Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging

Ananda Bandulasiri, Rabi N. Bhattacharya, Vic Patrangenaru

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

For all p > 2, k > p, a size-and-reflection-shape space S R Σp, 0k of k-ads in general position in Rp, invariant under translation, rotation and reflection, is shown to be a smooth manifold and is equivariantly embedded in a space of symmetric matrices, allowing a nonparametric statistical analysis based on extrinsic means. Equivariant embeddings are also given for the reflection-shape-manifold R Σp, 0k, a space of orbits of scaled k-ads in general position under the group of isometries of Rp, providing a methodology for statistical analysis of three-dimensional images and a resolution of the mathematical problems inherent in the use of the Kendall shape spaces in p-dimensions, p > 2. The Veronese embedding of the planar Kendall shape manifold Σ2k is extended to an equivariant embedding of the size-and-shape manifold S Σ2k, which is useful in the analysis of size-and-shape. Four medical imaging applications are provided to illustrate the theory.

Original languageEnglish (US)
Pages (from-to)1867-1882
Number of pages16
JournalJournal of Multivariate Analysis
Volume100
Issue number9
DOIs
StatePublished - Oct 1 2009

Keywords

  • Confidence region
  • Extrinsic means
  • Nonparametric bootstrap
  • Protein structures
  • Reflection shape
  • Size-and-reflection-shape
  • Size-and-shape
  • Statistical methods in medical imaging
  • Statistics on manifolds

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging'. Together they form a unique fingerprint.

  • Cite this