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master's thesis
Primjena Cahn-Hilliardove jednadžbe u obradi digitalne slike
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:707631
Armanda, Martina
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

Cite this document

Armanda, M. (2022). Primjena Cahn-Hilliardove jednadžbe u obradi digitalne slike (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:707631

Armanda, Martina. "Primjena Cahn-Hilliardove jednadžbe u obradi digitalne slike." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:707631

Armanda, Martina. "Primjena Cahn-Hilliardove jednadžbe u obradi digitalne slike." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:707631

Armanda, M. (2022). 'Primjena Cahn-Hilliardove jednadžbe u obradi digitalne slike', Master's thesis, University of Zagreb, Faculty of Science, accessed 14 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:707631

Armanda M. Primjena Cahn-Hilliardove jednadžbe u obradi digitalne slike [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 May 14] Available at: https://urn.nsk.hr/urn:nbn:hr:217:707631

M. Armanda, "Primjena Cahn-Hilliardove jednadžbe u obradi digitalne slike", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:707631

Metadata
TitlePrimjena Cahn-Hilliardove jednadžbe u obradi digitalne slike
Title (english)Applications of the Cahn-Hilliard equation in the digital image processing
AuthorMartina Armanda
MentorAndrej Novak (mentor)
Committee memberHrvoje Buljan (predsjednik povjerenstva)
Committee memberAndrej Novak (član povjerenstva)
Committee memberDavor Horvatić (član povjerenstva)
Committee memberNenad Pavin (član povjerenstva)
Committee memberMaro Cvitan (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2022-07-08, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Cahn-Hilliardova jednadžba nelinearna je difuzijska jednadžba četvrtog reda prvobitno izvedena za modeliranje razdvajanja faza u binarnim legurama. U radu prikazujemo brojne primjene jednadžbe, s naglaskom na primjenu u obradi digitalne slike. Ilustriramo jedan od izvoda ove jednadžbe koristeći se osnovama termodinamike. Uvodimo problem uslikavanja binarnih slika i kroz nekoliko primjera postupno razvijamo sofisticirane pristupe problemu. Također predstavljamo numeričku metodu za rješavanje Cahn-Hilliardove jednadžbe koja se temelji na metodi cijepanja konveksnosti. Na kraju ovu metodu uspoređujemo s nekoliko ranije poznatih primjera iz literature.
Abstract (english)
Cahn-Hilliard equation is a nonlinear fourth order diffusion equation originally derived to model phase separation in binary alloys. In this thesis, we present a number of applications with a focus on applications in digital image processing. We present one of the derivations of the equation by using basic thermodynamics. We introduce the problem of inpainting of binary digital images and through a few examples we gradually develop sophisticated approaches to the problem. We also introduce a numerical method for solving the Cahn-Hilliard equation that is based on the convexity splitting method. Finally, we compare this method with several approaches previously seen in the literature.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:707631
Study programmeTitle: Physics and Computer Science; specializations in: Education
Course: Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije fizike i informatike (magistar/magistra edukacije fizike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-09-08 11:29:05