ASSESSING DISSIMILARITY OF RANDOM SETS THROUGH CONVEX COMPACT APPROXIMATIONS, SUPPORT FUNCTIONS AND ENVELOPE TESTS

Vesna Gotovac, Kateřina Helisová, Ivo Ugrina

Abstract


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. 


Keywords
approximations; dissimilarity; envelope tests; random sets; stochastic geometry; support functions

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DOI: 10.5566/ias.1490

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)