Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments

01/03/2018

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by   Rabi Bhattacharya, et al.

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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.