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Conference Papers Year : 2004

A mathematical framework unifying various Shape from Shading approaches

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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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Dates and versions

inria-00590178 , version 1 (03-05-2011)

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  • HAL Id : inria-00590178 , version 1

Cite

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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