This contribution concerns comparing of random sets given (digital) images of their realisations. In classical statistics, being able to specify a particular model is of great benefit, since we can for example estimate and compare the model parameters. Unfortunately, it is not necessarily feasible. However, it may be enough to distinguish between two sets without specifying their probability distributions. This talk presents a measure of dissimilarity of random sets through a heuristic based on convex compact approximations and their support functions. For assessing dissimilarity two statistical approaches were used, namely envelope tests and tests of equality of distributions of two random convex compact sets based on N-distances. In the second one, the vector space of hedgehogs which are defined as differences of convex compact sets, is employed. The methodology is justified through simulation studies of common random models such as Boolean and Quermass-interaction processes with different parameters.