A unifying and rigorous Shape From Shading method adapted to realistic data and applications

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
2 DISIM - Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila]
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 : 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 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 and value functions. Also, it allows to generalize their results to the "perspective SFS" problem.
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Emmanuel Prados, Fabio Camilli, Olivier Faugeras. A unifying and rigorous Shape From Shading method adapted to realistic data and applications. Journal of Mathematical Imaging and Vision, Springer Verlag, 2006, 25 (3), pp.307--328. ⟨10.1007/s10851-006-6899-x⟩. ⟨inria-00377391⟩

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