A robust shape-from-shading using multiple surface normal approximations

We present a robust shape reconstruction method from a single shading image, which is able to give good estimate especially for the light direction having a relatively large slant angle. We derive four iterative shape-estimating relations by using the Jacobi iterative method and the four approximations of the surface normal, and combine them with weights to get a single relation. We show that it is stable enough to attain convergence. We also optimize the light direction through an eigenvalue analysis for the matrix of the combined iterative relation, to improve the shape by avoiding the small eigenvalues that cause serious distortions. Numerical examples using both synthetic and real images show the usefulness of the new method.