Shape curves and geodesic modelling

• 成果类型: Article
• 署名作者: Kenobi, Kim; Dryden, Ian L.; Le, Huiling
• 署名单位: University of Nottingham; University of Nottingham
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq027
• 发表日期: 2010
• 页码: 567584
• 关键词: STATISTICS; MANIFOLDS

摘要

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.