Existence and uniqueness in shape from shading

A generically valid proof of uniqueness for the surface solution to shape from shading is presented. Local surface solutions around a singular point have at most a fourfold ambiguity. These results apply to a reflectance function corresponding to illumination symmetric around the viewer direction of a uniform-albedo Lambertian object. Generic surfaces are studied, and their properties are established. It is noted that the proof may lead to new, faster algorithms for shape recovery. Questions of existence are also discussed. It is argued that most images are impossible in the sense that they cannot be a depiction of any physical object. The proof is based on ideas of dynamical systems theory, and global analysis