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Wasserstein Barycenter and its Application to Texture Mixing

Bernot, Marc; Rabin, Julien; Peyré, Gabriel; Delon, Julie (2012), Wasserstein Barycenter and its Application to Texture Mixing, in Bruckstein, Alfred M.; Ter Haar Romeny, Bart M.; Bronstein, Alexander M.; Bronstein, Michael M., Scale Space and Variational Methods in Computer Vision Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 – June 2, 2011, Revised Selected Papers, Springer : Berlin, p. 435-446. http://dx.doi.org/10.1007/978-3-642-24785-9_37

Type
Communication / Conférence
External document link
http://hal.archives-ouvertes.fr/hal-00476064/fr/
Date
2012
Conference title
Third International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2011)
Conference date
2011-05
Conference city
Ein-Gedi
Conference country
Israël
Book title
Scale Space and Variational Methods in Computer Vision Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 – June 2, 2011, Revised Selected Papers
Book author
Bruckstein, Alfred M.; Ter Haar Romeny, Bart M.; Bronstein, Alexander M.; Bronstein, Michael M.
Publisher
Springer
Series title
Lecture Notes in Computer Science
Series number
6667
Published in
Berlin
ISBN
978-3-642-24784-2
Number of pages
798
Pages
435-446
Publication identifier
http://dx.doi.org/10.1007/978-3-642-24785-9_37
Metadata
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Author(s)
Bernot, Marc
Rabin, Julien cc
Peyré, Gabriel
Delon, Julie
Abstract (EN)
This paper proposes a new definition of the averaging of discrete probability distributions as a barycenter over the Wasserstein space. Replacing the Wasserstein original metric by a sliced approximation over 1D distributions allows us to use a fast stochastic gradient descent algorithm. This new notion of barycenter of probabilities is likely to find applications in computer vision where one wants to average features defined as distributions. We show an application to texture synthesis and mixing, where a texture is characterized by the distribution of the response to a multiscale oriented filter bank. This leads to a simple way to navigate over a convex domain of color textures.
Subjects / Keywords
image processing; stochastic gradient; Wasserstein barycenter; optimal transport; texture synthesis; texture mixing

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