Katina Stanislav, Vittert Liberty, W Bowman Adrian
Institute of Mathematics & Statistics Masaryk University Brno Czech Republic.
Institute of Computer Science of the Czech Academy of Sciences Prague Czech Republic.
J R Stat Soc Ser C Appl Stat. 2021 Jun;70(3):691-713. doi: 10.1111/rssc.12482. Epub 2021 May 6.
The advent of high-resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high-resolution data require a functional approach. The starting point is a systematic and consistent description of each surface shape and a method for creating this is described. Three innovative forms of analysis are then introduced. The first uses surface integration to address issues of registration, principal component analysis and the measurement of asymmetry, all in functional form. Computational issues are handled through discrete approximations to integrals, based in this case on appropriate surface area weighted sums. The second innovation is to focus on sub-spaces where interesting behaviour such as group differences are exhibited, rather than on individual principal components. The third innovation concerns the comparison of individual shapes with a relevant control set, where the concept of a normal range is extended to the highly multivariate setting of surface shape. This has particularly strong applications to medical contexts where the assessment of individual patients is very important. All of these ideas are developed and illustrated in the important context of human facial shape, with a strong emphasis on the effective visual communication of effects of interest.
高分辨率成像技术的出现使得关于表面形状的数据广泛可得。基于地标点的形状分析方法已经成熟，但高分辨率数据需要一种功能性方法。起点是对每个表面形状进行系统且一致的描述，并描述了创建这种描述的方法。然后介绍了三种创新的分析形式。第一种使用表面积分来处理配准、主成分分析和不对称性测量等问题，所有这些都是以函数形式呈现。计算问题通过对积分的离散近似来处理，在这种情况下基于适当的表面积加权和。第二项创新是关注表现出有趣行为（如组间差异）的子空间，而不是单个主成分。第三项创新涉及将个体形状与相关对照组进行比较，其中正常范围的概念扩展到表面形状的高度多变量设置。这在个体患者评估非常重要的医学背景中有特别强大的应用。所有这些想法都在人类面部形状这一重要背景下得到发展和说明，特别强调对感兴趣效应的有效视觉传达。
