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Shape Statistics: Procrustes Superimpositions and Tangent Spaces

Shape Statistics: Procrustes Superimpositions and Tangent Spaces The shape of a set of labeled points corresponds to those attributes of the configuration that are invariant to the effects of translation, rotation, and scale. Procrustes distance may be used to compare different shapes and also serve as a metric that may be used to define multidimensional shape spaces. This paper demonstrates that the preshape space of planar triangles Procrustes aligned to a reference triangle corresponds to a unit hemisphere. An overview of methods used as linear approximations of D. G. Kendall's non-Euclidean shape space is given, and the equivalence of several methods based on orthogonal projections is shown. Some problems with approximations based on stereo graphic projections are also discussed. A simple example using artificial data is included. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Classification Springer Journals

Shape Statistics: Procrustes Superimpositions and Tangent Spaces

Rohlf, F. James
Journal of Classification , Volume 16 (2) – Feb 28, 2014
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27 pages

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Publisher
Springer Journals
Copyright
Copyright © 1999 by Springer-Verlag New York Inc.
Subject
Statistics; Statistical Theory and Methods; Pattern Recognition; Bioinformatics; Signal, Image and Speech Processing; Psychometrics; Marketing
ISSN
0176-4268
eISSN
1432-1343
DOI
10.1007/s003579900054
Publisher site
See Article on Publisher Site

Abstract

The shape of a set of labeled points corresponds to those attributes of the configuration that are invariant to the effects of translation, rotation, and scale. Procrustes distance may be used to compare different shapes and also serve as a metric that may be used to define multidimensional shape spaces. This paper demonstrates that the preshape space of planar triangles Procrustes aligned to a reference triangle corresponds to a unit hemisphere. An overview of methods used as linear approximations of D. G. Kendall's non-Euclidean shape space is given, and the equivalence of several methods based on orthogonal projections is shown. Some problems with approximations based on stereo graphic projections are also discussed. A simple example using artificial data is included.

Journal

Journal of Classification – Springer Journals

Published: Feb 28, 2014

There are no references for this article.