The continuous Lambertian shape from shading is studied using a PDE approach
in terms of Hamilton–Jacobi equations. The latter will then be characterized by a maximization
problem. In this paper we show the convergence of discretization and propose to use the wellknown
Chambolle–Pock primal-dual algorithm to solve numerically the shape from shading
problem. The saddle-point structure of the problem makes the Chambolle–Pock algorithm
suitable to approximate solutions of the discretized problems.