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Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
- Jean Feydy, Thibault Séjourné, François-Xavier Vialard, S. Amari, A. Trouvé, G. Peyré
- Computer ScienceAISTATS
- 18 October 2018
This paper studies the Sinkhorn Divergences, a family of geometric divergences that interpolates between MMD and OT, and provides theoretical guarantees for positivity, convexity and metrization of the convergence in law.
An Interpolating Distance Between Optimal Transport and Fisher–Rao Metrics
- Lénaïc Chizat, G. Peyré, Bernhard Schmitzer, François-Xavier Vialard
- Computer Science, MathematicsFound. Comput. Math.
- 1 September 2010
This paper defines a new transport metric that interpolates between the quadratic Wasserstein and the Fisher–Rao metrics and generalizes optimal transport to measures with different masses and proposes a numerical scheme making use of first-order proximal splitting methods.
Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation
- François-Xavier Vialard, L. Risser, D. Rueckert, C. Cotter
- Computer Science, MathematicsInternational Journal of Computer Vision
- 1 April 2012
The key contribution of this work is to provide an accurate estimation of the so-called initial momentum, which is a scalar function encoding the optimal deformation between two images through the Hamiltonian equations of geodesics.
Scaling algorithms for unbalanced optimal transport problems
Geodesic Regression for Image Time-Series
A generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration, which allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values.
Unbalanced optimal transport: Dynamic and Kantorovich formulations
Simultaneous Multi-scale Registration Using Large Deformation Diffeomorphic Metric Mapping
- L. Risser, François-Xavier Vialard, R. Wolz, M. Murgasova, Darryl D. Holm, D. Rueckert
- MathematicsIEEE Transactions on Medical Imaging
- 25 April 2011
The goal is to perform rich anatomical shape comparisons from volumetric images with the mathematical properties offered by the LDDMM framework, and proposes a strategy to quantitatively measure the feature differences observed at each characteristic scale separately.
Unbalanced Optimal Transport: Geometry and Kantorovich Formulation
This article presents a new class of "optimal transportation"-like distances between arbitrary positive Radon measures. These distances are defined by two equivalent alternative formulations: (i) a…
Invariant Higher-Order Variational Problems
- François Gay-Balmaz, Darryl D. Holm, D. Meier, T. Ratiu, François-Xavier Vialard
- 22 December 2010
We investigate higher-order geometric k-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in…
Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups
A variational approach for multiscale analysis of diffeomorphisms is developed in detail to generalize to several scales the semidirect product representation, and to illustrate the resulting diffeomorphic decomposition on synthetic and real images.