Statistics on manifolds and landmarks based image analysis: A nonparametric theory with applications

Rabi Bhattacharya; Vic Patrangenaru

doi:10.1016/j.jspi.2013.08.001

Statistics on manifolds and landmarks based image analysis: A nonparametric theory with applications

Rabi Bhattacharya
, Vic Patrangenaru

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

This paper provides an exposition of some recent developments in nonparametric inference on manifolds, along with a brief account of an emerging theory on data analysis on stratified spaces. Much of the theory is developed around the notion of Fréceht means with applications, for the most part, to landmark based shape spaces. A number of applications are illustrated with real data in such areas as paleomagnetism, morphometrics and medical diagnostics. Connections to scene recognition and machine vision are also explored.

Original language	English (US)
Pages (from-to)	1-22
Number of pages	22
Journal	Journal of Statistical Planning and Inference
Volume	145
DOIs	https://doi.org/10.1016/j.jspi.2013.08.001
State	Published - Feb 2014

Keywords

Fre'chet mean
Nonparametric inference on manifolds Kendall's shape spaces
Projective shape spaces
Reflection similarity shape
Stratified spaces

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1016/j.jspi.2013.08.001

Cite this

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title = "Statistics on manifolds and landmarks based image analysis: A nonparametric theory with applications",

abstract = "This paper provides an exposition of some recent developments in nonparametric inference on manifolds, along with a brief account of an emerging theory on data analysis on stratified spaces. Much of the theory is developed around the notion of Fr{\'e}ceht means with applications, for the most part, to landmark based shape spaces. A number of applications are illustrated with real data in such areas as paleomagnetism, morphometrics and medical diagnostics. Connections to scene recognition and machine vision are also explored.",

keywords = "Fre'chet mean, Nonparametric inference on manifolds Kendall's shape spaces, Projective shape spaces, Reflection similarity shape, Stratified spaces",

author = "Rabi Bhattacharya and Vic Patrangenaru",

note = "Funding Information: Many thanks go to our colleagues of the SAMSI Working Group (2010–2011) on sampling from stratified spaces, especially to Steve Marron and the group co-leaders Ezra Miller and Stephan Huckemann, and to Xiuwen Liu and Leif Ellingson for related joint work. We are also grateful to Susan Holmes for giving us access to her talks on phylogenetic trees in the Working Group of Trees at SAMSI in Fall 2010. The authors gratefully acknowledge support from NSF grants DMS-0806011 , 1107053 and DMS-0805977 , 1106935 .",

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language = "English (US)",

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T2 - A nonparametric theory with applications

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AU - Patrangenaru, Vic

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PY - 2014/2

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AB - This paper provides an exposition of some recent developments in nonparametric inference on manifolds, along with a brief account of an emerging theory on data analysis on stratified spaces. Much of the theory is developed around the notion of Fréceht means with applications, for the most part, to landmark based shape spaces. A number of applications are illustrated with real data in such areas as paleomagnetism, morphometrics and medical diagnostics. Connections to scene recognition and machine vision are also explored.

KW - Fre'chet mean

KW - Nonparametric inference on manifolds Kendall's shape spaces

KW - Projective shape spaces

KW - Reflection similarity shape

KW - Stratified spaces

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DO - 10.1016/j.jspi.2013.08.001

M3 - Article

AN - SCOPUS:84887606917

SN - 0378-3758

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SP - 1

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JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

ER -

Statistics on manifolds and landmarks based image analysis: A nonparametric theory with applications

Abstract

Keywords

ASJC Scopus subject areas

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