Kume, Alfred and Dryden, Ian L and Le, Huiling
(2007)
*Shape space smoothing splines for planar landmark data.*
Biometrika, 94
(3).
pp. 513-528.
ISSN 0006-3444 .
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Official URL http://dx.doi.org/10.1093/biomet/asm047 |

## Abstract

A method is developed for fitting smooth curves through a series of shapes of landmarks in two dimensions using unrolling and unwrapping procedures in Riemannian manifolds. An explicit method of calculation is given which is analogous to that of Jupp & Kent ( 1987) for spherical data. The resulting splines are called shape-space smoothing splines. The method resembles that of fitting smoothing splines in real spaces in that, if the smoothing parameter is zero, the resulting curve interpolates the data points, and if it is infinitely large the curve is a geodesic line. The fitted path to the data is defined such that its unrolled version at the tangent space of the starting point is a cubic spline fitted to the unwrapped data with respect to that path. Computation of the fitted path consists of an iterative procedure which converges quickly, and the resulting path is given in a discretised form in terms of a piecewise geodesic path. The procedure is applied to the analysis of some human movement data, and a test for the appropriateness of a mean geodesic curve is given

Item Type: | Article |
---|---|

Uncontrolled keywords: | cubic spline; shape space; shape-space spline; sphere; spherical smoothing spline; unrolling; unwrapping |

Subjects: | H Social Sciences > HA Statistics Q Science > QH Natural history > QH301 Biology |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Judith Broom |

Date Deposited: | 19 Dec 2007 18:26 |

Last Modified: | 28 May 2014 10:14 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/725 (The current URI for this page, for reference purposes) |

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