Representation of Radon Shape Diffusions via Hyperspherical Brownian Motion

April, 2006
Report Number: 
707
Authors: 
Victor M. Panaretos
Abstract: 

A framework is introduced for the study of general Radon shape diffusions, that is, shape diffusions induced by projections of randomly rotating shapes [Panaretos, 2006]. This is done via a convenient representation of unoriented Radon shape diffusions in (unoriented) D.G. Kendall shape space $\widetilde{\Sigma}_n^k$ 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 cna 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.

References:

Panaretos, V.M. (June 2006). The diffusion of Radon shape. Adv. App. Prob. 38 (2), forthcoming.

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