A Multiscale Approach to Optimal Transport

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Date
2011
Authors
Mérigot, Quentin
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd.
Abstract
In this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean plane. Our algorithm exploits the multiscale nature of this optimal transport problem. We iteratively simplify the target using Lloyd's algorithm, and use the solution of the simplified problem as a rough initial solution to the more complex one. This approach allows for fast estimation of distances between measures related to optimal transport (known as Earth-mover or Wasserstein distances). We also discuss the implementation of these algorithms, and compare the original one to its multiscale counterpart.
Description

        
@article{
10.1111:j.1467-8659.2011.02032.x
,
journal = {Computer Graphics Forum},
title = {{
A Multiscale Approach to Optimal Transport
}},
author = {
Mérigot, Quentin
},
year = {
2011
},
publisher = {
The Eurographics Association and Blackwell Publishing Ltd.
},
ISSN = {
1467-8659
},
DOI = {
10.1111/j.1467-8659.2011.02032.x
}
}
Citation
URI
https://doi.org/10.1111/j.1467-8659.2011.02032.x
Collections
30-Issue 5
SGP11: Eurographics Symposium on Geometry Processing