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Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces.
“La géométrie des espaces de Riemann”
Élie Cartan · 1925
Earlier work this paper cites.
“On the translocation of masses”
Leonid Kantorovich · 1942
Earlier work this paper cites.
“Introduction to integral geometry”
Luis Santal“’o · 1953
Earlier work this paper cites.
“A congruence theorem for trees.”
Paul Kelly · 1957
Earlier work this paper cites.
“A collection of mathematical problems”
Stanislaw Ulam · 1960
Earlier work this paper cites.
“Uniqueness theorems for surfaces in the large”
Aleksandr Aleksandrov · 1962
Earlier work this paper cites.
“Linear-intercept distributions do not characterize plane sets”
CL Mallows and JMC Clark · 1970
Earlier work this paper cites.
“Eigenvalue comparison theorems and its geometric applications”
Shiu-Yuen Cheng · 1975
Earlier work this paper cites.
“A counterexample to a theorem of S. Piccard”
Gary Bloom · 1977
Earlier work this paper cites.
“Beziehungen zwischen der Sehnenlängenverteilung und der Verteilung des Abstandes zweier zufälliger Punkte im Eikörper”
Frank Piefke · 1978
Earlier work this paper cites.
“Riemannian geometry as determined by the volumes of small geodesic balls”
A Gray and Lieven Vanhecke · 1979
Earlier work this paper cites.
“A topological application of the isoperimetric inequality”
Mikhael Gromov and Vitali Milman · 1983
Earlier work this paper cites.
“Hyperbolic groups”
Mikhael Gromov · 1987
Earlier work this paper cites.
“Volume of a small extrinsic ball in a submanifold”
Leon Karp and Mark Pinsky · 1989
Earlier work this paper cites.
“Polar factorization and monotone rearrangement of vector-valued functions”
Yann Brenier · 1991
Earlier work this paper cites.
“Special ball-homogeneous spaces”
G Calvaruso and L Vanhecke · 1997
Earlier work this paper cites.
“Modern graph theory”
B“’ela Bollob“’as and Bela Bollobas · 1998
Earlier work this paper cites.
“Semi-symmetric ball-homogeneous spaces and a volume conjecture”
G Calvaruso and Lieven Vanhecke · 1998
Earlier work this paper cites.
“A course in metric geometry”
Dmitri Burago, Yuri Burago and Sergei Ivanov · 2001
Earlier work this paper cites.
“Modeling the 3D coronary tree for labeling purposes”
Claire Chalopin, G“’erard Finet and Isabelle Magnin · 2001
Earlier work this paper cites.
“Polar factorization of maps on Riemannian manifolds”
Robert McCann · 2001
Earlier work this paper cites.
“Algebraic Topology”
Allen Hatcher · 2002
Earlier work this paper cites.
“Shape distributions”
Robert Osada, Thomas Funkhouser, Bernard Chazelle and David Dobkin · 2002
Earlier work this paper cites.
“Geometric structures as determined by the volume of generalized geodesic balls”
Neda Bokan, Mirjana Djori“’c and Udo Simon · 2003
Earlier work this paper cites.
“Reconstructing sets from interpoint distances”
Paul Lemke, Steven Skiena and Warren Smith · 2003
Earlier work this paper cites.
“Topics in optimal transportation”
C“’edric Villani · 2003
Earlier work this paper cites.
“On reconstructing n-point configurations from the distribution of distances or areas”
Mireille Boutin and Gregor Kemper · 2004
Earlier work this paper cites.
“The interpoint distance distribution as a descriptor of point patterns, with an application to spatial disease clustering”
Marco Bonetti and Marcello Pagano · 2005
Earlier work this paper cites.
“Tree matching applied to vascular system”
Arnaud Charnoz et al · 2005
Earlier work this paper cites.
“Robust global registration”
Natasha Gelfand, Niloy Mitra, Leonidas Guibas and Helmut Pottmann · 2005
Earlier work this paper cites.
“Diversity of ganglion cells in the mouse retina: unsupervised morphological classification and its limits”
Jee-Hyun Kong, Daniel Fish, Rebecca Rockhill and Richard Masland · 2005
Earlier work this paper cites.
“Matching with shape contexts”
Serge Belongie, Greg Mori and Jitendra Malik · 2006
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“Differential Geometry: Curves - Surfaces - Manifolds”, Student mathematical library
W. K“”uhnel and B. Hunt · 2006
Cited alongside, same era.
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Yonggang Shi et al · 2007
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“Signed chord length distribution. I”
Alexander Vlasov · 2007
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Filippo Santambrogio · 2015
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Jos“’e Berrendero, Antonio Cuevas and Beatriz Pateiro-L“’opez · 2016
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“Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition”
Manfredo Do · 2016
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