v1v2 (latest)
Computing Kantorovich-Wasserstein Distances on -dimensional histograms using -partite graphs

Abstract
This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of -dimensional histograms having bins each. We prove that this problem is equivalent to an uncapacitated minimum cost flow problem on a -partite graph with nodes and arcs, whenever the cost is separable along the principal -dimensional directions. We show numerically the benefits of our approach by computing the Kantorovich-Wasserstein distance of order 2 among two sets of instances: gray scale images and -dimensional biomedical histograms. On these types of instances, our approach is competitive with state-of-the-art optimal transport algorithms.
View on arXivComments on this paper