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We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks.
Les élèments aléatoires de nature quelconque dans un espace distancié
Maurice Fréchet · 1948
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On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures
I. Girsanov · 1960
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Bounds for the fundamental solution of a parabolic equation
D. G. Aronson · 1967
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Orbits of families of vector fields and integrability of distributions
Héctor J Sussmann · 1973
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Maximum likelihood from incomplete data via the EM algorithm
A. P. Dempster, N. M. Laird, and D. B. Rubin · 1977
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Shape manifolds, procrustean metrics, and complex projective spaces
David G Kendall · 1984
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Moment invariants for the vlasov equation
DD Holm, WP Lysenko, and JC Scovel · 1990
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Brownian Motion and Stochastic Calculus
Ioannis Karatzas and Steven E Shreve · 1991
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An integrable shallow water equation with peaked solitons
Roberto Camassa and Darryl D Holm · 1993
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General Pattern Theory: A Mathematical Study of Regular Structures
Ulf Grenander · 1994
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An infinite dimensional group approach for physics based models in pattern recognition
Alain Trouvé · 1995
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Deformable templates using large deformation kinematics
Gary E. Christensen, Richard Rabbitt, and Michael I. Miller · 1996
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Statistical methods in computational anatomy
M. Miller, A. Banerjee, G. Christensen, S. Joshi, N. Khaneja, U. Grenander, and L. Matejic · 1997
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Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces
Rainer Storn and Kenneth Price · 1997
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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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The Euler–Poincaré equations and semidirect products with applications to continuum theories
Darryl D Holm, Jerrold E Marsden, and Tudor S Ratiu · 1998
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A view of the EM algorithm that justifies incremental, sparse, and other variants
Radford M Neal and Geoffrey E Hinton · 1998
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Introduction to Mechanics and Symmetry
Jerrold E. Marsden and Tudor S. Ratiu · 1999
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On the metrics and Euler–Lagrange equations of computational anatomy
Michael I Miller, Alain Trouvé, and Laurent Younes · 2002
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Stochastic Differential Equations: An Introduction with Applications
Bernt Øksendal · 2003
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Unbiased diffeomorphic atlas construction for computational anatomy
Sarang Joshi, Brad Davis, Matthieu Jomier, and Guido Gerig · 2004
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Statistics on diffeomorphisms via tangent space representations
M. Vaillant, M.I. Miller, L. Younes, and A. Trouvé · 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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Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the epdiff equation
Darryl D. Holm and Jerrold E Marsden · 2005
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Simulation of conditioned diffusion and application to parameter estimation
Bernard Delyon and Ying Hu · 2006
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Towards a coherent statistical framework for dense deformable template estimation
Stephanie Allassonnière, Yali Amit, and Alain Trouvé · 2007
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Geometric dissipation in kinetic equations
Darryl D. Holm, Vakhtang Putkaradze, and Cesare Tronci · 2007
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Parametric inference for mixed models defined by stochastic differential equations
Geometry of image registration: The diffeomorphism group and momentum maps
Martins Bruveris and Darryl D Holm · 2015
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Variational principles for stochastic fluid dynamics
Darryl D Holm · 2015
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Anisotropic Distributions on Manifolds: Template Estimation and Most Probable Paths
Stefan Sommer · 2015
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Diffeomorphic Image Matching with Left-Invariant Metrics
Tanya Schmah, Laurent Risser, and François-Xavier Vialard · 2015
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Existence and uniqueness for stochastic 2D Euler flows with bounded vorticity
Zdzisław Brzeźniak, Franco Flandoli, and Mario Maurelli · 2016
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Simulation of multivariate diffusion bridges
Mogens Bladt, Samuel Finch, and Michael Sørensen · 2016
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Bayesian template estimation in computational anatomy
Jun Ma, Michael I. Miller, Alain Trouvé, and Laurent Younes · 2008
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Evolutions equations in computational anatomy
Laurent Younes, Felipe Arrate, and Michael I. Miller · 2009
Cited alongside, same era.
Double-bracket dissipation in kinetic theory for particles with anisotropic interactions
Darryl D Holm, Vakhtang Putkaradze, and Cesare Tronci · 2010
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Shapes and Diffeomorphisms
Laurent Younes · 2010
Cited alongside, same era.
The momentum map representation of images
Martins Bruveris, François Gay-Balmaz, Darryl D Holm, and Tudor S Ratiu · 2011
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Geometric Mechanics - Part I: Dynamics and Symmetry
Darryl D. Holm · 2011
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Statistical Shape Analysis: With Applications in R
Ian L Dryden and Kanti V Mardia · 2016
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Stochastic discrete hamiltonian variational integrators
Darryl D Holm and Tomasz M Tyranowski · 2016
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Variational principles for stochastic soliton dynamics
Darryl D Holm and Tomasz M Tyranowski · 2016
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Theano: A Python framework for fast computation of mathematical expressions
Theano Development Team · 2016
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A stochastic large deformation model for computational anatomy
Alexis Arnaudon, Darryl D Holm, Akshay Pai, and Stefan Sommer · 2017
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Solution properties of a 3D stochastic Euler fluid equation
Dan Crisan, Franco Flandoli, and Darryl D Holm · 2017
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Momentum maps and stochastic clebsch action principles
Ana Bela Cruzeiro, Darryl D Holm, and Tudor S Ratiu · 2017
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Differential geometry and stochastic dynamics with deep learning numerics
Line Kühnel, Alexis Arnaudon, and Stefan Sommer · 2017
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Most Likely Separation of Intensity and Warping Effects in Image Registration
Line Kühnel, Stefan Sommer, Akshay Pai, and Lars Lau Raket · 2017
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Langevin equations for landmark image registration with uncertainty
Stephen Marsland and Tony Shardlow · 2017
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Bridge Simulation and Metric Estimation on Landmark Manifolds
Stefan Sommer, Alexis Arnaudon, Line Kuhnel, and Sarang Joshi · 2017
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Guided proposals for simulating multi-dimensional diffusion bridges
Moritz Schauer, Frank van der Meulen, and Harry van Zanten · 2017
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Learning Shape Trends: Parameter Estimation in Diffusions on Shape Manifolds
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Continuous-discrete smoothing of diffusions
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Noise and dissipation on coadjoint orbits
Alexis Arnaudon, Alex L Castro, and Darryl D Holm · 2018
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Stochastic geometric models with non-stationary spatial correlations in lagrangian fluid flows
François Gay-Balmaz and Darryl D. Holm · 2018
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