SIMILARITY BETWEEN RANDOM SETS CONSISTING OF MANY COMPONENTS

Abstract

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.