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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Bandulasiri, Ananda²  Bhattacharya, Rabi N.³  Patrangenaru, Vic¹ 

[1] Florida State Univ, Dept Stat, Tallahassee, FL 32306 USA

[2] Sam Houston State Univ, Dept Math & Stat, Huntsville, TX 77341 USA

[3] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

关键词: 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;   

DOI  :  10.1016/j.jmva.2009.03.007

来源: Elsevier

【 摘 要 】

For all p > 2, k > p, a size-and-reflection-shape space SR Sigma(k)(p, 0) of k-ads in general position in R-p, 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 Sigma(k)(p, 0) a space of orbits of scaled k-ads in general position under the group of isometries of R-p, 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 Sigma(k)(2) is extended to an equivariant embedding of the size-and-shape manifold S Sigma(k)(2), which is useful in the analysis of size-and-shape. Four medical imaging applications are provided to illustrate the theory. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free