Dense photometric stereo using tensorial belief propagation

We address the normal reconstruction problem by photometric stereo using a uniform and dense set of photometric images captured at fixed viewpoint. Our method is robust to spurious noises caused by highlight and shadows and non-Lambertian reflections. To simultaneously recover normal orientations and preserve discontinuities, we model the dense photometric stereo problem into two coupled Markov random fields (MRFs): a smooth field for normal orientations, and a spatial line process for normal orientation discontinuities. We propose a very fast tensorial belief propagation method to approximate the maximum a posteriori (MAP) solution of the Markov network. Our tensor-based message passing scheme not only improves the normal orientation estimation from one of discrete to continuous, but also reduces storage and running time drastically. A convenient handheld device was built to collect a scattered set of photometric samples, from which a dense and uniform set on the lighting direction sphere is obtained. We present very encouraging results on a wide range of difficult objects to show the efficacy of our approach.