A multiscale approach to optimal transport - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Computer Graphics Forum Année : 2011

A multiscale approach to optimal transport

Résumé

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.
Fichier principal
Vignette du fichier
opttransport-preprint.pdf (1.08 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00604684 , version 1 (29-06-2011)

Identifiants

Citer

Quentin Mérigot. A multiscale approach to optimal transport. Computer Graphics Forum, 2011, 30 (5), pp.1584-1592. ⟨10.1111/j.1467-8659.2011.02032.x⟩. ⟨hal-00604684⟩
1081 Consultations
2906 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More