Many biological objects possess bilateral symmetry about a midline or midplane, up to a ``noise'' term. This paper uses landmark-based methods to measure departures from bilateral symmetry, especially for the two-group problem where one group is more asymmetric than the other. In this paper, we formulate our work in the framework of size-and-shape analysis including registration via rigid body motion. Our starting point is a vector of elementary asymmetry features defined at the individual landmark coordinates for each object. We introduce two approaches for testing. In the first, the elementary features are combined into a scalar composite asymmetry measure for each object. Then standard univariate tests can be used to compare the two groups. In the second approach, a univariate test statistic is constructed for each elementary feature. The maximum of these statistics lead to an overall test statistic to compare the two groups and we then provide a technique to extract the important features from the landmark data. Our methodology is illustrated on a pre-registered smile dataset collected to assess the success of cleft lip surgery on human subjects. The asymmetry in a group of cleft lip subjects is compared to a group of normal subjects, and statistically significant differences have been found by univariate tests in the first approach. Further, our feature extraction method leads to an anatomically plausible set of landmarks for medical applications.

翻译：许多生物对象在"噪声"项范围内具有关于中线或中平面的双侧对称性。本文采用基于标志点的方法来测量偏离双侧对称性的程度，特别针对其中一组比另一组更具非对称性的两组问题。我们在包含通过刚体运动进行配准的尺寸与形状分析框架中构建研究工作。我们的起点是为每个对象在其个体标志点坐标处定义的基本非对称特征向量。我们引入了两种检验方法：第一种方法将基本特征组合为每个对象的标量复合非对称度量，随后可采用标准单变量检验来比较两组对象；第二种方法为每个基本特征构建单变量检验统计量，这些统计量的最大值导出用于比较两组的整体检验统计量，并进一步提供从标志点数据中提取重要特征的技术。我们的方法学通过一个预先注册的微笑数据集进行说明，该数据集收集用于评估唇裂手术对人类受试者的成功程度。通过第一种方法的单变量检验发现，唇裂受试者组与正常受试者组的非对称性存在统计学显著差异。此外，我们的特征提取方法为医学应用生成了一组解剖学上合理的标志点。