Numerical solution of the Perspective Shape- from-Shading problem

We study the Perspective Shape from Shading problem from the numerical point of view pre- senting a simple algorithm to compute its solution. The scheme is based on a semi-Lagrangian approximation of the first order Hamilton-Jacobi equation related to the problem. The scheme is converging to the weak solution (in the viscosity sense) of the equation and allows to compute accurately regular as well as non regular solutions. Since the partial differential equation must be complemented with boundary conditions on the silhouette, we analyse the effect of various types of boundary conditions on the numerical solution. Some tests on synthetic and real images are presented.