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How to look at objects in a five-dimensional shape space: looking at geodesics

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

David G. Kendall
David G. Kendall*
Affiliation:
University of Cambridge
*
* Postal address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK.
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Abstract

This paper is the third in a series with the general title ‘How to look at the five-dimensional shape space Σ4,3. Parts I and II were concerned with distributions and diffusions respectively. Here we ‘look at’ geodesics.

Keywords

SHAPESTOCHASTIC GEOMETRYHIGH-DIMENSIONAL PLOTTING

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 35 - 43
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Menendez Pelayo, Valencia, Spain on 21–24 September 1993.

References

[1] Kendall, D. G. (1994) How to look at objects in a 5-dimensional shape-space. I: Looking at distributions. Teoriya Veroyatnost. 39, 242–247.Google Scholar
[2] Kendall, D. G. (1994) How to look at objects in a 5-dimensional shape-space. II: Looking at diffusions. In Probability, Statistics and Optimization , ed. Kelly, F. P., pp. 315–324. Wiley, Chichester.Google Scholar
[3] Le, Huiling (1991) On geodesics in euclidean shape spaces. J. London Math. Soc. (2) 44, 360–372.CrossRefGoogle Scholar
[4] Le, Huiling and Kendall, D. G. (1993) The riemannian structure of the euclidean shape spaces: a new environment for statistics. Ann. Statist. 21, 1225–1271.CrossRefGoogle Scholar
[5] O'Neill, B. (1983) Semi-riemannian Geometry. McGraw-Hill, New York.Google Scholar