Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments
Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments
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DOI：
10.1007/978-981-15-0298-9_1
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发表时间：
2018-01
期刊：
影响因子：
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通讯作者：
R. Bhattacharya;Lizhen Lin
中科院分区：
文献类型：
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作者：
R. Bhattacharya;Lizhen Lin
本文提供了一个非参数分析的数字观测图像和其他非欧几里德对象的最新方法的阐述。在度量空间（如流形和分层空间）上的弗雷歇分布方法在这奋进发挥了重要作用。除了理论问题的唯一性的Fréchet极小和样本Fréchet平均值的渐近分布下的唯一性，应用图像分析突出。此外，非参数贝叶斯理论被用于流形上的密度估计和分类问题。
This article provides an exposition of recent methodologies for nonparametric analysis of digital observations on images and other non-Euclidean objects. Fréchet means of distributions on metric spaces, such as manifolds and stratified spaces, have played an important role in this endeavor. Apart from theoretical issues of uniqueness of the Fréchet minimizer and the asymptotic distribution of the sample Fréchet mean under uniqueness, applications to image analysis are highlighted. In addition, nonparametric Bayes theory is brought to bear on the problems of density estimation and classification on manifolds.