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Sliced and Radon Wasserstein Barycenters of Measures

Abstract : This article details two approaches to compute barycenters of measures using 1-D Wasserstein distances along radial projections of the input measures. The first me- thod makes use of the Radon transform of the measures, and the second is the solution of a convex optimization problem over the space of measures. We show several properties of these barycenters and explain their relationship. We show numerical approximation schemes based on a discrete Radon transform and on the resolution of a non-convex optimization problem. We explore the respective merits and drawbacks of each approach on applications to two image processing problems: color transfer and texture mixing.
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Submitted on : Tuesday, November 12, 2013 - 6:00:02 PM
Last modification on : Friday, November 18, 2022 - 9:25:20 AM
Long-term archiving on: : Thursday, February 13, 2014 - 4:22:08 AM


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Nicolas Bonneel, Julien Rabin, Gabriel Peyré, Hanspeter Pfister. Sliced and Radon Wasserstein Barycenters of Measures. Journal of Mathematical Imaging and Vision, 2015, 1 (51), pp.22-45. ⟨10.1007/s10851-014-0506-3⟩. ⟨hal-00881872⟩



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