On the induced distribution of the shape of the projection of a randomly rotated configuration

On the induced distribution of the shape of the projection of a randomly rotated configuration

H. Le and D. Barden

Source: Adv. in Appl. Probab. Volume 42, Number 2 (2010), 331-346.

Abstract

Using the geometry of the Kendall shape space, in this paper we study the shape, as well as the size-and-shape, of the projection of a configuration after it has been rotated and, when the given configuration lies in a Euclidean space of an arbitrary dimension, we obtain expressions for the induced distributions of such shapes when the rotation is uniformly distributed.

First Page: Show

Primary Subjects: 60D05

Keywords: Kendall shape space; shape; size-and-shape; horizontal lift; Riemannian submersion

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aap/1275055231
Digital Object Identifier: doi:10.1239/aap/1275055231
Zentralblatt MATH identifier: 05735959
Mathematical Reviews number (MathSciNet): MR2675105

back to Table of Contents

References

Kendall, D. G. (1984). Shape manifolds, Procrustean metrics, and complex projective spaces. Bull. London Math. Soc. 16, 81--121.

Mathematical Reviews (MathSciNet): MR737237

Zentralblatt MATH: 0579.62100

Digital Object Identifier: doi:10.1112/blms/16.2.81

Kendall, D. G., Barden, D., Carne, T. K. and Le, H. (1999). Shape and Shape Theory. John Wiley, Chichester.

Mathematical Reviews (MathSciNet): MR1891212

Kendall, W. S. and Le, H. (2009). Statistical shape theory. In New Perspectives in Stochastic Geometry, eds W. S. Kendall and I. Molchanov, Oxford University Press, pp. 384--373.

O'Neill, B. (1983). Semi-Riemannian Geometry. Academic Press, New York.

Mathematical Reviews (MathSciNet): MR719023

Panaretos, V. M. (2006). The diffusion of Radon shape. Adv. Appl. Prob. 38, 320--335.

Mathematical Reviews (MathSciNet): MR2264947

Zentralblatt MATH: 1125.60005

Digital Object Identifier: doi:10.1239/aap/1151337074

Project Euclid: euclid.aap/1151337074

Panaretos, V. M. (2008). Representation of Radon shape diffusions via hyperspherical Brownian motion. Math. Proc. Camb. Phil. Soc. 145, 457--470.

Mathematical Reviews (MathSciNet): MR2442137

Zentralblatt MATH: 1180.60066

Digital Object Identifier: doi:10.1017/S0305004108001370

Panaretos, V. M. (2009). On random tomography with unobservable projection angles. Ann. Statist. 37, 3272\nobreakdash--3306.

Mathematical Reviews (MathSciNet): MR2549560

Zentralblatt MATH: 05644280

Digital Object Identifier: doi:10.1214/08-AOS673

Project Euclid: euclid.aos/1250515387

previous :: next