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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

Abstract

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. https://doi.org/10.1214/aos/1034713642

Information

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

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

Subjects:
Primary: 62H10
Secondary: 62H11

Rights: Copyright © 1995 Institute of Mathematical Statistics

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