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Shape curves and geodesic modelling

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  • Kim Kenobi
  • Ian L. Dryden
  • Huiling Le

Abstract

A family of shape curves is introduced that is useful for modelling the changes in shape in a series of geometrical objects. The relationship between the preshape sphere and the shape space is used to define a general family of curves based on horizontal geodesics on the preshape sphere. Methods for fitting geodesics and more general curves in the non-Euclidean shape space of point sets are discussed, based on minimizing sums of squares of Procrustes distances. Likelihood-based inference is considered. We illustrate the ideas by carrying out statistical analysis of two-dimensional landmarks on rats' skulls at various times in their development and three-dimensional landmarks on lumbar vertebrae from three primate species. Copyright 2010, Oxford University Press.

Suggested Citation

  • Kim Kenobi & Ian L. Dryden & Huiling Le, 2010. "Shape curves and geodesic modelling," Biometrika, Biometrika Trust, vol. 97(3), pages 567-584.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:3:p:567-584
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    File URL: http://hdl.handle.net/10.1093/biomet/asq027
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