对称凸随机闭集作为带域的Feret直径刻画
Description of the symmetric convex random closed sets as zonotopes from their Feret diameters
摘要：
本文利用Feret直径（又称卡尺直径）研究了二维随机闭集（RACS）。更具体地说，它示出，一个2-D对称凸RACS可以近似精确到我们想要的一些随机zonotopes（多面体形成的Minkowski总和的线段）的Hausdorff距离。这样的近似是完全定义从费雷特直径的2-D凸RACS。特别地，表示带形近似的面长度的随机向量的矩与RACS的Feret直径随机过程的矩相关。
英文摘要：
In this paper, the 2-D random closed sets (RACS) are studied by means of the Feret diameter, also known as the caliper diameter. More specifically, it is shown that a 2-D symmetric convex RACS can be approximated as precisely as we want by some random zonotopes (polytopes formed by the Minkowski sum of line segments) in terms of the Hausdorff distance. Such an approximation is fully defined from the Feret diameter of the 2-D convex RACS. Particularly, the moments of the random vector representing the face lengths of the zonotope approximation are related to the moments of the Feret diameter random process of the RACS.
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