Assessing Similarity of Random sets via Skeletons

The paper concerns a method for assessing similarity of realisations of random sets based on a construction of their morphological skeletons and a consequent covering of the realisations by unions of the so-called maximal discs. Since the realisations are considered to be binary images, the skeletons together with the corresponding discs can be viewed as realisations of marked point processes with specific properties. A special function for such marked point processes is defined. This function is analogous to the mark-weighted K -function. The function is then used for comparison of given realisations. More precisely, a random sample of the functions is taken from the realisations and the equality in distribution of the functions is tested by an envelope test and by a kernel test. The described procedure is illustrated on a simulation study with the aim to distinguish between realisations coming from different processes and to determine similarity of realisations coming from the same processes.