Regularized Discrete Optimal Transport
Ferradans, Sira; Papadakis, Nicolas; Rabin, Julien; Peyré, Gabriel; Aujol, Jean-François (2013), Regularized Discrete Optimal Transport, in Arjan Kuijper, Kristian Bredies, Thomas Pock, Horst Bischof, Scale Space and Variational Methods in Computer Vision 4th International Conference, SSVM 2013, Schloss Seggau, Leibnitz, Austria, June 2-6, 2013. Proceedings, Springer : Berlin Heidelberg, p. 428-439. 10.1007/978-3-642-38267-3_36
TypeCommunication / Conférence
External document linkhttps://hal.archives-ouvertes.fr/hal-00797078
Book titleScale Space and Variational Methods in Computer Vision 4th International Conference, SSVM 2013, Schloss Seggau, Leibnitz, Austria, June 2-6, 2013. Proceedings; SSVM 2013
Book authorArjan Kuijper, Kristian Bredies, Thomas Pock, Horst Bischof
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Abstract (EN)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.
Subjects / Keywordscolor transfer; Optimal Transport; variational regularization; proximal splitting; convex optimization; manifold learning
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