Estimate of the intensity of fibre processes via the spherical contact distribution function

In the statistical description of the shape of random geometrical objects, usually depicted in 2-dimensional image containing a proper window of observation, it is often relevant to measure the length of lines, describing for example the boundary of the object, or its texture, etc. Since images are formed by pixels, that is two-dimensional entities, while a line is a one-dimensional object, simple “pixel counting” techniques do not lead to accurate estimates of the length of lines, even with images having high resolution. Here a method to estimate the (mean) length of a (random) line per unit area is proposed, based on an estimator of the Spherical Contact Distribution Function of a random set and its properties are tested on simulated fibre processes.