Result: Regularized Discrete Optimal Transport

Title:
Regularized Discrete Optimal Transport
Authors:
Ferradans, Sira, Papadakis, Nicolas, Rabin, Julien, Peyré, Gabriel, Aujol, Jean-François
Contributors:
CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Modelling, Observations, Identification for Environmental Sciences (MOISE), Centre Inria de l'Université Grenoble Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Equipe Image - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Arjan Kuijper and Kristian Bredies and Thomas Pock and Horst Bischof, CPU, ANR-11-BS01-0014,TOMMI,Transport Optimal et Modèles Multiphysiques de l'Image(2011), European Project: 279593,EC:FP7:ERC,ERC-2011-StG_20101014,SIGMA-VISION(2011)
Source:
International Conference on Scale Space and Variational Methods in Computer Vision (SSVM'13) ; https://hal.science/hal-00797078 ; International Conference on Scale Space and Variational Methods in Computer Vision (SSVM'13), Jun 2013, Schloss Seggau, Leibnitz, Austria. pp.428-439, ⟨10.1007/978-3-642-38267-3_36⟩
Publisher Information:
CCSD
Springer
Publication Year:
2013
Collection:
Université Grenoble Alpes: HAL
Subject Terms:
Optimal Transport, manifold learning, proximal splitting, convex optimization, variational regularization, color transfer, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing
Subject Geographic:
Schloss Seggau, Leibnitz, Austria
Document Type:
Conference conference object
Language:
English
Relation:
info:eu-repo/grantAgreement/EC/FP7/279593/EU/Sparsity, Image and Geometry to Model Adaptively Visual Processings/SIGMA-VISION
DOI:
10.1007/978-3-642-38267-3_36
Availability:
https://hal.science/hal-00797078
https://hal.science/hal-00797078v1/document
https://hal.science/hal-00797078v1/file/OTRegul-SSVM13.pdf
https://doi.org/10.1007/978-3-642-38267-3_36
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edsbas.866701E9
Database:
BASE

Further Information

International audience ; 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.