Fast shape from shading

Extracting surface orientation and surface depth from a shaded image is one of the classic problems in computer vision. Many previous algorithms either violate integrability, i.e., the surface normals do not correspond to a feasible surface, or use regularization, which biases the solution away from the true answer. A recent iterative algorithm proposed by Horn overcomes both of these limitations but converges slowly. This paper uses a new algorithm, hierarchical basis conjugate gradient descent, to provide a faster solution to the same problem. This approach is similar to the multigrid techniques which have previously been used to speed the convergence, but it does not require heuristic approximations to the true irradiance equation. The paper compares the accuracy and the convergence rates of the new techniques to previous algorithms.