Estimators of the intensity of stationary planar fibre processes

In this article we introduce two classes of estimators of the intensity (i.e. mean length per unit of area) of a stationary planar fibre process and we study their asymptotic properties when the sample of fibres is ``enriched'''' by enlarging the window of observation. The estimators are based on counting the points of intersection of the fibre process with another test fibre process, satisfying suitable regularity conditions; the test process can be simulated and overlapped to a digital image of the fibre process under study. Estimators are applied to study the geometric structure of blood vessels generated on a mouse cornea by a simulated tumor.