A viscosity solution method for Shape-From-Shading without image boundary data

Emmanuel Prados (1) , Fabio Camilli (2) , Olivier Faugeras (3)

1 MOVI - Modeling, localization, recognition and interpretation in computer vision
2 DISIM - Department of Information Engineering, Computer Science and Mathematics = Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila]
3 ODYSSEE - Computer and biological vision

In this paper we propose a solution of the Lambertian Shape-From-Shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. 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. Moreover, it allows to characterize the viscosity solutions by their minimums"; 2) it unifies the works of Rouy and Tourin, Falcone et al., Prados and Faugeras, based on the notion of viscosity solutions and the work of Dupuis and Oliensis dealing with classical solutions.

Mots clés: Shape-from-shading; Mathematical model; Numerical analysis; Computer vision; Weak solution; Viscosity solution

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

Emmanuel Prados, Fabio Camilli, Olivier Faugeras. A viscosity solution method for Shape-From-Shading without image boundary data. ESAIM: Mathematical Modelling and Numerical Analysis, 2006, 40 (2), pp.393--412. ⟨inria-00377394⟩