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
Type
Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00881872Date
2015Journal name
Journal of Mathematical Imaging and VisionVolume
51Number
1Publisher
Springer
Pages
22-45
Publication identifier
Metadata
Show full item recordAbstract (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 / Keywords
Barycenter of measures; Wasserstein distance; Radon transform; Optimal transportRelated items
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