Abstract
We discuss the uniqueness of 3-D shape recovery of a polyhedron from a single shaded image. We show that multiple convex (and/or concave) shape solutions usually exist for a polyhedron of which three or more facets meet at an apex (like a pyramid). It has discussed how to check and avoid the superstrictness for a complex polyhedron. However, there is different problem for a simple polyhedron without superstrictness. Horn has shown a numerical example in which two convex and two concave shape solutions exist for a trihedral corner. We describe that multiple shape solutions exist for a pyramid analytically. We also show the shape can be uniquely determined by using interreflections as a constraint to limit the shape solution for a concave polyhedron.
