Resolving the Generalized Bas-Relief Ambiguity by Entropy Minimization

It is well known in the photometric stereo literature that uncalibrated photometric stereo, where light source strength and direction are unknown, can recover the surface geometry of a Lambertian object up to a 3-parameter linear transform known as the generalized bas relief (GBR) ambiguity. Many techniques have been proposed for resolving the GBR ambiguity, typically by exploiting prior knowledge of the light sources, the object geometry, or non-Lambertian effects such as specularities. A less celebrated consequence of the GBR transformation is that the albedo at each surface point is transformed along with the geometry. Thus, it should be possible to resolve the GBR ambiguity by exploiting priors on the albedo distribution. To the best of our knowledge, the only time the albedo distribution has been used to resolve the GBR is in the case of uniform albedo. We propose a new prior on the albedo distribution : that the entropy of the distribution should be low. This prior is justified by the fact that many objects in the real-world are composed of a small finite set of albedo values.