Tscheschel A, Stoyan D
Institute for Stochastics, Freiberg University of Mining and Technology, Germany.
J Microsc. 2003 Jul;211(Pt 1):80-8. doi: 10.1046/j.1365-2818.2003.01194.x.
The specific Euler number is an important topological characteristic in many applications. It is considered here for the case of random networks, which may appear in microscopy either as primary objects of investigation or as secondary objects describing in an approximate way other structures such as, for example, porous media. For random networks there is a simple and natural estimator of the specific Euler number. For its estimation variance, a simple Poisson approximation is given. It is based on the general exact formula for the estimation variance. In two examples of quite different nature and topology application of the formulas is demonstrated.
比欧拉数是许多应用中一个重要的拓扑特征。本文针对随机网络的情况进行探讨，随机网络在显微镜学中可能作为主要研究对象出现，或者作为以近似方式描述其他结构（如多孔介质）的次要对象出现。对于随机网络，存在一个简单且自然的比欧拉数估计量。针对其估计方差，给出了一个简单的泊松近似。它基于估计方差的一般精确公式。通过两个性质和拓扑结构截然不同的例子展示了这些公式的应用。
