Uncalibrated photometric stereo based on elevation angle recovery from BRDF symmetry of isotropic materials

This paper addresses the problem of uncalibrated photometric stereo with isotropic reflectances. Existing methods face difficulty in solving for the elevation angles of surface normals when the light sources only cover the visible hemisphere. Here, we introduce the notion of 'constrained half-vector symmetry' for general isotropic BRDFs and show its capability of elevation angle recovery. This sort of symmetry can be observed in a 1D BRDF slice from a subset of surface normals with the same azimuth angle, and we use it to devise an efficient modeling and solution method to constrain and recover the elevation angles of surface normals accurately. To enable our method to work in an uncalibrated manner, we further solve for light sources in the case of general isotropic BRDFs. By combining this method with the existing ones for azimuth angle estimation, we can get state-of-the-art results for uncalibrated photometric stereo with general isotropic reflectances.