In recent years random sets were recognized as a valuable tool in modelling different processes from fields like biology, biomedicine or material sciences. Nevertheless, the full potential of applications has not still been reached and one of the main problems in advancement is the usual inability to correctly differentiate between underlying processes generating real world realisations. This paper presents a measure of dissimilarity of stationary and isotropic random sets through a heuristic based on convex compact approximations, support functions and envelope tests. The choice is justified through simulation studies of common random models like Boolean and Quermass-interaction processes.

Random sets play an essential role in modelling several phenomena in biology, medicine and material science. However, sometimes it is hard to describe them using a specific model. Therefore it can also be difficult to classify them or to compare their realisations. This contribution proposes a similarity measure between two random sets whose realisations consist of many components based on just one realisation of each of them. The similarity measure is obtained in a non-parametric way taking into account the shapes and the positions of the components. The procedure is justified by a simulation study and consequently applied to real biomedical data of histological images of mammary tissue.

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