PAPADAKIS, Nicolas; PEYRÉ, Gabriel; OUDET, Edouard

doi:10.1137/130920058

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PAPADAKIS, Nicolas
Institut de Mathématiques de Bordeaux [IMB]

PEYRÉ, Gabriel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

OUDET, Edouard
Equations aux Dérivées Partielles [EDP]

Langue

Article de revue

Ce document a été publié dans

SIAM Journal on Imaging Sciences. 2014-01-28, vol. 7, n° 1, p. 212-238

Society for Industrial and Applied Mathematics

Résumé en anglais

This article reviews the use of first order convex optimization schemes to solve the discretized dynamic optimal transport problem, initially proposed by Benamou and Brenier. We develop a staggered grid discretization that is well adapted to the computation of the $L^2$ optimal transport geodesic between distributions defined on a uniform spatial grid. We show how proximal splitting schemes can be used to solve the resulting large scale convex optimization problem. A specific instantiation of this method on a centered grid corresponds to the initial algorithm developed by Benamou and Brenier. We also show how more general cost functions can be taken into account and how to extend the method to perform optimal transport on a Riemannian manifold.< Réduire

Mots clés en anglais

computational fluid dynamic

Optimal transport

staggered grid

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192815

DOI

http://dx.doi.org/10.1137/130920058

Projet Européen

97690

Project ANR

Transport Optimal et Modèles Multiphysiques de l'Image - ANR-11-BS01-0014

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251