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Given two distributions $P$ and $S$ of equal total mass, the Earth Mover's Distance measures the cost of transforming one distribution into the other, where the cost of moving a unit of mass is equal to the distance over which it is moved.
On the translocation of masses
L. V. Kantorovich · 1942
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The polynomial solvability of convex quadratic programming
M. K. Kozlov, S. P. Tarasov, and L. G. Khachiyan · 1980
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Interior path following primal-dual algorithms. Part II: Convex quadratic programming
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An O ( n 3 L ) O(n^{3}L) primal interior point algorithm for convex quadratic programming
D. Goldfarb and S. Liu · 1990
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The earth mover’s distance as a metric for image retrieval
Y. Rubner, C. Tomasi, and L. J. Guibas · 2000
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Fast contour matching using approximate earth mover’s distance
K. Grauman and T. Darrell · 2004
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Matching point sets with respect to the earth mover’s distance
S. Cabello, P. Giannopoulos, C. Knauer, and G. Rote · 2008
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Optimal Transport: Old and New
C. Villani · 2008
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Spectral Gromov-Wasserstein distances for shape matching
F. Mémoli · 2009
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F. de Goes, D. Cohen-Steiner, P. Alliez, and M. Desbrun · 2011
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Q. Mérigot · 2011
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F. de Goes, K. Breeden, V. Ostromoukhov, and M. Desbrun · 2012
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R. Sharathkumar and P. K. Agarwal · 2012
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D. Geiß, R. Klein, R. Penninger, and G. Rote · 2013
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Faster algorithms for the geometric transportation problem
P. K. Agarwal, K. Fox, D. Panigrahi, K. R. Varadarajan, and A. Xiao · 2017
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Dynamical optimal transport on discrete surfaces
H. Lavenant, S. Claici, E. Chien, and J. Solomon · 2018
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An algorithm for optimal transport between a simplex soup and a point cloud
Q. Mérigot, J. Meyron, and B. Thibert · 2018
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Dynamic smooth compressed quadtrees
I. van der Hoog, E. Khramtcova, and M. Löffler · 2018
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A friendly smoothed analysis of the simplex method
D. Dadush and S. Huiberts · 2020
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Preconditioning for the geometric transportation problem
A. B. Khesin, A. Nikolov, and D. Paramonov · 2021
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Convolutional Wasserstein distances: Efficient optimal transportation on geometric domains
J. Solomon, F. de Goes, G. Peyré, M. Cuturi, A. Butscher, A. Nguyen, T. Du, and L. Guibas · 2015
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Optimal mass transport for shape matching and comparison
Z. Su, Y. Wang, R. Shi, W. Zeng, J. Sun, F. Luo, and X. Gu · 2015
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Mémoire sur la théorie des déblais et des remblais
G. Monge
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A near-linear time approximation scheme for geometric transportation with arbitrary supplies and spread
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