Photometric Stereo via Expectation Maximization

This paper presents a robust and automatic approach to photometric stereo, where the two main components, namely surface normals and visible surfaces, are respectively optimized by expectation maximization (EM). A dense set of input images is conveniently captured using a digital video camera while a handheld spotlight is being moved around the target object and a small mirror sphere. In our approach, the inherently complex optimization problem is simplified into a two-step optimization, where EM is employed in each step: 1) Using the dense input, the weight or importance of each observation is alternately optimized with the normal and albedo at each pixel and 2) using the optimized normals and employing the Markov random fields (MRFs), surface integrabilities and discontinuities are alternately optimized in visible surface reconstruction. Our mathematical derivation gives simple updating rules for the EM algorithms, leading to a stable, practical, and parameter-free implementation that is very robust even in the presence of complex geometry, shadows, highlight, and transparency. We present high-quality results on normal and visible surface reconstruction, where fine geometric details are automatically recovered by our method.