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

Ananda Bandulasiri, Rabindra N Bhattacharya, Vic Patrangenaru

Research output: Contribution to journalArticle

20 Citations (Scopus)

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 2009

Fingerprint

Nonparametric Inference
Medical Imaging
Medical imaging
Shape Space
Statistical methods
Equivariant
Statistical Analysis
Smooth Manifold
Orbits
Symmetric matrix
Isometry
Orbit
Three-dimensional
Invariant
Imaging
Inference
Methodology
Statistical analysis

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, Probability and Uncertainty
  • Numerical Analysis
  • Statistics and Probability

Cite this

Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging. / Bandulasiri, Ananda; Bhattacharya, Rabindra N; Patrangenaru, Vic.

In: Journal of Multivariate Analysis, Vol. 100, No. 9, 10.2009, p. 1867-1882.

Research output: Contribution to journalArticle

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