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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

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OTRegul-SSVM13.pdf (2.712Mb)
Type
Communication / Conférence
External document link
https://hal.archives-ouvertes.fr/hal-00797078
Date
2013
Conference country
AUSTRIA
Book title
Scale Space and Variational Methods in Computer Vision 4th International Conference, SSVM 2013, Schloss Seggau, Leibnitz, Austria, June 2-6, 2013. Proceedings; SSVM 2013
Book author
Arjan Kuijper, Kristian Bredies, Thomas Pock, Horst Bischof
Publisher
Springer
Published in
Berlin Heidelberg
ISBN
978-3-642-38266-6
Pages
428-439
Publication identifier
10.1007/978-3-642-38267-3_36
Metadata
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Author(s)
Ferradans, Sira
Papadakis, Nicolas
Rabin, Julien cc
Peyré, Gabriel
Aujol, Jean-François
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 / Keywords
color transfer; Optimal Transport; variational regularization; proximal splitting; convex optimization; manifold learning

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