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On procrustean mean shapes and the shape of the means

Published online by Cambridge University Press:  01 July 2016

Hulling Le
Hulling Le*
Affiliation:
University of Nottingham
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Extract

Two sets of k labelled points, or configurations, in ℝm are defined to have the same shape if they differ only in translation, rotation and scaling. An important matter in practice is the estimation of the shape of the means; the shape determined by the means of data on the vertices of configurations. However, statistical models for vertices-based shapes always involve some unknown samplewise nuisance parameters associated with ambiguity of location, rotation and scaling. The use of procrustean mean shapes for a finite set of configurations, which are usually formulated directly in terms of their vertices, will enable one to eliminate these nuisance parameters.

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 336 - 337
Copyright
Copyright © Applied Probability Trust 1996 

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References

[1] Le, H. (1995) Mean size-and-shapes and mean shapes: a geometric point of view. Adv. Appl. Prob. 27, 44–55.CrossRefGoogle Scholar