Fast viscosity solutions for shape from shading under a more realistic imaging model

Shape from shading SFS has been a classical and impor- tant problem in the domain of computer vision. The goal of SFS is to reconstruct the 3-D shape of an object from its 2-D intensity image. To this end, an image irradiance equation describing the relation between the shape of a surface and its corresponding brightness variations is used. Then it is derived as an explicit partial differential equation PDE. Using the nonlinear programming principle, we propose a detailed solu- tion to Prados and Faugeras's implicit scheme for approximating the viscosity solution of the resulting PDE. Furthermore, by combining im- plicit and semi-implicit schemes, a new approximation scheme is pre- sented. In order to accelerate the convergence speed, we adopt the Gauss-Seidel idea and alternating sweeping strategy to the approxima- tion schemes. Experimental results on both synthetic and real images are performed to demonstrate that the proposed methods are fast and accurate. © 2009 Society of Photo-Optical Instrumentation Engineers.