Physics-like invariants for vision

Unlike geometric invariants, the invariants described here concern the physical processes that form images, involving shading, IR, radar, sonar, etc. The image formed by such a process depends on many variables in addition to the geometry, such as the characteristics of the lighting or other incident radiation, the imaging system, etc. Most of these variables are not known in advance, so the recovery of shape is difficult. The problem could be greatly simplified if we could find invariants of the situation, namely quantities that stay unchanged 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. As an example we use the shape from shading problem, but the methods have a much wider applicability