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Diffeomorphic density matching by optimal information transport

Journal article
Authors M. Bauer
S. Joshi
Klas Modin
Published in SIAM Journal on Imaging Sciences
Volume 8
Issue 3
Pages 1718-1751
Publication year 2015
Published at Department of Mathematical Sciences, Mathematics
Pages 1718-1751
Language en
Keywords Density matching , Diffeomorphism groups , Fisher–rao metric , Image registration , Information geometry , Optimal transport , Random sampling
Subject categories Geometry, Computational Mathematics


We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher–Rao information metric on the space of probability densities and right-invariant metrics on the infinite-dimensional manifold of diffeomorphisms. This optimal information transport, and modifications thereof, allow us to construct numerical algorithms for density matching. The algorithms are inherently more efficient than those based on optimal mass transport or diffeomorphic registration. Our methods have applications in medical image registration, texture mapping, image morphing, nonuniform random sampling, and mesh adaptivity. Some of these applications are illustrated in examples.

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