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.

中文翻译：

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三维表面形状的功能数据分析和可视化

高分辨率成像的出现使得表面形状的数据变得广泛。基于地标的形状分析方法已经很成熟，但高分辨率数据需要功能性方法。出发点是对每个表面形状进行系统且一致的描述，并描述了创建这种形状的方法。然后介绍了三种创新的分析形式。第一个使用表面积分来解决配准、主成分分析和不对称性测量的问题，所有这些都以函数形式进行。计算问题通过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。第二个创新是关注表现出有趣行为（例如群体差异）的子空间，而不是单个主要成分。第三项创新涉及单个形状与相关控制集的比较，其中正常范围的概念被扩展到表面形状的高度多元设置。这在医疗环境中具有特别强的应用，其中对个体患者的评估非常重要。所有这些想法都是在人类面部形状的重要背景下发展和说明的，重点强调感兴趣效果的有效视觉传达。