Morphological characterization of point patterns

A triplet of function s for the statistical characterization of planar point patterns is introduced. They are related to the integral-geometric quantities area, boundary length and Euler number of patterns of discs centred at the given points. These functions are able to give information on the distribution of a given point pattern which the traditional summary statistics of point process theory do not offer and so can lead to an improved statistical description. The paper describes the statistical estimation of the new characteristics. Some examples illustrate their application in the exploratory analysis of point patterns of tree positions in forests, in comparison to results obtained by means of second-order and distance characteristics.