Abstract: The reverse of 3D figures based on 2D gray image of the surface (shape from shading) has become the focus topic in industry and academia. Firstly the mathematical physics model that describes the question is presented and is converted into minimization of functional with variational principle, and with finite difference and nonlinear least square method,the uestion of minimization is come down to solving system of linear equations. Finally, using the iterative formula that the algorithm produces, a synthetic image is calculated. And the surface is reconstructed in the software CAXA. The result shows the reconstructing method is efficiency and feasible.

Key words: Reverse Engineering Shape from shading, Surface 3D Reconstruction