Unifying Approaches and Removing Unrealistic Assumptions in Shape from Shading: Mathematics Can Help

This article proposes a solution of the Lambertian Shape From Shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solutions. The power of our approach is twofolds: 1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Note that, in the previous SFS work of Rouy et al. [23,15], Falcone et al. [8], Prados et al. [22,20], the characterization of a viscosity solution and its computation require the knowledge of its values on the boundary of the image. This was quite unrealistic because in practice such values are not known. 2) it unifies the work of Rouy et al. [23,15], Falcone et al. [8], Prados et al. [22,20], based on the notion of viscosity solutions and the work of Dupuis and Oliensis [6] dealing with classical (C 1) solutions. Also, we generalize their work to the “perspective SFS” problem recently introduced by Prados and Faugeras 20.