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A Survey of the Statistical Theory of Shape
David G. Kendall
Vol. 4, No. 2 (May, 1989), pp. 87-99
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2245331
Page Count: 13
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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 Rm. 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.
Statistical Science © 1989 Institute of Mathematical Statistics