A Non-local Approach to Shape from Ambient Shading

We study the mathematical and numerical aspects of the estimation of the 3-D shape of a Lambertian scene seen under diffuse illumination. This problem is known as "shape from ambient shading" (SFAS), and its solution consists of integrating a strongly non-local and non-linear Integro-Partial Differential Equation (I-PDE). We provide a first analysis of this global I-PDE, whereas previous work had focused on a local version that ignored effects such as occlusion of the light field. We also design an original approximation scheme which, following Barles and Souganidis' theory, ensures the correctness of the numerical approximations, and discuss about some numerical issues.