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A mathematical framework unifying various Shape from Shading approaches

Emmanuel Prados 1 Olivier Faugeras 1 Fabio Camilli 2
1 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 : By slightly modifying the notion of singular viscosity solutions [Ishii-Ramaswamy:95,Camilli-Siconolfi:99,Camilli:01,Camilli-Siconolfi:02] we define a new mathematical framework allowing to unify the various theoretical results proposed in the Shape from shading literature. We demonstrate the existence and the uniqueness of the new solution for a class of Hamilton-Jacobi equations including the classical Shape-From-Shading equations [Prados-Faugeras:03], in a bounded locally Lipschitz domain. Some stability results are proved. Finally, we propose a provably convergent numerical method for approximating the solution and we demonstrate its relevance and its efficiency by numerical experiments on real images.
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Conference papers
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https://hal.inria.fr/inria-00590178
Contributor : Team Perception <>
Submitted on : Tuesday, May 3, 2011 - 9:29:48 AM
Last modification on : Tuesday, July 30, 2019 - 10:58:03 AM

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  • HAL Id : inria-00590178, version 1

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Emmanuel Prados, Olivier Faugeras, Fabio Camilli. A mathematical framework unifying various Shape from Shading approaches. Mathematics and Image Analysis (MIA '04), Sep 2004, Paris, France. ⟨inria-00590178⟩

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