TY - GEN

T1 - Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data

T2 - International Conference on Probability Theory and Statistical Physics, 2016

AU - Bhattacharya, Rabi

AU - Lin, Lizhen

N1 - Publisher Copyright:
© Springer Nature Singapore Pte Ltd. 2019.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Fréchet means

KW - Image analysis

KW - Nonparametric Bayes

KW - Nonparametric inference on manifolds

KW - Statistics on manifolds

KW - Stratified spaces

UR - http://www.scopus.com/inward/record.url?scp=85085734856&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85085734856&partnerID=8YFLogxK

U2 - 10.1007/978-981-15-0298-9_1

DO - 10.1007/978-981-15-0298-9_1

M3 - Conference contribution

AN - SCOPUS:85085734856

SN - 9789811502972

T3 - Springer Proceedings in Mathematics and Statistics

SP - 1

EP - 43

BT - Sojourns in Probability Theory and Statistical Physics - II - Brownian Web and Percolation, A Festschrift for Charles M. Newman

A2 - Sidoravicius, Vladas

PB - Springer

Y2 - 25 March 2016 through 27 March 2016

ER -