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Journal of the London Mathematical Society 2003 68(2):511-526; doi:10.1112/S0024610703004393
© 2003 by London Mathematical Society
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© The London Mathematical Society

Unrolling Shape Curves

Huiling Le

School of Mathematical Sciences, University of Nottingham University Park, Nottingham NG7 2RD, huiling.le{at}nottingham.ac.uk

Received 12 October 2001. Revision received 11 December 2002.

The relationship between the connections on two Riemannian manifolds that are related by a Riemannian submersion are used to characterise parallel translation on shape space in terms of its behaviour on the pre-shape sphere and so to derive a concrete procedure for the unrolling, or development, of curves in shape space onto tangent spaces. This will enable one to adapt to shape spaces the standard statistical procedures for fitting curves to Euclidean data.


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