Shape from shading using Ritz method with tent basis

A robust approach to recover the shape of an object from shading information is presented. The scheme is derived based on the perturbation method that minimizes a cost function for computing a surface height from a single image given the imaging model and light direction. To describe the desired solution variables as a linear combination of a set of basis functions, the Ritz method is applied in our approach to discretize the cost function associated with the regularized shape from shading problem. This kind of discretization is simple and the concept of signal representation by a set of weighted basis functions can be clearly stated. To enhance the robustness of alternative scheme, two new constraints are added into the cost function. They constrain the behavior of high-order change rate between the variables, and bound the variables more tightly. Thus, the changes of variables will be more regular. Hence, new constraints strengthen the relations between the input image and the reconstructed surface height. After finding the weighting coefficients using a perturbation method, the solution of the SFS problem will finally be decided