Use of four surface normal approximations and optimization of light direction for robust shape reconstruction from single images

We present a robust shape-from-shading method, by which we are able to estimate accurate shapes from single shading images whose slant angles are relatively large. First, we derive four iterative relations for shape estimation by applying the Jacobi¿s iterative method and by using four approximations of the surface normal, and combine them with weights to get a single relation. This enables us to achieve stable shape estimation with a fair degree of accuracy. Second, we optimize the light direction in slant angle through the eigenvalue analysis for the matrix of the combined iterative relation, to reduce the remaining distortions. Numerical examples using both synthetic and real images show the usefulness of the method.