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In this paper the optimal transport and the metamorphosis perspectives are combined.
On the translocation of masses
Leonid Vital’evich Kantorovitch · 1942
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Theory of sound: Vol. 2
J.W. Strutt · 1945
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On a problem of monge
Leonid Vital’evich Kantorovich · 1948
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On the volume elements on a manifold
Jürgen Moser · 1965
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Sur la géométrie différentielle des groupes de lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits
Vladimir Arnold · 1966
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Lectures in pattern theory volume
U Grenander · 1981
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Weak lower semicontinuous envelope of functionals defined on a space of measures
Luigi Ambrosio and Giuseppe Buttazzo · 1988
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Mathematical Elasticity, Volume I: Three-dimensional elasticity
Philippe G. Ciarlet · 1988
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Multipolar viscous fluids
J. Nečas and M. Šilhavý · 1991
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Topological methods in hydrodynamics
V. Arnold and B. Khesin · 1998
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Variational problems on flows of diffeomorphisms for image matching
D. Dupuis, U. Grenander, and M.I. Miller · 1998
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Variational problems on flows of diffeomorphisms for image matching
Paul Dupuis, Ulf Grenander, and Michael I Miller · 1998
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Partial differential equations and Monge-Kantorovich mass transfer
Lawrence C. Evans · 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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A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
Jean-David Benamou and Yann Brenier · 2000
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Landmark matching via large deformation diffeomorphisms
S. C. Joshi and M. I. Miller · 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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Group actions, homeomorphisms, and matching: a general framework
M. I. Miller and L. Younes · 2001
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Computational anatomy: Computing metrics on anatomical shapes
M. F. Beg, M.I. Miller, A. Trouvé, and L. Younes · 2002
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On the metrics and Euler-Lagrange equations of computational anatomy
M.I. Miller, A. Trouvé, and L. Younes · 2002
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Minimizing Flows for the Monge–Kantorovich Problem
Sigurd Angenent, Steven Haker, and Allen Tannenbaum · 2003
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Lecture notes on optimal transport problems
Luigi Ambrosio · 2003
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Topics in optimal transportation
Cédric Villani · 2003
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Area-preserving mappings for the visualization of medical structures
Lei Zhu, Steven Haker, and Allen Tannenbaum · 2003
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Principal geodesic analysis for the study of nonlinear statistics of shape
P.T. Fletcher, Conglin Lu, S.M. Pizer, and Sarang Joshi · 2004
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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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Computing large deformation metric mappings via geodesic flows of diffeomorphisms
M. Faisal Beg, Michael I. Miller, Alain Trouvé, and Laurent Younes · 2005
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A mixed finite element method for nonlinear diffusion equations
Martin Burger, José A. Carrillo, and Marie-Therese Wolfram · 2010
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A gradient flow scheme for nonlinear fourth order equations
Bertram Düring, Daniel Matthes, and Josipa Pina Milišic · 2010
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An efficient numerical method for the solution of the L2 optimal mass transfer problem
Eldad Haber, Tauseef Rehman, and Allen Tannenbaum · 2010
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Geodesic methods in computer vision and graphics
Gabriel Peyré, Mickael Péchaud, Renaud Keriven, and Laurent D Cohen · 2010
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Geodesic shape retrieval via optimal mass transport
Julien Rabin, Gabriel Peyré, and Laurent D Cohen · 2010
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A model for the optimal planning of an urban area
Giuseppe Buttazzo and Filippo Santambrogio · 2005
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Numerical solution of the Monge–Ampère equation by a Newton’s algorithm
Grégoire Loeper and Francesca Rapetti · 2005
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Metamorphoses through Lie group action
Alain Trouvé and Laurent Younes · 2005
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Gradient flows: in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2006
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Numerical methods for fully nonlinear elliptic equations of the Monge–Ampère type
Edward J Dean and Roland Glowinski · 2006
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Histogram based segmentation using Wasserstein distances
Tony Chan, Selim Esedoglu, and Kangyu Ni · 2007
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Louis-Philippe Saumier, Martial Agueh, and Boualem Khouider · 2010
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Conformal Wasserstein distances: Comparing surfaces in polynomial time
Yaron Lipman and Ingrid Daubechies · 2011
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Gromov–Wasserstein distances and the metric approach to object matching
Facundo Mémoli · 2011
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Wasserstein regularization of imaging problem
Julien Rabin and Gabriel Peyré · 2011
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A continuum mechanical approach to geodesics in shape space
Benedikt Wirth, Leah Bar, Martin Rumpf, and Guillermo Sapiro · 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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Classification of periodic activities using the Wasserstein distance
Laurent Oudre, Jérémie Jakubowicz, Pascal Bianchi, and Chantal Simon · 2012
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Wasserstein active contours
Gabriel Peyré, Jalal Fadili, and Julien Rabin · 2012
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Wasserstein barycenter and its application to texture mixing
Julien Rabin, Gabriel Peyré, Julie Delon, and Marc Bernot · 2012
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Regularized discrete optimal transport
Sira Ferradans, Nicolas Papadakis, Julien Rabin, Gabriel Peyré, and Jean-François Aujol · 2013
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A Hierarchical Approach to Optimal Transport
Bernhard Schmitzer and Christoph Schnörr · 2013
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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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Optimal transport with proximal splitting
Nicolas Papadakis, Gabriel Peyré, and Edouard Oudet · 2014
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Variational time discretization of geodesic calculus
Martin Rumpf and Benedikt Wirth · 2014
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Time Discrete Geodesic Paths in the Space of Images
B. Berkels, A. Effland, and M. Rumpf · 2015
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