Sliced and Radon Wasserstein Barycenters of Measures
This article details two approaches to compute barycenters of measures using 1-D Wasserstein distances along radial projections of the input measures. The first method makes use of the Radon transform of the measures, and the second is the solution of a convex optimization problem over the space of...
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| Published in | Journal of mathematical imaging and vision Vol. 51; no. 1; pp. 22 - 45 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.01.2015
Springer Verlag |
| Subjects | |
| Online Access | Get full text |
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| 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 method 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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| AbstractList | 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. This article details two approaches to compute barycenters of measures using 1-D Wasserstein distances along radial projections of the input measures. The first method 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. |
| Author | Pfister, Hanspeter Bonneel, Nicolas Rabin, Julien Peyré, Gabriel |
| Author_xml | – sequence: 1 givenname: Nicolas surname: Bonneel fullname: Bonneel, Nicolas organization: Harvard University, CNRS-LIRIS – sequence: 2 givenname: Julien surname: Rabin fullname: Rabin, Julien organization: GREYC, Université de Caen – sequence: 3 givenname: Gabriel surname: Peyré fullname: Peyré, Gabriel email: gabriel.peyre@ceremade.dauphine.fr organization: CNRS-CEREMADE, Université Paris-Dauphine – sequence: 4 givenname: Hanspeter surname: Pfister fullname: Pfister, Hanspeter organization: Harvard University |
| BackLink | https://hal.science/hal-00881872$$DView record in HAL |
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| Keywords | Radon transform Wasserstein distance Barycenter of measures Optimal transport |
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| Snippet | This article details two approaches to compute barycenters of measures using 1-D Wasserstein distances along radial projections of the input measures. The... |
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| SubjectTerms | Applications of Mathematics Computer Science Engineering Sciences Image Processing and Computer Vision Mathematical Methods in Physics Mathematics Numerical Analysis Signal and Image Processing Signal,Image and Speech Processing |
| Title | Sliced and Radon Wasserstein Barycenters of Measures |
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