A New Formulation for Shape from Shading for Non-Lambertian Surfaces

Lamberts model for diffuse reflection is a main assumption in most of shape from shading (SFS) literature. Even with this simplified model, the SFS is still a difficult problem. Nevertheless, Lamberts model has been proven to be an inaccurate approximation of the diffuse component of the surface reflectance. In this paper, we propose a new solution of the SFS problem based on a more comprehensive diffuse reflectance model: the Oren and Nayar model. In this work, we slightly modify this more realistic model in order to take into account the attenuation of the illumination due to distance. Using the modified non-Lambertian reflectance, we design a new explicit Partial Differential Equation (PDE) and then solve it using Lax-Friedrichs Sweeping method. Our experiments on synthetic data show that the proposed modeling gives a unique solution without any information about the height at the singular points of the surface. Additional results for real data are presented to show the efficiency of the proposed method . To the best of our knowledge, this is the first non-Lambertian SFS formulation that eliminates the concave/convex ambiguity which is a well known problem in SFS.