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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorFerradans, Sira*
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPapadakis, Nicolas
HAL ID: 169
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
dc.contributor.authorAujol, Jean-François*
dc.subjectoptimal transporten
dc.subjectcolor transferen
dc.subjectvariational regularizationen
dc.subjectconvex optimizationen
dc.subjectproximal splittingen
dc.subjectmanifold learningen
dc.titleRegularized Discrete Optimal Transporten
dc.typeArticle accepté pour publication ou publié
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 where one must 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 image color palettes. Furthermore, the regularization of the transport plan helps remove colorization artifacts due to noise amplification. We also extend this framework to compute the barycenter 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.en
dc.relation.isversionofjnlnameSIAM Journal on Imaging Sciences
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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