Statistical Science

A Survey of the Statistical Theory of Shape

David G. Kendall

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Abstract

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.

Article information

Source
Statist. Sci. Volume 4, Number 2 (1989), 87-99.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.ss/1177012582

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/ss/1177012582

Mathematical Reviews number (MathSciNet)
MR1007558

Citation

Kendall, David G. A Survey of the Statistical Theory of Shape. Statistical Science 4 (1989), no. 2, 87--99. doi:10.1214/ss/1177012582. http://projecteuclid.org/euclid.ss/1177012582.


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See also

  • See Comment: Fred L. Bookstein. [A Survey of the Statistical Theory of Shape]: Comment. Statist. Sci., Volume 4, Number 2 (1989), 99--105.
  • See Comment: Christopher G. Small. [A Survey of the Statistical Theory of Shape]: Comment. Statist. Sci., Volume 4, Number 2 (1989), 105--108.
  • See Comment: Kanti V. Mardia. [A Survey of the Statistical Theory of Shape]: Comment: Some Contributions to Shape Analysis. Statist. Sci., Volume 4, Number 2 (1989), 108--111.
  • See Comment: Wilfrid S. Kendall. [A Survey of the Statistical Theory of Shape]: Comment. Statist. Sci., Volume 4, Number 2 (1989), 111--113.
  • See Comment: Geoffrey S. Watson. [A Survey of the Statistical Theory of Shape]: Comment. Statist. Sci., Volume 4, Number 2 (1989), 113--115.
  • See Comment: Dietrich Stoyan. [A Survey of the Statistical Theory of Shape]: Comment. Statist. Sci., Volume 4, Number 2 (1989), 115--116.
  • See Comment: David G. Kendall. [A Survey of the Statistical Theory of Shape]: Rejoinder. Statist. Sci., Volume 4, Number 2 (1989), 116--120.