Photometric Stereo from Maximum Feasible Lambertian Reflections

We present a Lambertian photometric stereo algorithm robust to specularities and shadows and it is based on a maximum feasible subsystem (Max FS) framework. A Big-M method is developed to obtain the maximum subset of images that satisfy the Lambertian constraint among the whole set of captured photometric stereo images which include non-Lambertian reflections such as specularities and shadows. Our algorithm employs purely algebraic pixel-wise optimization without relying on probabilistic/physical reasoning or initialization, and it guarantees the global optimality. It can be applied to the image sets with the number of images ranging from four to hundreds, and we show that the computation time is reasonably short for a medium number of images (10~100). Experiments are carried out with various objects to demonstrate the effectiveness of the algorithm.