Kybernetika 45 no. 6, 931-945, 2009

On Estimation of Intrinsic Volume Densities of Stationary Random Closed Sets via Parallel Sets in the Plane

Tomáš Mrkvička and Jan Rataj


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.


random closed set, convex ring, curvature measure, intrinsic volume


60D05, 62G05