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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 $\widetilde(\Sigman^k$ 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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Title
Representation of Radon Shape Diffusions via Hyperspherical Brownian Motion
Creator
Panaretos, Victor M., Author
Published
Statistics Department, University of California, Berkeley, University of California at Berkeley, Berkeley, California, April 2006
Full Collection Name
Statistics Technical Reports
Other Identifiers
707
Type
Text
Format
technical reports
Archive
Mathematics Statistics Library
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