Shape-space smoothing splines for planar landmark data
成果类型：
Article
署名作者：
Kume, Alfred
署名单位：
University of Kent; University of Nottingham
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asm047
发表日期：
2007
页码：
513528
关键词：
摘要：
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.
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