6. Random point models

The simplest models of random closed sets are random point models, where the elementary random set is a random point. Random point fields are then simple, locally finite spatial distributions of random points, whose realizations are called spatial point patterns .

In practice, the geometric objects concerned in practical applications are either directly (but rarely) points, or (more often) objects that can be modelled, at least to a first approximation, by points (e.g. the centers of gravity or symmetry of the geometric objects under consideration)....