论文标题
平均固定随机闭合集的平均欧拉特征
Mean Euler characteristic of stationary random closed sets
论文作者
论文摘要
积分几何形状的翻译交集公式产生了与固定观察窗口相交的固定随机闭合集的平均欧拉特征的表达式。我们在以正覆盖范围的设置和使用标志度量的设置中制定了这一结果，以产生曲率度量作为边缘。作为一个应用程序，我们考虑使用$ c^{1,1} $实现的固定随机字段的游览集，尤其是固定的高斯字段，并获得从文献中扩展的结果。
The translative intersection formula of integral geometry yields an expression for the mean Euler characteristic of a stationary random closed set intersected with a fixed observation window. We formulate this result in the setting of sets with positive reach and using flag measures which yield curvature measures as marginals. As an application, we consider excursion sets of stationary random fields with $C^{1,1}$ realizations, in particular, stationary Gaussian fields, and obtain results which extend those known from the literature.
