Shape from Intensity Gradient - Systems, Man and Cybernetics, Part A, IEEE Transactions on

Unlike existing global shape-from-shading (SFS) algorithms which involve the brightness constraint in their formulation, we propose a new SFS algorithm which replaces the brightness constraint with an intensity gradient constraint. This is a global approach which obtains the solution by the minimization of an error function over the entire image. Through the linearization of the gradient of the reflectance map and the discretization of the surface gradient, the intensity gradient can be expressed as a linear function of the surface height. A quadratic error function, which involves the intensity gradient constraint and the traditional smoothness constraint, is minimized efficiently by solving a sparse linear system using the multigrid technique. Neither the information at singular points nor the information at occluding boundaries is needed for the initialization of the height. Results for real images are presented to show the robustness of the algorithm, and the execution time is demonstrated to prove its efficiency.