Statistical assessment of bilateral symmetry of shapes
Statistical assessment of bilateral symmetry of shapes
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DOI：
10.1093/biomet/87.2.285
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发表时间：
2000-06-01
期刊：
影响因子：
2.7
通讯作者：
Moreton, IJ
中科院分区：
文献类型：
--
作者：
Mardia, KV;Bookstein, FL;Moreton, IJ
本文提出了对地标数据分析测量物体双边对称性的问题，并开发了各种新的测试程序和探索性数据分析。这一发展与测量方向不对称性和波动不对称性的基本生物学问题有关。我们区分两种类型的对称性：对象对称性和匹配对称性，并在各向同性地标变异性和非各向同性的假设下提供测试。这些测试需要对 Procrustes 形状流形进行新颖的统计和几何分析。为了描述样本内对称和不对称的成分，引入了主成分分析的扩展，并通过适当的变形技术进行了说明。使用各种真实的例子来说明这项工作的实际意义。
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.