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

Gotovac, Vesna (2017) Assessing dissimilarity of random sets through convex compact approximations and support functions. Doctoral thesis, Faculty of Science > Department of Mathematics.

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Abstract

In recent years random sets were recognized as a valuable tool in modelling different processes in fields like biology, biomedicine or material sciences. Nevertheless, the full potential of these applications has not yet been reached and one of the main problems in their advancement is the usual inability to correctly differentiate between underlying processes which generate real-world realisations. This research introduces 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 the envelope test and the test of equality of distributions of two random convex compact sets based on \(\mathfrak{N}\)-distances. In the latter, 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 the distinction between sample images of mastophatic breast tissue and mammary cancer.

Item Type: Thesis (Doctoral thesis)
Keywords: approximations, dissimilarity, envelope tests, kernel tests, random sets, stochastic geometry, support functions
Supervisor: Koceić Bilan, Nikola and Helisova, Katerina
Date: 2017
Number of Pages: 91
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 24 May 2017 12:35
Last Modified: 24 May 2017 12:35
URI: http://digre.pmf.unizg.hr/id/eprint/5533

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