Primjena Cahn-Hilliardove jednadžbe u obradi digitalne slike

master's thesis

• Title (english): Applications of the Cahn-Hilliard equation in the digital image processing
• Author: Martina Armanda
• Mentor: Andrej Novak (mentor)
• Committee member: Hrvoje Buljan (predsjednik povjerenstva)
• Committee member: Andrej Novak (član povjerenstva)
• Committee member: Davor Horvatić (član povjerenstva)
• Committee member: Nenad Pavin (član povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-07-08, 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: Cahn-Hilliardova jednadžba; digitalna slika; uslikavanje; cijepanje konveksnosti
• Keywords (english): Cahn-Hilliard equation; digital image; inpainting; convexity splitting
• Language: croatian
• URN:NBN: urn:nbn:hr:217:707631
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-09-08 11:29:05