A multi-dimensional scaling approach to shape analysis

Dryden, Ian L and Kume, Alfred and Le, Huiling and Wood, Andrew T.A. (2008) A multi-dimensional scaling approach to shape analysis. Biometrika, 95 (4). pp. 779-798. ISSN 0006-3444. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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We propose an alternative to Kendall's shape space for reflection shapes of configurations in Rm with k labelled vertices, where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations. The proposed approach embeds the space of such shapes into the space P( k - 1) of ( k - 1) x ( k - 1) real symmetric positive semidefinite matrices, which is the closure of an open subset of a Euclidean space, and defines mean shape as the natural projection of Euclidean means in P( k - 1) on to the embedded copy of the shape space. This approach has strong connections with multi- dimensional scaling, and the mean shape so defined gives good approximations to other commonly used definitions of mean shape. We also use standard perturbation arguments for eigenvalues and eigenvectors to obtain a central limit theorem which then enables the application of standard statistical techniques to shape analysis in two or more dimensions.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Suzanne Duffy
Date Deposited: 11 Mar 2010 11:23
Last Modified: 04 Jul 2014 15:54
Resource URI: https://kar.kent.ac.uk/id/eprint/15045 (The current URI for this page, for reference purposes)
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