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

Ananda Bandulasiri, Rabi N. Bhattacharya and Vic Patrangenaru

Journal of Multivariate Analysis, 2009, vol. 100, issue 9, 1867-1882

Abstract: For all p>2,k>p, a size-and-reflection-shape space of k-ads in general position in , 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 , a space of orbits of scaled k-ads in general position under the group of isometries of , 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 is extended to an equivariant embedding of the size-and-shape manifold , which is useful in the analysis of size-and-shape. Four medical imaging applications are provided to illustrate the theory.

Keywords: Reflection; shape; Size-and-shape; Size-and-reflection-shape; Statistics; on; manifolds; Extrinsic; means; Nonparametric; bootstrap; Confidence; region; Statistical; methods; in; medical; imaging; Protein; structures (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (5)

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