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December 1995 Shape changes in the plane for landmark data
Michael J. Prentice, Kanti V. Mardia
Ann. Statist. 23(6): 1960-1974 (December 1995). DOI: 10.1214/aos/1034713642


This paper deals with the statistical analysis of matched pairs of shapes of configurations of landmarks in the plane. We provide inference procedures on the complex projective plane for a basic measure of shape change in the plane, on observing that shapes of configurations of $(k + 1)$ landmarks in the plane may be represented as points on $\mathbb{C} P^{k-1}$ and that complex rotations are the only maps on $\mathbb{C} S^{k-1}$ which preserve the usual Hermitian inner product. Specifically, if $u_1, \dots, u_n$ are fixed points on $\mathbb{C} P^{k-1}$ represented as $\mathbb{C} S^{k-1}/U(1)$ and $v_1, \dots, v_n$ are random points on $\mathbb{C} P^{k-1}$ such that the distribution of $v_j$ depends only on $||v_j^* Au_j||^2$ for some unknown complex rotation matrix A, then this paper provides asymptotic inference procedures for A. It is demonstrated that shape changes of a kind not detectable as location shifts by standard Euclidean analysis can be found by this frequency domain method. A numerical example is given.


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Michael J. Prentice. Kanti V. Mardia. "Shape changes in the plane for landmark data." Ann. Statist. 23 (6) 1960 - 1974, December 1995.


Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0858.62039
MathSciNet: MR1389860
Digital Object Identifier: 10.1214/aos/1034713642

Primary: 62H10
Secondary: 62H11

Rights: Copyright © 1995 Institute of Mathematical Statistics