Robust surface normal estimation via greedy sparse regression

Photometric Stereo (PST) is a widely used technique of estimating surface normals from an image set. However, it often produces inaccurate results for non-Lambertian surface reflectance. In this study, PST is reformulated as a sparse recovery problem where non-Lambertian errors are explicitly identified and corrected. We show that such a problem can be accurately solved via a greedy algorithm called Orthogonal Matching Pursuit (OMP). Furthermore, we introduce a smoothness constraint by expanding the pixel-wise sparse PST into a joint sparse recovery problem where several adjacent pixels are processed simultaneously, and employ a Sequential Compressive - Multiple Signal Classification (SeqCS-MUSIC) algorithm based on Simultaneous Orthogonal Matching Pursuit (S-OMP) to reach a robust solution. The performance of OMP and SeqCS-MUSIC is evaluated on synthesized and real-world datasets, and we found that these greedy algorithms are overall more robust to non-Lambertian errors than other state-of-the-art sparse approaches with little loss of efficiency.