## Statistical Science

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

### A Survey of the Statistical Theory of Shape

#### 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 in Project Euclid: 19 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.ss/1177012582

**Digital Object Identifier**

doi:10.1214/ss/1177012582

**Mathematical Reviews number (MathSciNet)**

MR1007558

**Zentralblatt MATH identifier**

0672.60018

**JSTOR**

links.jstor.org

**Keywords**

Central place theory convex polygon Delaunay tessellation galaxy quasar riemannian submersion singular tessellation spherical triangle stochastic physical chemistry void

#### Citation

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

#### 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.Project Euclid: euclid.ss/1177012583
- See Comment: Christopher G. Small. [A Survey of the Statistical Theory of Shape]: Comment. Statist. Sci., Volume 4, Number 2 (1989), 105--108.Project Euclid: euclid.ss/1177012584
- 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.Project Euclid: euclid.ss/1177012585
- See Comment: Wilfrid S. Kendall. [A Survey of the Statistical Theory of Shape]: Comment. Statist. Sci., Volume 4, Number 2 (1989), 111--113.Project Euclid: euclid.ss/1177012586
- See Comment: Geoffrey S. Watson. [A Survey of the Statistical Theory of Shape]: Comment. Statist. Sci., Volume 4, Number 2 (1989), 113--115.Project Euclid: euclid.ss/1177012587
- See Comment: Dietrich Stoyan. [A Survey of the Statistical Theory of Shape]: Comment. Statist. Sci., Volume 4, Number 2 (1989), 115--116.Project Euclid: euclid.ss/1177012588
- See Comment: David G. Kendall. [A Survey of the Statistical Theory of Shape]: Rejoinder. Statist. Sci., Volume 4, Number 2 (1989), 116--120.Project Euclid: euclid.ss/1177012589