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Regularized Discrete Optimal Transport

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
hal.structure.identifierDuke University [Durham]
dc.contributor.authorFERRADANS, Sira
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAPADAKIS, Nicolas
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.date.accessioned2024-04-04T03:17:46Z
dc.date.available2024-04-04T03:17:46Z
dc.date.issued2014
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194337
dc.description.abstractEnThis article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two features are crucial for image processing tasks, which necessitate to take into account families of multimodal histograms, with large mass variation across modes. The corresponding relaxed and regularized transportation problem is the solution of a convex optimization problem. Depending on the regularization used, this minimization can be solved using standard linear programming methods or first order proximal splitting schemes. The resulting transportation plan can be used as a color transfer map, which is robust to mass variation across images color palettes. Furthermore, the regularization of the transport plan helps to remove colorization artifacts due to noise amplification. We also extend this framework to the computation of barycenters of distributions. The barycenter is the solution of an optimization problem, which is separately convex with respect to the barycenter and the transportation plans, but not jointly convex. A block coordinate descent scheme converges to a stationary point of the energy. We show that the resulting algorithm can be used for color normalization across several images. The relaxed and regularized barycenter defines a common color palette for those images. Applying color transfer toward this average palette performs a color normalization of the input images.
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.title.enRegularized Discrete Optimal Transport
dc.typeArticle de revue
dc.identifier.doi10.1137/130929886
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
dc.identifier.arxiv1307.5551
dc.description.sponsorshipEuropeSparsity, Image and Geometry to Model Adaptively Visual Processings
bordeaux.journalSIAM Journal on Imaging Sciences
bordeaux.page1853-1882
bordeaux.volume7
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01188963
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01188963v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Imaging%20Sciences&rft.date=2014&rft.volume=7&rft.issue=3&rft.spage=1853-1882&rft.epage=1853-1882&rft.au=FERRADANS,%20Sira&PAPADAKIS,%20Nicolas&PEYR%C3%89,%20Gabriel&AUJOL,%20Jean-Fran%C3%A7ois&rft.genre=article


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