SPARSE BAYESIAN REGRESSION BASED PHOTOMETRIC STEREO FOR GENERAL DIFFUSE SURFACES

            Photometric stereo involves estimating the surface normals of an object given appearance variations in multiple images taken under different lighting conditions. Most conventional algorithms for non-Lambertian photometric stereo can be partitioned into two categories. The first category is built upon stable outlier rejection techniques while assuming a dense Lambertian structure for the inliers, and thus performance degrades when general diffuse regions are present. The second utilizes complex reflectance representations and non-linear optimization over pixels to handle non-Lambertian surfaces, but does not explicitly account for shadows or other forms of corrupting outliers. In this paper, we present a purely pixel-wise photometric stereo method that stably and efficiently handles various non-Lambertian effects by assuming that appearances can be decomposed into a sparse, non-diffuse component (e.g., shadows, specularities, etc.) and a diffuse component represented by a monotonic function of the surface normal and lighting dot-product. This function is constructed using a piecewise linear approximation to the inverse diffuse model, leading to closed-form estimates of the surface normals and model parameters in the absence of non-diffuse corruptions. The latter are modeled as latent variables embedded within a hierarchical Bayesian model such that we may accurately compute the unknown surface normals while simultaneously separating diffuse from non-diffuse components. Extensive evaluations are performed that show state-of-the-art performance using both synthetic and real-world images.