Diffeomorphic density matching by optimal information transport
SIAM JOURNAL ON IMAGING SCIENCES(2015)
摘要
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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关键词
density matching,information geometry,Fisher-Rao metric,optimal transport,image registration,diffeomorphism groups,random sampling
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