Sliced and Radon Wasserstein Barycenters of Measures
作者： Nicolas Bonneel , Julien Rabin , Gabriel Peyré , Hanspeter Pfister
DOI: 10.1007/S10851-014-0506-3
关键词: Image processing 、 Convex optimization 、 Applied mathematics 、 Space (mathematics) 、 Discrete radon transform 、 Optimization problem 、 Mixing (mathematics) 、 Mathematical optimization 、 Radon 、 Radon transform 、 Mathematics
摘要: This article details two approaches to compute barycenters of measures using 1-D Wasserstein distances along radial projections the input measures. The first method makes use Radon transform measures, and second is solution a convex optimization problem over space We show several properties these explain their relationship. numerical approximation schemes based on discrete resolution non-convex problem. explore respective merits drawbacks each approach applications image processing problems: color transfer texture mixing.
archives-ouvertes.fr
springer.com
acm.org
dauphine.fr参考文章(34)
Sira Ferradans, Gui-Song Xia, Gabriel Peyré, Jean-François Aujol, Static and Dynamic Texture Mixing Using Optimal Transport international conference on scale space and variational methods in computer vision. pp. 137- 148 ,(2013) , 10.1007/978-3-642-38267-3_12
Jérémie Bigot, Thierry Klein, Consistent estimation of a population barycenter in the Wasserstein space ,(2013)
Claude Dellacherie, Paul André Meyer, Probabilities and potential Hermann , North-Holland Pub. Co , Sole distributors for the U.S. and Canada, Elsevier North-Holland. ,(1978)
Jean-François Aujol, Sira Ferradans, Gabriel Peyré, Gui-Song Xia, Optimal Transport Mixing of Gaussian Texture Models Université Paris-Dauphine. ,(2012)
Erik Reinhard, Tania Pouli, Colour Spaces for Colour Transfer Lecture Notes in Computer Science. pp. 1- 15 ,(2011) , 10.1007/978-3-642-20404-3_1
Cédric Villani, Topics in Optimal Transportation ,(2003)
Sigurdur Helgason, S Helgason, None, The Radon Transform ,(1980)
Arnaud Doucet, Marco Cuturi, Fast Computation of Wasserstein Barycenters international conference on machine learning. pp. 685- 693 ,(2014)
Julien Rabin, Gabriel Peyré, Julie Delon, Marc Bernot, Wasserstein Barycenter and Its Application to Texture Mixing Lecture Notes in Computer Science. ,vol. 6667, pp. 435- 446 ,(2012) , 10.1007/978-3-642-24785-9_37
Martial Agueh, Guillaume Carlier, Barycenters in the Wasserstein Space Siam Journal on Mathematical Analysis. ,vol. 43, pp. 904- 924 ,(2011) , 10.1137/100805741