Representation of Radon shape diffusions via hyperspherical Brownian motion

Autores: Victor M. Panaretos
Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 2, 2008, págs. 457-470
Idioma: inglés
DOI: 10.1017/s0305004108001370
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Resumen
- 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.