A multiscale approach to optimal transport

Abstract : In this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean plane. Our algorithm exploits the multiscale nature of this optimal transport problem. We iteratively simplify the target using Lloyd's algorithm, and use the solution of the simplified problem as a rough initial solution to the more complex one. This approach allows for fast estimation of distances between measures related to optimal transport (known as Earth-mover or Wasserstein distances). We also discuss the implementation of these algorithms, and compare the original one to its multiscale counterpart.
Type de document :
Article dans une revue
Computer Graphics Forum, Wiley, 2011, 30 (5), pp.1584-1592. <10.1111/j.1467-8659.2011.02032.x>
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00604684
Contributeur : Quentin Mérigot <>
Soumis le : mercredi 29 juin 2011 - 15:15:46
Dernière modification le : vendredi 5 juin 2015 - 13:32:03
Document(s) archivé(s) le : lundi 12 novembre 2012 - 09:51:58

Fichier

opttransport-preprint.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Quentin Mérigot. A multiscale approach to optimal transport. Computer Graphics Forum, Wiley, 2011, 30 (5), pp.1584-1592. <10.1111/j.1467-8659.2011.02032.x>. <hal-00604684>

Partager

Métriques

Consultations de
la notice

659

Téléchargements du document

948