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Representation of Radon shape diffusions via hyperspherical Brownian motion

Published online by Cambridge University Press:  01 September 2008

VICTOR M. PANARETOS
VICTOR M. PANARETOS*
Affiliation:
Department of Statistics, University of California, Berkeley, U.S.A. e-mail: [email protected]
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Abstract

A framework is introduced for the study of general Radon shape diffusions, that is, shape diffusions induced by projections of randomly rotating shapes. This is done via a convenient representation of unoriented Radon shape diffusions in (unoriented) D.G. Kendall shape space through a Brownian motion on the hypersphere. This representation leads to a coordinate system for the generalized version of Radon diffusions since it is shown that shape can be essentially identified with unoriented shape in the projected case. A bijective correspondence between Brownian motion on real projective space and Radon shape diffusions is established. Furthermore, equations are derived for the general (unoriented) Radon diffusion of shape-and-size, and stationary measures are discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 2 , September 2008 , pp. 457 - 470
Copyright
Copyright © Cambridge Philosophical Society 2008

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