Diffeomorphic Density Matching by Optimal Information Transport
Diffeomorphic Density Matching by Optimal Information Transport
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DOI：
10.1137/151006238
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发表时间：
2015-01-01
影响因子：
2.1
通讯作者：
Modin, Klas
中科院分区：
文献类型：
--
作者：
Bauer, Martin;Joshi, Sarang;Modin, Klas
我们解决以下问题：给定流形上的两个光滑密度，找到将一个密度转换为另一个密度的最优微分同构。我们的框架建立在概率密度空间上的Fisher-Rao信息度量和无限维微分同态流形上的右不变度量之间的联系上。这种最优信息传输及其修改，使我们能够构建密度匹配的数值算法。该算法比基于最优质量输运或差分配准的算法本质上更有效。我们的方法在医学图像配准、纹理映射、图像变形、非均匀随机采样和网格自适应等方面都有应用。其中一些应用程序在示例中进行了说明。
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.