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

Gotovac, Vesna

prikaz prve stranice dokumenta Assessing dissimilarity of random sets through convex compact approximations and support functions

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doctoral thesis

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

Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:126277

Gotovac, Vesna

University of Zagreb
Faculty of Science
Department of Mathematics

Cite this document

APA 6th Edition

Gotovac, V. (2017). Assessing dissimilarity of random sets through convex compact approximations and support functions (Doctoral thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:126277

MLA 8th Edition

Gotovac, Vesna. "Assessing dissimilarity of random sets through convex compact approximations and support functions." Doctoral thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:126277

Chicago 17th Edition

Harvard

Gotovac, V. (2017). 'Assessing dissimilarity of random sets through convex compact approximations and support functions', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 01 February 2023, https://urn.nsk.hr/urn:nbn:hr:217:126277

Vancouver

Gotovac V. Assessing dissimilarity of random sets through convex compact approximations and support functions [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2023 February 01] Available at: https://urn.nsk.hr/urn:nbn:hr:217:126277

IEEE

V. Gotovac, "Assessing dissimilarity of random sets through convex compact approximations and support functions", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:126277

Cite this item: https://urn.nsk.hr/urn:nbn:hr:217:126277

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Metadata

Title	Assessing dissimilarity of random sets through convex compact approximations and support functions
Title (croatian)	Ispitivanje sličnosti slučajnih skupova aproksimacijama konveksnim tijelima i njihovim potpornim funkcijama
Author	Vesna Gotovac
Mentor	Nikola Koceić Bilan (mentor)
Mentor	Kateřina Helisová https://orcid.org/0000-0002-0586-5949 (komentor)
Committee member	Zbyněk Pawlas https://orcid.org/0000-0002-1042-8073 (predsjednik povjerenstva)
Committee member	Bojan Basrak (član povjerenstva)
Committee member	Kateřina Helisová https://orcid.org/0000-0002-0586-5949 (član povjerenstva)
Granter	University of Zagreb Faculty of Science (Department of Mathematics) Zagreb
Defense date and country	2017-04-28, Croatia
Scientific / art field, discipline and subdiscipline	NATURAL SCIENCES Mathematics
Universal decimal classification (UDC)	51 - Mathematics
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.
Abstract (croatian)	Posljednjih godina slučajni skupovi su prepoznati kao koristan alat kod modeliranja raznih procesa u područjima znanosti kao što su biologija, biomedicina i nauka o materijalima. Pun potencijal ove primjene nije još dosegnut, a jedna od glavnih prepreka je najčešće nemogućnost razlikovanja pozadinskih procesa koji generiraju opažene realizacije. U ovoj disertaciji se uvodi mjera različitosti slučajnih skupova putem heuristike bazirane na aproksimaciji konveksnim tijelima i njihovim potpornim funkcijama. Za ocjenu različitosti korištena su dva statistička pristupa, ovojnični test rangova te test jednakosti po distribuciji dva slučajna konveksna tijela baziran na \(\mathfrak{N}\)--udaljenostima. Pri konstrukciji drugo spomenutog testa neki pojmovi su poopćeni na vektorski prostor ježeva kojeg tvore formalne razlike konveksinih tijela u \(\mathbb{R}^d\). Simulacijska studija koja opravdava korištenu metodologiju je provedena na standardnim modelima slučajnih skupova kao što su Boolean i Quermass-interaction procesi. Također je prikazan primjer primjene predložene metodologije na ispitivanje sličnosti uzoraka slika mastopatičnog tkiva dojke i raka mliječne žlijezde.
Keywords
Keywords (croatian)
Language	english
URN:NBN	urn:nbn:hr:217:126277
Study programme	Title: Mathematics Study programme type: university Study level: postgraduate Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
Type of resource	Text
Extent	91 str.
File origin	Born digital
Access conditions	Access restricted to students and staff of home institution
Terms of use
Repository	Repository of the Faculty of Science
Created on	2019-03-08 11:26:28