Provably Convergent Methods for the Linear and Nonlinear Shape from Shading Problem

In this paper we present provably convergent algorithms for the linear and nonlinear Shape from Shading problem in the case of a Lambertian reflectance map. For the linear problem we discuss two explicit methods and one implicit method, for which we prove convergence for certain light directions. The method for the nonlinear Shape from Shading problem is based on a linear approximation of the image irradiance equation. For the resulting linear PDE the implicit method for the linear problem can be applied. We prove convergence of this method for all light directions.