Shape from Shading Under Various Imaging Conditions

Most of the shape from shading (SFS) algorithms have been developed under the simplifying assumptions of a Lambertian surface, an orthographic projection, and a distant light source. Due to the difficulty of the SFS problem, only a small number of algorithms have been proposed for surfaces with non-Lambertian reflectance, and among those, only very few algorithms are applicable for surfaces with specular and diffuse reflectance. In this paper we propose a unified framework that is capable of solving the SFS problem under various settings of imaging conditions i.e., Lambertian or non-Lambertian, orthographic or perspective projection, and distant or nearby light source. The proposed algorithm represents the image irradiance equation of each setting as an explicit Partial Differential Equation (PDF). In our implementation we use the Lax-Friedrichs sweeping method to solve this PDF. To demonstrate the efficiency of the proposed algorithm, several comparisons with the state of the art of the SFS literature are given.