从二维截面看随机场的三维形态
3D morphology of a random field from its 2D cross-section
摘要：
我们表明，这两个随机取向的三轴椭球（代表等值面的各向同性的三维随机场）的纵横比可以确定从一个单一的二维截面的样品使用的概率分布的连续性F的结构中看到的截面（F=0的圆和F=1的线）。F的概率分布具有鲁棒的形式，具有对椭球的长宽比敏感的尖锐的最大值和截断。我们证明了具有随机分布尺寸的三轴椭球的长宽比仍然可以从F的概率分布中恢复出来。这种方法适用于许多形状识别和分类问题，这里以银河系湍流星际介质中的中性氢密度为例。气体的分布是平行的，平均轴比为1：2：20。
英文摘要：
We show that both aspect ratios of randomly oriented triaxial ellipsoids (representing isosurfaces of an isotropic 3D random field) can be determined from a single 2D cross-section of their sample using the probability distribution of the filamentarity F of the structures seen in the cross-section (F=0 for a circle and F=1 for a line). The probability distribution of F has a robust form with a sharp maximum and truncation that are sensitive to the ellipsoids' aspect ratios. We show that the aspect ratios of triaxial ellipsoids with randomly distributed dimensions can still be recovered from the probability distribution of F. This method is applicable to many shape recognition and classification problems, here illustrated with neutral hydrogen density in the turbulent interstellar medium of the Milky Way. The gas distribution is shown to be filamentary with the mean axis ratio 1:2:20.
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