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• W2087219114 abstract "For all p>2,k>p, a size-and-reflection-shape space SRΣp,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 RΣp,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 SΣ2k, which is useful in the analysis of size-and-shape. Four medical imaging applications are provided to illustrate the theory." @default.
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• W2087219114 date "2009-10-01" @default.
• W2087219114 modified "2023-10-11" @default.
• W2087219114 title "Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging" @default.
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• W2087219114 doi "https://doi.org/10.1016/j.jmva.2009.03.007" @default.
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