Statistical assessment of bilateral symmetry of shapes

• 成果类型: Article
• 署名作者: Mardia, KV; Bookstein, FL; Moreton, IJ
• 署名单位: University of Leeds; University of Michigan System; University of Michigan; University of Leeds
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/87.2.285
• 发表日期: 2000
• 页码: 285300
• 关键词: fluctuating asymmetry

摘要

This paper formulates the problem of measuring bilateral symmetry of objects analytically for landmark data, and develops various new testing procedures and exploratory data analyses. The development is linked with the fundamental biological problem of measuring directional asymmetry and fluctuating asymmetry. We distinguish two types of symmetry, object symmetry and matching symmetry, and provide tests under assumptions of isotropic landmark variability as well as non-isotropy. The tests require novel statistical and geometrical analyses of the Procrustes shape manifold. For describing components of symmetry and asymmetry within samples, an extension of principal component analysis is introduced and illustrated by appropriate deformation techniques. Various real examples are used to illustrate the practical relevance of this work.