Representation of Radon Shape Diffusions via Hyperspherical Brownian Motion

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 $\tilde{\Sigma}^k_n$ 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.

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Mathematical Proceedings of the Cambridge Philosophical Society, 145, 2, 457-470

 Record created 2009-03-31, last modified 2018-03-17

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