A mathematical framework unifying various Shape from Shading approaches
Résumé
By slightly modifying the notion of singular viscosity solutions [Ishii-Ramaswamy:95,Camilli-Siconolfi:99,Camilli:01,Camilli-Siconolfi:02] we define a new mathematical framework allowing to unify the various theoretical results proposed in the Shape from shading literature. We demonstrate the existence and the uniqueness of the new solution for a class of Hamilton-Jacobi equations including the classical Shape-From-Shading equations [Prados-Faugeras:03], in a bounded locally Lipschitz domain. Some stability results are proved. Finally, we propose a provably convergent numerical method for approximating the solution and we demonstrate its relevance and its efficiency by numerical experiments on real images.