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A theorem of McCann shows that for any two absolutely continuous probability measures on R^d there exists a monotone transformation sending one probability measure to the other.
Differential and Integral Calculus
R. Courant · 1936
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Theory of reproducing kernels
N. Aronszajn · 1950
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Real and complex analysis
W. Rudin · 1966
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Estimation of the mean of a multivariate normal distribution
C. Stein · 1981
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Spline Models for Observational Data
G. Wahba · 1990
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Topics in matrix analysis
R. Horn and C. Johnson · 1991
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Existence and uniqueness of monotone measure-preserving maps
R. McCann · 1995
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Variational problems on flows of diffeomorphisms for image matching
P. Dupuis, U. Grenander, and M. Miller · 1998
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Computational anatomy: an emerging discipline
U. Grenander and M. Miller · 1998
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Diffeomorphisms groups and pattern matching in image analysis
A Trouvé · 1998
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Large deformation fluid diffeomorphisms for landmark and image matching
M Miller, S Joshi, and G Christensen · 1999
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Group actions, homeomorphisms, and matching: A general framework
M. Miller and L. Younes · 2001
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The euler-lagrange equation for interpolating sequence of landmark datasets
M. Beg, M. Miller, A. Trouvé, and L. Younes · 2003
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Use of exchangeable pairs in the analysis of simulations
C. Stein, P. Diaconis, S. Holmes, and G. Reinert · 2004
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Statistics on diffeomorphisms via tangent space representations
M. Vaillant, M. Miller, L. Younes, and A. Trouvé · 2004
Cited alongside, same era.
Stein’s method for normal approximation
L. Chen and Q. Shao · 2005
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Local geometry of deformable templates
A. Trouvé and Younes L · 2005
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Computing anb average anatomical atlas using lddmm and geodesic shooting
M. Beg and A. Khan · 2006
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Geodesic shooting for computational anatomy
M. Miller, A. Trouvé, and L. Younes · 2006
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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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Transport of relational structures in groups of diffeomorphisms
L. Younes, A. Qiu, R. Winslow, and M. Miller · 2008
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Computing large deformation metric mappings via geodesic flows of diffeomorphisms
M. Beg, M. Miller, A. Trouvé, and L. Younes · 2005
Cited alongside, same era.
Large deformation diffeomorphic metric mapping of vector fields
Y. Cao, M. Miller, R. Winslow, and L. Younes · 2005
Cited alongside, same era.
Shapes and diffeomorphisms
L. Younes · 2010
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Two-dimensional density estimation using smooth invertible transformations
E. Anderes and M. Coram · 2011
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