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The Fréchet mean shape and the shape of the means

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Huiling Le  and
Alfred Kume
Huiling Le*
Affiliation:
University of Nottingham
Alfred Kume*
Affiliation:
University of Nottingham
*
∗ Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
∗ Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
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Abstract

We identify the Fréchet mean shape with respect to the Riemannian metric of a class of probability measures on Bookstein's shape space of labelled triangles and show, in contrast to the case of Kendall's shape space, that the Fréchet mean shape of the probability measure on Bookstein's shape space induced from independent normal distributions on vertices, having the same covariance matrix σ2I2, is not necessarily the shape of the means.

Keywords

Kendall's shape spaceBookstein's shape spaceFréchet mean shapeshape of the means

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 32 , Issue 1 , March 2000 , pp. 101 - 113
Copyright
Copyright © Applied Probability Trust 2000 

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