WAVELET-BASED SHAPE FROM SHADING

This paper proposes a wavelet-based approach for 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. To derive the algorithm, the formulation of Horn and Brooks ((Eds.) Shape from Shading, MIT Press, Cambridge, MA, 1989), which combines several constraints into an objective function, is adopted. 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. Instead of solving the problem directly by using Euler equation or numerical techniques, the objective function is first converted into the 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 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 is a great improvement in the accuracy as well as the convergence speed of the SFS problem. Experimental results, using both synthetic and real images, prove that the proposed method is indeed better than traditional methods. (C) 1995 Academic Press, Inc.