PAPADAKIS, Nicolas; PEYRÉ, Gabriel; OUDET, Edouard

doi:10.1137/130920058

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Licencia de uso del documento

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]

Idioma

Article de revue

Este ítem está publicado en

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

Society for Industrial and Applied Mathematics

Resumen en inglés

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.< Leer menos

Palabras clave en inglés

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

Proyecto europeo

97690

Proyecto ANR

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

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251