Three-dimensional reconstruction of hybrid surfaces using perspective shape from shading

Shape from shading (SFS) is a way to reconstruct the three-dimensional shape of an object from a single intensity image. In this paper, we propose a new perspective SFS approach for reconstructing the three-dimensional shape of hybrid surfaces which have both diffuse reflection and specular reflection. For this purpose, a hybrid reflectance model composed of a linear combination of Oren-Nayar model and Ward model is used to express the hybrid surfaces. A new imaging model incorporating a perspective camera projection, a near point light source located at the optical center of the camera and the hybrid reflectance model is established. Based on the new model, the image irradiance equation is formulated as a non-linear partial differential equation (PDE), which is related to a static Hamilton-Jacobi equation considering the boundary conditions. The viscosity solution of the resultant Hamilton-Jacobi equation is approximated by using numerical Hamiltonian and first-order and high-order fixed-point iterative sweeping method. Experiments are performed on both synthetic and real images and the results demonstrate the effectiveness of the proposed approach.