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ON SIMPLEX SHAPE SPACES

Published online by Cambridge University Press:  30 October 2001

HUILING LE  and
DENNIS BARDEN
HUILING LE
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD
DENNIS BARDEN
Affiliation:
Girton College, Cambridge CB3 0JG
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Abstract

The right-invariant Riemannian metric on simplex shape spaces in fact makes them particular Riemannian symmetric spaces of non-compact type. In the paper, the general properties of such symmetric spaces are made explicit for simplex shape spaces. In particular, a global matrix coordinate representation is suggested, with respect to which several geometric features, important for shape analysis, have simple and easily computable expressions. As a typical application, it is shown how to locate the Fréchet means of a class of probability measures on the simplex shape spaces, a result analogous to that for Kendall's shape spaces.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 501 - 512
Copyright
The London Mathematical Society 2001

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