Correlations between Planar Random Structures, with an Ecological Application

Abstract

Abstract This paper suggests some characteristics which may help to detect and quantify “correlations” between planar geometrical structures such as point patterns/point processes, fibre systems/fibre processes and region patterns/random sets. Typical examples of “correlations” are mutual attraction or inhibition. Some of the characteristics are related to moment‐measures, the definition of the others is similar to that of quantities in the mathematical morphology of M ATHERON and S ERRA . For all quantities unbiased estimators are given. Also the detection of orientations in random structures is discussed. An ecological example demonstrates the application of the characteristics.