A Novel Shape from Shading Algorithm for Non-Lambertian Surfaces

3D shape reconstruction is a classical problem in the field of computer vision. Shape from shading (SFS) is one approach to obtain the 3D shape from a single shading image. And Lambertian surfaces are an important assumption in traditional SFS methods. However, Lambertian reflectance model used to express the reflectance property of diffuse reflection is proved to be inaccurate. In this paper, we present a novel SFS algorithm for non-Lambertian diffuse surfaces. The Oren-Nayer reflectance model is used to approximate the reflectance property of the diffuse reflection. The image irradiance equation for diffuse surfaces is established with the assumptions that the camera performs an orthographic projection and its direction is as same as the point light source´s. Then, the equation is derived as an Eikonal partial differential equation (PDE) which consists of the shape of the surfaces. The viscosity solution of the resultant PDE is solved by using the high-order Godunov fast sweeping scheme. Experiments are conducted on both synthetic and real images and the results show the effectiveness of the presented algorithm.