Inhomogeneous K-function for germ-grain models

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.