Optimal Transport with Proximal Splitting
Language
en
Article de revue
This item was published in
SIAM Journal on Imaging Sciences. 2014-01-28, vol. 7, n° 1, p. 212-238
Society for Industrial and Applied Mathematics
English Abstract
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 ...Read more >
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.Read less <
English Keywords
computational fluid dynamic
Optimal transport
staggered grid
European Project
97690
ANR Project
Transport Optimal et Modèles Multiphysiques de l'Image - ANR-11-BS01-0014
Origin
Hal imported