Data from: Shape variation in outline shapes

A general morphometric method for describing shape variation in a sample consisting of landmarks and multiple outline shapes is developed in this paper. A distance metric is developed for such data and is used to embed the data in a low-dimensional Euclidean space. The Euclidean space is used to generate summary statistics such as mean and principal shape variation which are implicitly represented in the original space using elements of the sample. A new distance metric for outline shapes is proposed based on Procrustes distance that does not require the extraction of discrete points along the curve. The outline distant metric can be naturally combined with distances between landmarks. A method for aligning outlines and multiple outlines is developed that minimises the distance metric. The method is compared to semi-landmarks on synthetic data and two real data sets. Conclusion: outline methods produce useful and valid results when suitably constrained by landmarks and are useful visualisation aids, but questions remain about their suitability for answering biological questions until appropriate distance metrics can be biologically validated.

本文提出了一种通用形态测量方法，用于描述由地标点（landmarks）与多轮廓形状组成的样本中的形状变异。针对此类数据设计了一种距离度量，并将其应用于将数据嵌入低维欧几里得空间。借助该欧几里得空间，可生成均值、主形状变异等汇总统计量，而这些统计量可通过样本元素在原始空间中隐式表达。本文提出了一种基于普洛克鲁斯泰斯距离（Procrustes distance）的轮廓形状新型距离度量，无需沿曲线提取离散点。该轮廓距离度量可与地标点间的距离自然结合。此外，本文还提出了一种可最小化该距离度量的轮廓与多轮廓对齐方法。通过合成数据集与两个真实数据集，将该方法与半地标点（semi-landmarks）方法进行了对比。结论：当通过地标点进行适当约束时，轮廓方法可产出实用且有效的结果，可作为有效的可视化辅助工具；但在合适的距离度量得到生物学验证之前，其在解答生物学问题方面的适用性仍有待商榷。