Directions and projective shapes

• 成果类型: Article
• 署名作者: Mardia, KV; Patrangenaru, V
• 署名单位: University of Leeds; Texas Tech University System; Texas Tech University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000273
• 发表日期: 2005
• 页码: 1666-1699
• 关键词: extrinsic sample means; MANIFOLDS

摘要

This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space, as well as an appropriate coordinate system for this shape space. For generic configurations of k points in m dimensions, the resulting projective shape space is identified as a product of k - m - 2 copies of axial spaces RPm. This identification leads to the need for developing multivariate directional and multivariate axial analysis and we propose parametric models, as well as nonparametric methods, for these areas. In particular, we investigate the Frechet extrinsic mean for the multivariate axial case. Asymptotic distributions of the appropriate parametric and nonparametric tests are derived. We illustrate our methodology with examples from machine vision.