Shape curves and geodesic modelling

Kim Kenobi*, Ian L. Dryden, Huiling Le

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (SciVal)

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.

Original languageEnglish
Pages (from-to)567-584
Number of pages18
JournalBiometrika
Volume97
Issue number3
DOIs
Publication statusPublished - Sept 2010

Keywords

  • Complex Watson distribution
  • Curve fitting
  • Geodesic
  • Growth
  • Landmark
  • Likelihood
  • Non-Euclidean space
  • Polynomial
  • Shape
  • Size

Fingerprint

Dive into the research topics of 'Shape curves and geodesic modelling'. Together they form a unique fingerprint.

Cite this