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undergraduate thesis
Prepoznavanje kružnica i elipsi
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. urn:nbn:hr:126:599722
Nikić, Patrick
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Geometry and Mathematics Teaching Mathematics Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Nikić, P. (2017). Prepoznavanje kružnica i elipsi (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:599722

Nikić, Patrick. "Prepoznavanje kružnica i elipsi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:599722

Nikić, Patrick. "Prepoznavanje kružnica i elipsi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:599722

Nikić, P. (2017). 'Prepoznavanje kružnica i elipsi', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 07 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:599722

Nikić P. Prepoznavanje kružnica i elipsi [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2025 January 07] Available at: https://urn.nsk.hr/urn:nbn:hr:126:599722

P. Nikić, "Prepoznavanje kružnica i elipsi", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:599722

Metadata
TitlePrepoznavanje kružnica i elipsi
Title (english)Circle and Ellipse Detection
AuthorPatrick Nikić
MentorRudolf Scitovski (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Geometry and Mathematics Teaching Mathematics Research Group)
Osijek
Defense date and country2017-09-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Numerical Mathematics
Abstract
Cilj ovoga završnoga rada je dati pregled osnovnih obilježja elipse i opisati odabrane algoritme za prepoznavanje kružnica i elipsi u podacima i na slikama. Opisat ćemo inačicu k-means algoritma za prepoznavanje kružnica i protumačiti kako se elipsa može interpretirati kao Mahalanobis kružnica sa nekom pozitivno definitnom matricom. Baviti ćemo se problemom prepoznavanja više elipsi u ravnini na temelju podataka koji dolaze iz skupa elipsi čiji broj nije unaprijed poznat. Biti će opisan algoritam za prepoznavanje elipsi koji se temelji na statistčkom modelu elipse. Nadalje, u svrhu efikasne implementacije prethodnog algoritma, predstavit ćemo konstrukciju C++ programa istoga. Konačno, testirati ćemo program na različitim generiranim primjerima i primjerima iz svakodnevnog života.
Abstract (english)
The aim of this final thesis is to provide an overview of the basic characteristics of the ellipse and to describe selected algorithms for circle and ellipse detection from data and images. We will describe a version of the k-means algorithm for circle detection and explain how the ellipse can be considered as a Mahalanobis circle with some positive definite matrix. We will address the problem of detecting multiple ellipses in the plane based on the data coming from a set of ellipses whose number is not known in advance. An algorithm for ellipse detection, which relies on a statistical model of the ellipse, will be described. Furthermore, in order to efficiently implement the previous algorithm, we will present a C++ implementation of it. Finally, we will test the program on different generated examples and examples in everyday life.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:599722
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-11-14 10:54:45