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May, 1989 A Survey of the Statistical Theory of Shape
David G. Kendall
Statist. Sci. 4(2): 87-99 (May, 1989). DOI: 10.1214/ss/1177012582


This is a review of the current state of the "theory of shape" introduced by the author in 1977. It starts with a definition of "shape" for a set of $k$ points in $m$ dimensions. The first task is to identify the shape spaces in which such objects naturally live, and then to examine the probability structures induced on such a shape space by corresponding structures in $\mathbf{R}^m$. Against this theoretical background one formulates and solves statistical problems concerned with shape characteristics of empirical sets of points. Some applications (briefly sketched here) are to archeology, astronomy, geography and physical chemistry. We also outline more recent work on "size-and-shape," on shapes of sets of points in riemannian spaces, and on shape-theoretic aspects of random Delaunay tessellations.


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David G. Kendall. "A Survey of the Statistical Theory of Shape." Statist. Sci. 4 (2) 87 - 99, May, 1989.


Published: May, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0672.60018
MathSciNet: MR1007558
Digital Object Identifier: 10.1214/ss/1177012582

Keywords: Central place theory , convex polygon , Delaunay tessellation , galaxy , quasar , Riemannian submersion , singular tessellation , spherical triangle , stochastic physical chemistry , void

Rights: Copyright © 1989 Institute of Mathematical Statistics


Vol.4 • No. 2 • May, 1989
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