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Multiphysics optimal transportation and image analysis

Afaf Bouharguane 1 Emmanuel Maitre 1 Edouard Oudet 1 Nicolas Papadakis 2
1 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : Benamou and Brenier formulation of Monge transportation problem has proven to be of great interest in image processing to compute warpings and distances between pair of images. In some applications, however, the built-in minimization of kinetic energy does not give satisfactory results. In particular cases where some specific regions represent physical objects, it does not make sense, as produces genuine optimal transport, to split, merge or arbitrarily deform these regions along the optimal path. The aim of this work is to introduce several extended energies to take care of physical properties of the image in the interpolation process. We present algorithms to compute approximations of the corresponding generalized optimal transportation plans.
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https://hal.archives-ouvertes.fr/hal-00740671
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Submitted on : Wednesday, October 10, 2012 - 4:12:12 PM
Last modification on : Friday, July 3, 2020 - 4:52:07 PM
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Afaf Bouharguane, Emmanuel Maitre, Edouard Oudet, Nicolas Papadakis. Multiphysics optimal transportation and image analysis. 2012. ⟨hal-00740671⟩

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