Nonparametric estimation of means on Hilbert manifolds and extrinsic analysis of mean shapes of contours

Leif Ellingson, Vic Patrangenaru, Frits Ruymgaart

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample spaces. To perform inference on these means, we appeal to the concept of neighborhood hypotheses from functional data analysis and derive a one-sample test. We then consider the analysis of shapes of contours lying in the plane. By embedding the corresponding sample space of such shapes, which is a Hilbert manifold, into a space of Hilbert-Schmidt operators, we can define extrinsic mean shapes of random planar contours and their sample analogues. We then apply the general methods to this problem while considering the computational restrictions faced when utilizing digital imaging data. Comparisons of computational cost are provided to another method for analyzing shapes of contours.

Original languageEnglish
Pages (from-to)317-333
Number of pages17
JournalJournal of Multivariate Analysis
StatePublished - Nov 2013


  • Automated randomized landmark selection
  • Data analysis on Hilbert manifolds
  • Digital image analysis
  • Extrinsic mean
  • Nonparametric bootstrap
  • Planar contours
  • Statistical shape analysis


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