FERRADANS, Sira; PAPADAKIS, Nicolas; RABIN, Julien; PEYRÉ, Gabriel; AUJOL, Jean-François

doi:10.1007/978-3-642-38267-3_36

Métadonnées

Licence d’utilisation du document

FERRADANS, Sira
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

PAPADAKIS, Nicolas
Modelling, Observations, Identification for Environmental Sciences [MOISE]
Institut de Mathématiques de Bordeaux [IMB]

RABIN, Julien
Equipe Image - Laboratoire GREYC - UMR6072

Langue

Communication dans un congrès

Ce document a été publié dans

International Conference on Scale Space and Variational Methods in Computer Vision (SSVM'13), 2013-06-03, Schloss Seggau, Leibnitz. 2013-06-03, vol. 7893, p. 428-439

Springer

Résumé en anglais

This article introduces a generalization of discrete Optimal Transport that includes a regularity penalty and a relaxation of the bijectivity constraint. The corresponding transport plan is solved by minimizing an energy which is a convexification of an integer optimization problem. We propose to use a proximal splitting scheme to perform the minimization on large scale imaging problems. For un-regularized relaxed transport, we show that the relaxation is tight and that the transport plan is an assignment. In the general case, the regularization prevents the solution from being an assignment, but we show that the corresponding map can be used to solve imaging problems. We show an illustrative application of this discrete regularized transport to color transfer between images. This imaging problem cannot be solved in a satisfying manner without relaxing the bijective assignment constraint because of mass variation across image color palettes. Furthermore, the regularization of the transport plan helps remove colorization artifacts due to noise amplification.< Réduire

Mots clés en anglais

Optimal Transport

manifold learning

proximal splitting

convex optimization

variational regularization

color transfer

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189657

DOI

http://dx.doi.org/10.1007/978-3-642-38267-3_36

Projet Européen

Sparsity, Image and Geometry to Model Adaptively Visual Processings

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