Sliced and Radon Wasserstein Barycenters of Measures
Pfister, Hanspeter; Peyré, Gabriel; Rabin, Julien; Bonneel, Nicolas (2015), Sliced and Radon Wasserstein Barycenters of Measures, Journal of Mathematical Imaging and Vision, 51, 1, p. 22-45. http://dx.doi.org/10.1007/s10851-014-0506-3
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00881872
Journal nameJournal of Mathematical Imaging and Vision
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Abstract (EN)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.
Subjects / KeywordsBarycenter of measures; Wasserstein distance; Radon transform; Optimal transport
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