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Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
TLDR
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
TLDR
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
TLDR
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.
Geodesic Regression for Image Time-Series
TLDR
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.
Simultaneous Multi-scale Registration Using Large Deformation Diffeomorphic Metric Mapping
TLDR
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
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
TLDR
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.
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