summary:A method of estimation of intrinsic volume densities for stationary random closed sets in $\mathbb{R}^d$ based on estimating volumes of tiny collars has been introduced in T. Mrkvička and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch. Proc. Appl. 118 (2008), 2, 213-231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation radii in the discrete approximation, which differs from the standard techniques used for measuring parallel sets in image analysis. A method of reducing the bias is proposed and tested on simulated data.
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机译：摘要：T。Mrkvička和J.Rataj引入了一种基于估计小项圈体积的$ \ mathbb {R} ^ d $中的平稳随机封闭集合的固有体积密度的方法，有关固有体积密度的估计固定随机封闭集，斯托克。程序应用118（2008），2，213-231。在此注释中，在2维上证明了更强的渐近一致性。将详细讨论该方法的实现。重要的一步是确定离散近似中的膨胀半径，这与用于测量图像分析中的平行集合的标准技术不同。提出了一种减小偏差的方法，并在模拟数据上进行了测试。
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