Efficient Numerical Techniques for Perspective Shape from Shading

The shape-from-shading (SfS) problem is a classic problem in computer vision. The task in SfS is to compute on the basis of the shading variation in a given 2-D image the 3-D depth of the depicted scene. The corresponding mathematical model eventually leads to a boundary value problem for a Hamilton-Jacobi equation. In this paper we evaluate and compare suitable numerical methods. We begin with a brief discussion of four state-of-the-art-approaches in this field. Then we give an extensive numerical comparison, thus evaluating recent improvements in this area. In the course of doing this, we introduce efficient variations of existing schemes. By this systematic investigation, we complement and extend previous works on the numerical side. The paper is finished by a conclusion.