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This paper is concerned by the study of barycenters for random probability measures in the Wasserstein space.
Les éléments aléatoires de nature quelconque dans un espace distancié
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Relations between weak and uniform convergence of measures with applications
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Strong law of large numbers for measures of central tendency and dispersion of random variables in compact metric spaces
H. Sverdrup-Thygeson · 1981
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Procrustes methods in the statistical analysis of shape
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General pattern theory - A mathematical study of regular structures
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Convex analysis and variational problems
I. Ekeland and R. Témam · 1999
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On a product of positive semidefinite matrices
A.R. Meenakshi and C. Rajian · 1999
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Large sample theory of intrinsic and extrinsic sample means on manifolds (i)
R. Bhattacharya and V. Patrangenaru · 2003
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On the Monge-Kantorovich problem and image warping
S. Haker and A. Tannenbaum · 2003
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Probability measures on metric spaces of nonpositive curvature
K.-T. Sturm · 2003
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Topics in Optimal Transportation
C. Villani · 2003
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Optimal mass transport for registration and warping
S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent · 2004
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Large sample theory of intrinsic and extrinsic sample means on manifolds (ii)
R. Bhattacharya and V. Patrangenaru · 2005
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Local geometry of deformable templates
A. Trouvé and L. Younes · 2005
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Towards a coherent statistical framework for dense deformable template estimation
S. Allassonnière, Y. Amit, and A. Trouvé · 2007
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Semi-parametric estimation of shifts
F. Gamboa, J.-M. Loubes, and E. Maza · 2007
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Pattern Theory: From Representation to Inference
U. Grenander and M. Miller · 2007
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J. Bigot, S. Gadat, and J.M. Loubes · 2009
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Wassertein barycenter and its applications to texture mixing
J. Rabin, G. Peyré, J. Delon, and M. Bernot · 2011
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Shape spaces
A. Trouvé and L. Younes · 2011
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Stochastic algorithms for computing means of probability measures
M. Arnaudon, C. Dombry, A. Phan, and L. Yang · 2012
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Statistical models for deformable templates in image and shape analysis
S. Allassonnière, J. Bigot, J. Glaunès, F. Maire, and F. Richard · 2013
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Optimal transportation with infinitely many marginals
B. Pass · 2013
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Fast computation of wasserstein barycenters
M. Cuturi and A. Doucet · 2014
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