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We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass.
Sublinear functions of measures and variational integrals
C. Goffman and J. Serrin · 1964
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Optimization by vector space methods
D. G. Luenberger · 1969
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Convex analysis and measurable multifunctions
C. Castaing and M. Valadier · 1977
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Multifonctions s.c.i. et régularisée s.c.i. essentielle
G. Bouchitté and M. Valadier · 1987
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Integral representation of convex functionals on a space of measures
G. Bouchitté and M. Valadier · 1988
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New lower semicontinuity results for nonconvex functionals defined on measures
G. Bouchitté and G. Buttazzo · 1990
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Functions of Bounded Variation and Free Discontinuity Problems
L. Ambrosio, N. Fusco, and D. Pallara · 2000
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A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem
J.-D. Benamou and Y. Brenier · 2000
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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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Minimizing flows for the Monge–Kantorovich problem
S. Angenent, S. Haker, and A. Tannenbaum · 2003
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Laplacian eigenmaps for dimensionality reduction and data representation
M. Belkin and P. Niyogi · 2003
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Numerical resolution of an “unbalanced” mass transport problem
J.-D. Benamou · 2003
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Aspects of total variation regularized L1 function approximation
T. F. Chan and S. Esedoglu · 2005
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An efficient earth mover’s distance algorithm for robust histogram comparison
H. Ling and K. Okada · 2007
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A linear time histogram metric for improved SIFT matching
O. Pele and M. Werman · 2008
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A new class of transport distances between measures
J. Dolbeault, B. Nazaret, and G. Savaré · 2009
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Fast and robust earth mover’s distances
O. Pele and W. Werman · 2009
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Optimal Transport: Old and New
C. Villani · 2009
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Sinkhorn distances: Lightspeed computation of optimal transportation distances
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Imaging with Kantorovich–Rubinstein discrepancy
J. Lellmann, D. A. Lorenz, C. Schönlieb, and T. Valkonen · 2014
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Adaptive color transfer with relaxed optimal transport
J. Rabin, S. Ferradans, and N. Papadakis · 2014
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Iterative Bregman projections for regularized transportation problems
J.-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré · 2015
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Unbalanced optimal transport: Dynamic and Kantorovich formulations
L. Chizat, G. Peyré, B. Schmitzer, and F.-X. Vialard · 2015
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