Maximum Likelihood Estimation of Depth Maps Using Photometric Stereo

Photometric stereo and depth-map estimation provide a way to construct a depth map from images of an object under one viewpoint but with varying illumination directions. While estimating surface normals using the Lambertian model of reflectance is well established, depth-map estimation is an ongoing field of research and dealing with image noise is an active topic. Using the zero-mean Gaussian model of image noise, this paper introduces a method for maximum likelihood depth-map estimation that accounts for the propagation of noise through all steps of the estimation process. Solving for maximum likelihood depth-map estimates involves an independent sequence of nonlinear regression estimates, one for each pixel, followed by a single large and sparse linear regression estimate. The linear system employs anisotropic weights, which arise naturally and differ in value to related work. The new depth-map estimation method remains efficient and fast, making it practical for realistic image sizes. Experiments using synthetic images demonstrate the method´s ability to robustly estimate depth maps under the noise model. Practical benefits of the method on challenging imaging scenarios are illustrated by experiments using the Extended Yale Face Database B and an extensive data set of 500 reflected light microscopy image sequences.