A Unifying and Rigorous Shape from Shading Method Adapted to Realistic Data and Applications

We propose a new method for the Lambertian Shape From Shading (SFS) problem based on the notion of Crandall-Lions viscosity solution. This method has the advantage of requiring the knowledge of the solution (the surface to be reconstructed) only on some part of the boundary and/or of the singular set (the set of the points at maximal intensity). Moreover it unifies in an unique mathematical formulation the works of Rouy et al. [50, 34], Falcone et al. [21], Prados et al. [49, 46, 48], based on the notion of viscosity solutions and the work of Dupuis and Oliensis [17] dealing with classical solutions and value functions. Also, it allows to generalize their results to the "perspective SFS" problem recently simultaneously introduced in [46, 55, 13]. While the theoretical part has been developed in [44], in this paper we give some stability results and we describe numerical schemes for the SFS based on this method. We construct provably convergent and robust algorithms. Finally, ...

• Type: Journal
• Year: 2006
• Where: JMIV
• Authors: Emmanuel Prados, Fabio Camilli, Olivier D. Faugeras
• Keywords: Crandall-Lions Viscosity Solution, Et Al, JMIV 2006, Viscosity Solutions