research-article

Earth mover's distances on discrete surfaces

Authors:

Justin Solomon,

Leonidas Guibas,

Adrian ButscherAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 33, Issue 4

Article No.: 67, Pages 1 - 12

https://doi.org/10.1145/2601097.2601175

Published: 27 July 2014 Publication History

Abstract

We introduce a novel method for computing the earth mover's distance (EMD) between probability distributions on a discrete surface. Rather than using a large linear program with a quadratic number of variables, we apply the theory of optimal transportation and pass to a dual differential formulation with linear scaling. After discretization using finite elements (FEM) and development of an accompanying optimization method, we apply our new EMD to problems in graphics and geometry processing. In particular, we uncover a class of smooth distances on a surface transitioning from a purely spectral distance to the geodesic distance between points; these distances also can be extended to the volume inside and outside the surface. A number of additional applications of our machinery to geometry problems in graphics are presented.

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Earth mover's distances on discrete surfaces

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 33, Issue 4

July 2014

1366 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2601097

Issue’s Table of Contents

Copyright © 2014 ACM.

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Published: 27 July 2014

Published in TOG Volume 33, Issue 4

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Tsai RTurnquist A(2024)A volumetric approach to Monge's optimal transport on surfacesJournal of Computational Physics10.1016/j.jcp.2024.113352517(113352)Online publication date: Nov-2024
https://doi.org/10.1016/j.jcp.2024.113352
Li YSi SLiu XZou LWu WLiu XZhang L(2024)Three-dimensional reconstruction of cotton plant with internal canopy occluded structure recoveryComputers and Electronics in Agriculture10.1016/j.compag.2023.108370215:COnline publication date: 27-Feb-2024
https://dl.acm.org/doi/10.1016/j.compag.2023.108370
Han AMishra BJawanpuria PGao J(2024)Riemannian block SPD coupling manifold and its application to optimal transportMachine Language10.1007/s10994-022-06258-w113:4(1595-1622)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s10994-022-06258-w
Berti LFacca EPutti M(2023)Numerical solution of the $ L^1 $-optimal transport problem on surfacesAdvances in Computational Science and Engineering10.3934/acse.2023017(0-0)Online publication date: 2023
https://doi.org/10.3934/acse.2023017
Pang BZheng ZWang GWang P(2023)Learning the Geodesic Embedding with Graph Neural NetworksACM Transactions on Graphics10.1145/361831742:6(1-12)Online publication date: 5-Dec-2023
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Taşkesen BShafieezadeh-Abadeh SKuhn DNatarajan K(2023)Discrete Optimal Transport with Independent Marginals is #P-HardSIAM Journal on Optimization10.1137/22M148204433:2(589-614)Online publication date: 1-Jun-2023
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