Wavelet-based shape from shading

This paper proposes a wavelet-based approach to solving the shape from shading (SFS) problem. The proposed method takes advantage of the nature of wavelet theory, which can be applied to efficiently and accurately represent "things", to develop a faster algorithm for reconstructing better surfaces. In order to improve the robustness of the algorithm, two new constraints are introduced into the objective function to strengthen the relation between an estimated surface and its counterpart in the original image. Thus, solving the SFS problem becomes a constrained optimization process. In the first stage of the process, the set of function variables to be solved is represented by a wavelet format. Due to this format, the set of differential operators of different orders which is involved in the whole process can be approximated with the connection coefficients of Daubechies bases. In each iteration of the optimization process an appropriate step size which will result in maximum decrease of the objective function is determined. After finding correct iterative schemes, the solution of the SFS problem will finally be decided. Compared with conventional algorithms, the proposed scheme makes great improvements on the accuracy as well as the convergence speed of the SFS problem.