Lestrel P E, Bodt A, Swindler D R
Section of Orthodontics, School of Dentistry University of California, Los Angeles 90024.
Am J Phys Anthropol. 1993 May;91(1):117-29. doi: 10.1002/ajpa.1330910108.
The primate cranial base (CB) represents a complex irregular structure even when limited to two dimensions, making it difficult to describe quantitatively using the conventional metrical approach composed of angles and distances. Consequently, a curve-fitting procedure, elliptical Fourier functions (EFF), was utilized, which accurately defines the form of complex two-dimensional morphologies. A longitudinal Macaca nemestrina sample consisting of 14 females and 15 males was utilized. Lateral headfilms, 1 to 8 years, were available (275 headfilms). Because the x-rays were not always taken at precise one-year intervals, a number of headfilms were excluded, which reduced the sample to 181. The CB boundary outline was carefully traced onto acetate sheets and 54 points located. The observed points were digitized and used to compute size-standardized EFF's with 20 harmonics. From each EFF, a set of 150 expected distances to the CB boundary was generated using the centroid as an origin. Superimposition of the CB's on the centroid also provided a detailed picture of the relative shape changes with respect to that center. Statistically significant shape differences were found as a function of age and sexual dimorphism. These age changes consisted of a gradual anteroposterior lengthening with a concomitant narrowing in the superoinferior direction. Specifically, a lengthening of the dorsal clivus and an anterior migration of the hypophyseal fossa could also be discerned. Thus, Fourier descriptors provide a particularly powerful method for documenting, both visually and numerically, the shape changes of complex two dimensional morphologies.
灵长类动物的颅底（CB）即使仅限于二维时也是一个复杂的不规则结构，这使得使用由角度和距离组成的传统测量方法进行定量描述变得困难。因此，采用了一种曲线拟合程序，即椭圆傅里叶函数（EFF），它能准确地定义复杂二维形态的形式。使用了一个纵向的豚尾猕猴样本，其中包括14只雌性和15只雄性。有1至8岁的侧位头颅X线片（共275张）。由于X线片并非总是精确地每隔一年拍摄一次，因此排除了一些头颅X线片，样本数量减少到181个。将CB边界轮廓小心地描绘在醋酸纤维片上，并确定了54个点。对观察到的点进行数字化处理，并用于计算具有20个谐波的尺寸标准化EFF。从每个EFF中，以质心为原点生成一组到CB边界的150个预期距离。将CB叠加在质心上，也提供了相对于该中心的相对形状变化的详细图像。发现了具有统计学意义的形状差异与年龄和两性异形有关。这些年龄变化包括前后逐渐延长，同时在上下方向变窄。具体而言，还可以看出斜坡背侧延长以及垂体窝向前移位。因此，傅里叶描述符为直观和数值记录复杂二维形态的形状变化提供了一种特别强大的方法。
