Formulas for stationary planar fibre processes III – intersections with fibre systems

Abstract

Intersections of stationary fibre processes in the plane with arbitrary curved lines of finite total length are considered. It is shown that the mean number of intersection points can be calculated from the intensity and angle distribution of the fibre process and the angle distribution of the curved line. Conversely, if the mean number of intersection points is known for all positions of the cuived line? then it is possible to determine the intensity and angle distribution of the fibre process.

Keywords:

• Stochastic geometry
• stereology
• random set
• random manifold
• fibre process
• point process
• random measure