Naslov
Assessing dissimilarity of random sets through convex compact approximations and support functions

Autori
Gotovac, Vesna

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Prirodoslovno-matematički fakultet, Matematički odsjek

Mjesto
Zagreb

Datum
27.04

Godina
2017

Stranica
92

Mentor
Koceić-Bilan, Nikola ; Helisová, Kateřina

Ključne riječi
approximations ; dissimilarity ; envelope tests ; kernel tests ; random sets ; stochastic geometry ; support functions

Sažetak
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 is still not reached and one of the main problems in advancement is the usual inability to correctly differentiate between underlying processes generating real world realisations. This research presents a measure of dissimilarity of random sets through a heuristic based on convex compact approximations and 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 like Boolean and Quermass-interaction processes. Also an example of the application of proposed methodology to real data is presented concerning distinguishing between sample images of mastophatic breast tissue and mammary cancer.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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