Sliced and Radon Wasserstein Barycenters of Measures

• Published in: Journal of mathematical imaging and vision Vol. 51; no. 1; pp. 22 - 45
• Main Authors: Bonneel, Nicolas, Rabin, Julien, Peyré, Gabriel, Pfister, Hanspeter
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.01.2015; Springer Verlag
• Subjects: 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; Radon transform; Wasserstein distance; Barycenter of measures; Optimal transport

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...