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
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
3 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : 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.
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Emmanuel Prados, Fabio Camilli, Olivier Faugeras. A viscosity solution method for Shape-From-Shading without image boundary data. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2006, 40 (2), pp.393--412. ⟨inria-00377394⟩

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