Inhomogeneous K-function for germ–grain models

Abstract

In this paper, we propose the definition of the inhomogeneous K-function for germ–grain models, based on the reduced second order measure for general random sets. In general, grains in a germ–grain model can overlap, and the inhomogeneous K-function defined for point processes cannot be directly extended. This function can be used for analyzing the interactions between grains and distinguishing between realizations of different germ–grain models. Its effectiveness is tested by means of a simulation study. Finally, as an illustration, it is applied to a sample of images of peripheral blood smears obtained from patients with Sickle Cell Disease, in order to decide whether the sample belongs to the thin, thick or morphological zone.