Unique Shape Recovery of a Polyhedron Based on Interreflections

Abstract

We discuss the uniqueness of 3-D shape recovery of a polyhedron from a single shading image, and propose an approach to uniquely determine the concave shape solution by using interreflections as a constraint. In this paper, we show that if interreflection distribution is not considered, multiple convex (or concave) shape solutions usually exist for a pyramid with three or more visible facets. However, if interreflection distribution is used as a constraint to limit the number of shape solutions (for a concave polyhedron), polyhedral shape can be uniquely determined. Interreflections, which considered to be deleterious in conventional approaches, are an important constraint for shape-from-shading.