Viscosity Solution

Abstract : Viscosity solution is a notion of weak solution for a class of partial differential equations of Hamilton-Jacobi type. The range of applications of the notions of viscosity solution and Hamilton-Jacobi equations is enormous, including common class of partial differential equations such as evolutive problems and problems with boundary conditions, equations arising in optimal control theory, differential games, second-order equations arising in stochastic optimal control and stochastic differential games, geometric equations, etc. In computer vision, it also has various applications. In particular, the distance functions which are the viscosity solutions of the Eikonal equations are widely used. Also, all these notions have played an important role in shape representation, morphology, tractography and in general, in image processing. Finally viscosity solutions provide powerful tools to analyse the Shape from shading problem.
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Chapitre d'ouvrage
Katsushi Ikeuchi. Encyclopedia of Computer Vision, Springer, 2011
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Fabio Camilli, Emmanuel Prados. Viscosity Solution. Katsushi Ikeuchi. Encyclopedia of Computer Vision, Springer, 2011. 〈inria-00546110〉

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