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We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems.
On the translocation of masses
Leonid V. Kantorovič · 1942
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On a functional space and certain extremum problems
Leonid V. Kantorovič and Gennadi Š. Rubinšteĭn · 1957
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Geometric Measure Theory
Herbert Federer · 1969
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Duality for the sum of convex functions in general Banach spaces
Hedi Attouch and Haïm Brezis · 1986
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Geometric Measure Theory: A Beginner’s Guide
Frank Morgan · 1987
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Mass transportation problems. Vol. I
Svetlozar T. Rachev and Ludger Rüschendorf · 1998
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Convex analysis and variational problems
Ivar Ekeland and Roger Temam · 1999
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Geometry of sets and measures in Euclidean spaces: Fractals and rectifiability
Pertti Mattila · 1999
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Functions of bounded variation and free discontinuity problems
Luigi Ambrosio, Nicola Fusco, and Diego Pallara · 2000
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The earth mover’s distance as a metric for image retrieval
Yossi Rubner, Carlo Tomasi, and Leonidas J Guibas · 2000
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Oscillating patterns in image processing and nonlinear evolution equations
Yves Meyer · 2001
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Regularity properties for Monge transport density and for solutions of some shape optimization problem
Luigi De Pascale and Aldo Pratelli · 2002
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Edge-preserving and scale-dependent properties of total variation regularization
David Strong and Tony Chan · 2003
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Modeling textures with total variation minimization and oscillating patterns in image processing
Luminita A Vese and Stanley J Osher · 2003
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Fast contour matching using approximate earth mover’s distance
Kristen Grauman and Trevor Darrell · 2004
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Optimal mass transport for registration and warping
Steven Haker, Lei Zhu, Allen Tannenbaum, and Sigurd Angenent · 2004
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Gradient flows in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2005
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A model for the optimal planning of an urban area
Giuseppe Buttazzo and Filippo Santambrogio · 2005
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Aspects of total variation regularized L 1 L^{1} function approximation
Tony F. Chan and Selim Esedoglu · 2005
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Structure-texture image decomposition—modeling, algorithms, and parameter selection
Jean-François Aujol, Guy Gilboa, Tony Chan, and Stanley Osher · 2006
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Denoising by BV-duality
Stefan Kindermann, Stanley Osher, and Jinjun Xu · 2006
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Measure theory. Vol. I, II
V. I. Bogachev · 2007
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An efficient earth mover’s distance algorithm for robust histogram comparison
Haibin Ling and Kazunori Okada · 2007
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Facundo Mémoli · 2007
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Wotao Yin, Donald Goldfarb, and Stanley Osher · 2007
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Gromov-Wasserstein distances and the metric approach to object matching
Facundo Mémoli · 2011
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Facundo Mémoli · 2011
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George O. Mohler, Andrea L. Bertozzi, Thomas A. Goldstein, and Stanley J. Osher · 2011
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Wasserstein regularization of imaging problems
Julien Rabin and Gabriel Peyré · 2011
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An optimal transportation approach for nuclear structure-based pathology
Wei Wang, John A. Ozolek, Dejan Slepcev, Ann B Lee, Cheng Chen, and Gustavo K. Rohde · 2011
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Regularized regression and density estimation based on optimal transport
Martin Burger, Marzena Franek, and Carola-Bibiane Schönlieb · 2012
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Michael Grant and Stephen Boyd · 2008
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Conformal Wasserstein distance: II. Computational aspects and extensions
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Modelling convex shape priors and matching based on the Gromov-Wasserstein distance
Bernhard Schmitzer and Christoph Schnörr · 2013
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Object segmentation by shape matching with Wasserstein modes
Bernhard Schmitzer and Christoph Schnörr · 2013
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Convex variational image restoration with histogram priors
Paul Swoboda and Christoph Schnörr · 2013
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CVX: Matlab software for disciplined convex programming, version 2.1
Michael Grant and Stephen Boyd · 2014
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An accelerated forward-backward algorithm for monotone inclusions
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