A mathematical and algorithmic study of the Lambertian SFS problem for orthographic and pinhole cameras
Emmanuel Prados, Olivier D. Faugeras · 2003
This report proposes a mathematical and algorithmic study of the Lambertian SFS problem for orthographic and pinhole cameras. Our approach is based upon the notion of viscosity solutions of Hamilton-Jacobi equations. This approach provides a mathematical framework in whichwe can prove the well-posedness of the problem (proof of the existence of a solution and characterization of all solutions). This mathematical approach allows also to prove the correctness of our methods. In particular, we describe a simple monotonous stability condition for the studied decentered schemes and we prove the convergence of their solutions toward the viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Also, we show that this theory naturally applies to the SFS problems.