Rao C R, Suryawanshi S
Statistics Department, Pennsylvania State University, University Park 16802, USA.
Proc Natl Acad Sci U S A. 1996 Oct 29;93(22):12132-6. doi: 10.1073/pnas.93.22.12132.
Two objects with homologous landmarks are said to be of the same shape if the configurations of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. The observations on an object are coordinates of its landmarks with reference to a set of orthogonal coordinate axes in an appropriate dimensional space. The origin, choice of units, and orientation of the coordinate axes with respect to an object may be different from object to object. In such a case, how do we quantify the shape of an object, find the mean and variation of shape in a population of objects, compare the mean shapes in two or more different populations, and discriminate between objects belonging to two or more different shape distributions. We develop some methods that are invariant to translation, rotation, and scaling of the observations on each object and thereby provide generalizations of multivariate methods for shape analysis.
如果一个物体的地标配置可以通过平移、旋转/反射和缩放与另一个物体的地标配置完全匹配，那么具有同源地标的两个物体就被认为具有相同的形状。对一个物体的观测是其地标相对于适当维度空间中的一组正交坐标轴的坐标。坐标轴的原点、单位选择以及相对于一个物体的方向在不同物体之间可能会有所不同。在这种情况下，我们如何量化一个物体的形状，找到一组物体中形状的均值和变化，比较两个或更多不同群体中的平均形状，并区分属于两个或更多不同形状分布的物体。我们开发了一些方法，这些方法对于每个物体观测值的平移、旋转和缩放是不变的，从而提供了形状分析多元方法的推广。
