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
TypeCommunication / Conférence
External document linkhttp://hal.archives-ouvertes.fr/hal-00476064/fr/
Conference titleThird International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2011)
Book titleScale Space and Variational Methods in Computer Vision Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 – June 2, 2011, Revised Selected Papers
Book authorBruckstein, Alfred M.; Ter Haar Romeny, Bart M.; Bronstein, Alexander M.; Bronstein, Michael M.
Series titleLecture Notes in Computer Science
Number of pages798
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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 / Keywordsimage processing; stochastic gradient; Wasserstein barycenter; optimal transport; texture synthesis; texture mixing
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