Anisotropic Distributions on Manifolds: Template Estimation and Most Probable Paths
Anisotropic Distributions on Manifolds: Template Estimation and Most Probable Paths
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流形上的各向异性分布：模板估计和最可能路径
DOI：
10.1007/978-3-319-19992-4_15
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
S. Sommer
中科院分区：
文献类型：
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作者：
S. Sommer
我们利用各向异性扩散过程将正态分布推广到流形，并构造了一个基于流形值数据的模板和协方差结构的似然估计框架。该过程避免了当在平均值的切空间中执行PCA之前首次估计平均值或模板时出现的线性化。我们推导了到达采样数据点的最可能路径的流动方程，并且我们使用通常不是测地线的路径来估计模型的可能性。与现有的模板估计方法相比，考虑各向异性会导致算法不基于测地线距离。为了说明各向异性的影响并指出进一步的应用，我们在地标匹配问题中出现的球面和有限维LDDMM流形上进行了各向异性分布的实验。
We use anisotropic diffusion processes to generalize normal distributions to manifolds and to construct a framework for likelihood estimation of template and covariance structure from manifold valued data. The procedure avoids the linearization that arise when first estimating a mean or template before performing PCA in the tangent space of the mean. We derive flow equations for the most probable paths reaching sampled data points, and we use the paths that are generally not geodesics for estimating the likelihood of the model. In contrast to existing template estimation approaches, accounting for anisotropy thus results in an algorithm that is not based on geodesic distances. To illustrate the effect of anisotropy and to point to further applications, we present experiments with anisotropic distributions on both the sphere and finite dimensional LDDMM manifolds arising in the landmark matching problem.