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August 2005 Directions and projective shapes
Kanti V. Mardia, Vic Patrangenaru
Ann. Statist. 33(4): 1666-1699 (August 2005). DOI: 10.1214/009053605000000273


This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space, as well as an appropriate coordinate system for this shape space. For generic configurations of k points in m dimensions, the resulting projective shape space is identified as a product of km−2 copies of axial spaces ℝPm. This identification leads to the need for developing multivariate directional and multivariate axial analysis and we propose parametric models, as well as nonparametric methods, for these areas. In particular, we investigate the Frećhet extrinsic mean for the multivariate axial case. Asymptotic distributions of the appropriate parametric and nonparametric tests are derived. We illustrate our methodology with examples from machine vision.


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Kanti V. Mardia. Vic Patrangenaru. "Directions and projective shapes." Ann. Statist. 33 (4) 1666 - 1699, August 2005.


Published: August 2005
First available in Project Euclid: 5 August 2005

zbMATH: 1078.62068
MathSciNet: MR2166559
Digital Object Identifier: 10.1214/009053605000000273

Primary: 62H11
Secondary: 62H10 , 62H35

Keywords: Bootstrapping , directional statistics , equivariant embedding , extrinsic means , machine vision , projective frame , projective shape space , Projective transformations , shape analysis , tangent approximation

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 4 • August 2005
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