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Regularized Discrete Optimal Transport

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorFERRADANS, Sira
hal.structure.identifierModelling, Observations, Identification for Environmental Sciences [MOISE]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAPADAKIS, Nicolas
hal.structure.identifierEquipe Image - Laboratoire GREYC - UMR6072
dc.contributor.authorRABIN, Julien
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPEYRÉ, Gabriel
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAUJOL, Jean-François
dc.contributor.editorArjan Kuijper and Kristian Bredies and Thomas Pock and Horst Bischof
dc.date.accessioned2024-04-04T02:22:31Z
dc.date.available2024-04-04T02:22:31Z
dc.date.created2012-12-20
dc.date.issued2013-06-03
dc.date.conference2013-06-03
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189657
dc.description.abstractEnThis 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.
dc.description.sponsorshipTransport Optimal et Modèles Multiphysiques de l'Image - ANR-11-BS01-0014
dc.language.isoen
dc.publisherSpringer
dc.subject.enOptimal Transport
dc.subject.enmanifold learning
dc.subject.enproximal splitting
dc.subject.enconvex optimization
dc.subject.envariational regularization
dc.subject.encolor transfer
dc.typeCommunication dans un congrès
dc.identifier.doi10.1007/978-3-642-38267-3_36
dc.subject.halInformatique [cs]/Traitement des images
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
dc.description.sponsorshipEuropeSparsity, Image and Geometry to Model Adaptively Visual Processings
bordeaux.page428-439
bordeaux.volume7893
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleInternational Conference on Scale Space and Variational Methods in Computer Vision (SSVM'13)
bordeaux.countryAT
bordeaux.conference.citySchloss Seggau, Leibnitz
bordeaux.peerReviewedoui
hal.identifierhal-00797078
hal.version1
hal.invitednon
hal.proceedingsoui
hal.conference.end2013-06-06
hal.popularnon
hal.audienceInternationale
dc.title.itRegularized Discrete Optimal Transport
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00797078v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2013-06-03&rft.volume=7893&rft.spage=428-439&rft.epage=428-439&rft.au=FERRADANS,%20Sira&PAPADAKIS,%20Nicolas&RABIN,%20Julien&PEYR%C3%89,%20Gabriel&AUJOL,%20Jean-Fran%C3%A7ois&rft.genre=unknown


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