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

Rabindra N Bhattacharya, Vic Patrangenaru

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalJournal of Statistical Planning and Inference
Volume145
DOIs
StatePublished - Feb 2014

Fingerprint

Landmarks
Image Analysis
Image analysis
Statistics
Stratified Space
Shape Space
Nonparametric Inference
Machine Vision
Computer vision
Data analysis
Diagnostics
Inference
Machine vision

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, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

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