Directional analysis of fibre processes related to Boolean models (Q1337196)

This paper deals with the directional analysis of the boundary of a stationary non-isotropic planar Boolean model \(\Xi\) with convex grains. Statistical characteristics obtained from linear intersections (which depend on the angle between the test lines and a fixed direction) are plugged in the relationships between both the rose of intersections of \(\partial\Xi\) and the rose of the mean chord lengths and the family of intensity parameters of the intersection point processes. The most important result is the uniform strong consistency of the suggested empirical counterparts of the rose of intersections and the directional distribution function when the sampling region is filling the whole plane.