Biometrics, biomathematics and the morphometric synthesis
Biometrics, biomathematics and the morphometric synthesis
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DOI：
10.1016/0092-8240(95)00329-0
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发表时间：
1996-03-01
影响因子：
3.5
通讯作者：
Bookstein, FL
中科院分区：
文献类型：
--
作者：
Bookstein, FL
在当代形态计量学的核心-生物形状变化的定量研究-是两种原本不同的方法风格的综合，一个贡献的传统是协方差矩阵的多元分析，最初是作为生物统计学发展起来的，现在在广泛的应用统计学中占主导地位。这种方法，仅仅在协方差结构的线性几何中表达，忽略了原始测量的生物数学方面，另一个支流强调生物形式变化的直接可视化。然而，使客观的生物意义的功能，在这些图表中看到的总是成问题的，也表示的变化，作为区别于成对的差异，被证明是不可行的。联合收割机这两个变种的生物数学建模成一个有效的praxis生物形状的定量研究是一个目标，虽然本世纪的大部分时间认真寻求。这一目标最终在20世纪80年代实现，当时数理统计、多元生物测定、非欧几何和计算机图形学的技术被结合在一个连贯的新工具系统中，用于对界标点及其所处的生物医学图像进行完整的区域化定量分析。（生物标记的几何点，如“鼻梁”）作为生物数学基元。地标的配置的形状被定义为关于欧几里德相似性组的等价类，然后表示为大卫肯德尔的形状空间，一个黎曼流形与Procrustes距离作为度量的单点。所有传统的多变量策略结转到形状变化和协变的研究时，形状被解释在切线空间的形状流形在一个平均形状。对于这种分析的生物数学解释，人们需要一个与许多不同几何尺度上的局部生物理论过程和解释的现实相兼容的切线空间的基础，并且需要图形来可视化平均形状差异和其他统计对比。这两种需求都可以通过薄板样条来实现，这是一种具有非常有用的线性代数的变形函数。样条还链接的地标的生物特征的图像的变形分析，从地标originatedarese.This的历史和主要工具，这种合成在其biomethematical和生物统计学的背景下，并证明其有用性的焦点神经解剖异常精神分裂症的研究。
At the core of contemporary morphometrics-the quantitative study of biological shape variation-is a synthesis of two originally divergent methodological styles, One contributory tradition is the multivariate analysis of covariance matrices originally developed as biometrics and now dominant across a broad expanse of applied statistics. This approach, couched solely in the linear geometry of covariance structures, ignores biomathematical aspects of the original measurements, The other tributary emphasizes the direct visualization of changes in biological form. However, making objective the biological meaning of the features seen in those diagrams was always problematical; also, the representation of variation, as distinct from pairwise difference, proved infeasible.To combine these two variants of biomathematical modeling into a valid praxis for quantitative studies of biological shape was a goal earnestly sought though most of this century. That goal was finally achieved in the 1980s when techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry and computer graphics were combined in a coherent new system of tools for the complete regionalized quantitative analysis of landmark points together with the biomedical images in which they are seen.In this morphometric synthesis, correspondence of landmarks (biologically labeled geometric points, like ''bridge of the nose'') across specimens is taken as a biomathematical primitive. The shapes of configurations of landmarks are defined as equivalence classes with respect to the Euclidean similarity group and then represented as single points in David Kendall's shape space, a Riemannian manifold with Procrustes distance as metric. All conventional multivariate strategies carry over to the study of shape variation and covariation when shapes are interpreted in the tangent space to the shape manifold at an average shape. For biomathematical interpretation of such analyses, one needs a basis for the tangent space compatible with the reality of local biotheoretical processes and explanations at many different geometric scales, and one needs graphics for visualizing average shape differences and other statistical contrasts there. Both of these needs are managed by the thin-plate spline, a deformation function that has an unusually helpful linear algebra. The spline also links the biometrics of landmarks to deformation analysis of the images from which the landmarks originally arose.This article reviews the history and principal tools of this synthesis in their biomathematical and biometrical context and demonstrates their usefulness in a study of focal neuroanatomical anomalies in schizophrenia.