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A non-local approach to shape from ambient shading

Emmanuel Prados 1 Nitin Jindal 2 Stefano Soatto 3
1 STEEP - Sustainability transition, environment, economy and local policy
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann
2 PERCEPTION - Interpretation and Modelling of Images and Videos
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : We describe a mathematical and algorithmic study of Shape From Shading problem for scenes illuminated by ambient lighting. The ambient lighting is here modelled by a (whole) spherical light source of infinite radius centered on the object of interest. The mathematical formulation of this problem results in resolving a strongly non-local and non-linear Integro-Partial Differential Equation (I-PDE). The first contribution of this report is to provide a first theoretical study of this global I-PDE, when previous theoretical works only deal with a local version obtained by ignoring the shadow, i.e. the occlusion of the light field by the surface itself. We give a comparison result in the C^1 space which allows to characterize the set of the solutions. The second contribution consists in providing a monotonic, consistent and stable approximation scheme for the I-PDE which, according to Barles and Souganidis' theory, classically ensures the correctness of the numerical approximations. We then explain how to implement the associated numerical algorithm and show and discuss about some numerical results. Contrary to our previous conference paper, this technical report contains the detailed proofs of all stated theorems.
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Submitted on : Wednesday, November 2, 2011 - 11:46:53 AM
Last modification on : Tuesday, October 19, 2021 - 11:13:10 PM
Long-term archiving on: : Thursday, March 30, 2017 - 6:19:02 PM


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  • HAL Id : inria-00637531, version 1


Emmanuel Prados, Nitin Jindal, Stefano Soatto. A non-local approach to shape from ambient shading. [Research Report] RR-7783, INRIA. 2011, pp.24. ⟨inria-00637531⟩



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