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). The performance of OMP is evaluated on synthesized and real-world datasets: we found that the greedy algorithm is overall more robust to non-Lambertian errors than other state-of-the-art sparse approaches with little loss of efficiency. Along with providing an overview of current methods, novel contributions in this paper are as follows: we propose an alternative sparse formulation for PST; in previous PST studies (Wu et al., Robust photometric stereo via low-rank matrix completion and recovery, 2010), (S. Ikehata et al., Robust photometric stereo using sparse regression, 2012), the surface normal vector and the error vector are treated as two entities and are solved independently. In this study, we convert their formulation into a new canonical form of the sparse recovery problem by combining the two vectors into one large vector in a new “stacked” formulation in this domain. This allows for a large repertoire of existing sparse recovery algorithms to be more straightforwardly applied to the PST problem. In our application of the OMP greedy algorithm, we show that greedy solvers can indeed be applied, with this study supplying the first of such attempt at employing greedy approaches to estimate surface normals within the framework of PST. We numerically compare the performance of several normal vector recovery methods. Most notably, this is the first detailed test on complex images of the normal estimation accuracy of our previously proposed method, least median of squares (LMS).