Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances
Computation
2019-08-06 v3 Optimization and Control
Abstract
We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with homogeneous of degree one transport cost. Our algorithm is built on multilevel primal-dual algorithms. Several numerical examples and a complexity analysis are provided to demonstrate its computational speed. On some commonly used image examples of size , the proposed algorithm gives solutions within seconds on a single CPU, which is much faster than the state-of-the-art algorithms.
Keywords
Cite
@article{arxiv.1810.00118,
title = {Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances},
author = {Jialin Liu and Wotao Yin and Wuchen Li and Yat Tin Chow},
journal= {arXiv preprint arXiv:1810.00118},
year = {2019}
}