A Microfacet-Based Reflectance Model for Photometric Stereo with Highly Specular Surfaces

A precise, stable and invertible model for surface reflectance is the key to the success of photometric stereo with real world materials. Recent developments in the field have enabled shape recovery techniques for surfaces of various types, but an effective solution to directly estimating the surface normal in the presence of highly specular reflectance remains elusive. In this paper, we derive an analytical isotropic microfacet-based reflectance model, based on which a physically interpretable approximate is tailored for highly specular surfaces. With this approximate, we identify the equivalence between the surface recovery problem and the ellipsoid of revolution fitting problem, where the latter can be described as a system of polynomials. Additionally, we devise a fast, non-iterative and globally optimal solver for this problem. Experimental results on both synthetic and real images validate our model and demonstrate that our solution can stably deliver superior performance in its targeted application domain.