The development of techniques for the acquisition of high-resolution 3D images, such as computed tomography and magnetic resonance imaging, has opened new avenues to the study of complex morphologies. Detailed descriptions of internal and external traits can be now obtained, allowing the intensive sampling of surface points. In this paper, we introduce a morphometric and statistical framework, grounded on Procrustes and Procrustes-like techniques as well as standard spatial statistics, to explicitly describe and incorporate the spatial pattern of these surface points into the analyses. We exemplified this approach by analyzing ontogenetic changes in a sample of human brain endocasts and inter-specific differences between primate skulls. An intensive sampling of points on 3D surfaces was performed by automatic techniques and the morphometric variation among specimens was measured by the residuals obtained after the alignment of points. Our results showed that shape changes in both examples are spatially structured. Different results were attained by using methods that incorporate or not the spatial structure in the evaluation of the effect of specific biological factors on shape variation. Particularly, these analyses indicated that the effect of biological factors acting at local scales can be confounded with more systemic factors (by example, the effect of the diet on the facial skeleton) if the spatial structure is not taken into account. Overall, our results suggest that the intensive description of shape differences among structures using densely sampled points on 3D surfaces combined with spatial statistical methods can be used to explore problems not widely addressed in morphological studies.

中文翻译：

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几何形态计量数据中空间模式的描述和分析

用于采集高分辨率3D图像的技术的发展，例如计算机断层扫描和磁共振成像，为研究复杂形态学开辟了新途径。现在可以获得内部和外部特征的详细描述，从而可以对表面点进行大量采样。在本文中，我们介绍了基于Procrustes和类似Procrustes的技术以及标准空间统计的形态计量学和统计框架，以明确描述这些表面点的空间模式并将其纳入分析中。我们通过分析人类脑内铸物样本中的个体发育变化以及灵长类动物头骨之间的种间差异来举例说明这种方法。通过自动技术对3D表面上的点进行密集采样，并通过对齐点后获得的残差来测量样本之间的形貌变化。我们的结果表明，两个示例中的形状变化都是空间结构的。通过使用在评估特定生物学因素对形状变化的影响时是否纳入空间结构的方法，可以获得不同的结果。特别是，这些分析表明，如果不考虑空间结构，则可以将生物因子在局部尺度上的作用与更多全身性因素（例如饮食对面部骨骼的影响）混淆。总体，