TENSOR BIOMETRICS FOR CHANGES IN CRANIAL SHAPE
TENSOR BIOMETRICS FOR CHANGES IN CRANIAL SHAPE
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DOI：
10.1080/03014468400007321
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发表时间：
1984-01-01
影响因子：
1.7
通讯作者：
BOOKSTEIN, FL
中科院分区：
文献类型：
--
作者：
BOOKSTEIN, FL
阿西·汤普森的笛卡尔变换方法可以适用于群体差异和形状趋势的生物计量学研究。这种扩展的关键是对称张量，这是一个三角形到另一个三角形的线性变形的数学表示。这些张量可以很容易地从同源地标的笛卡尔坐标形式的数据中计算出来，例如在x线体位测量中常用的数据。这篇文章展示了张量如何使对形状总体的严格统计分析成为可能，而不需要事先规定特定的形状度量。相反，一项研究的结果包括提取最清楚地表明所研究的群体差异或治疗效果的特定形状测量。只涉及传统的多元统计技术，如霍特林的T2。许多地标的配置可以通过显示它们的平均差作为双正交网格对来分析，仔细阅读它可以选择更严格分析的地标三角形。该技术在两项颅面测量研究中得到了体现：描述和预测正常颅面生长，以及与Apert综合征和Crouzon综合征相关的颅面畸形的比较。
D''Arcy Thompson''s method of Cartesian transformations can be adapted to the biometric study of group differences and trends in shape. The key to this extension is the symmetric tensor, a mathematical representation of the linear deformation taking one triangle onto another. These tensors may easily be computed from data that come in the form of Cartesian coordinates of homologous landmarks, such as are customary in roentgenographic cephalometrics. This article shows how the tensors make possible the rigorous statistical analysis of populations of shapes without requiring the specification of particular shape measures in advance. Instead, the findings of a study include the extraction of particular shape measures most clearly manifesting the group difference or treatment effect under study. Only conventional multivariate statistical techniques, such as Hotelling''s T2, are involved. Configurations of many landmarks can be analyzed via the display of their mean difference as a biorthogonal grid pair, perusal of which leads to the selection of triangles of landmarks for more rigorous analysis. The techniques are exemplified in 2 cephalometric studies: the description and prediction of normal craniofacial growth, and a comparison of the craniofacial deformities associated with Apert''s and Crouzon''s syndromes.