Invariants for recovering shape from shading

Abstract

The image formed by shading depends on many variables, including the shape of the object, the lighting characteristics, the imaging system, etc. Most of these variables are not known in advance, so the calculation of shape from shading is difficult. The problem could be greatly simplified if we could find invariants of the situation, namely quantities that stay constant as some of the unknown variables change. In this paper we apply known methods of mathematical physics to finding invariants of physical imaging processes. These methods take advantage of various symmetries, which can be part of a model-based approach to recognition. We concentrate on the shape from shading problem, but the methods have a much wider applicability.