor ner, has been given by Horn. However, how many solutions exist for a g eneral polyhedron wasn't described. We analytically show that multiple convex (and concave) shape solutions usually exist for a pyramid usin g a reflectance map, if interreflection distribution is not considered . However, if interreflection distribution is used as a constraint tha t limits the shape solution for a concave polyhedron, the polyhedral s hape can be uniquely determined. Interreflections, which were consider ed to be deleterious in conventional approaches, are used as a constra int to determine the shape solution in our approach.