Numerical analysis of an adjusted Cahn-Hilliard equation for binary image inpainting

Poole, Gary A (2017) Numerical analysis of an adjusted Cahn-Hilliard equation for binary image inpainting. Doctoral thesis (PhD), University of Sussex.

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Abstract

This thesis aims to analyse a finite element method applied to an adjusted Cahn-Hilliard equation that has been used for digital image inpainting applications. We consider both the standard model with a smooth double well potential and an alternative where an obstacle potential has been used. Existence and uniqueness results are derived for both formulations by adapting techniques existing in literature for other problems.

For each formulation we then propose approximations, by discretising first in space and then in time, and we derive error bounds between the weak solution of the original formulation and the solution of the discrete approximations in terms of the discretisation parameters.

We then propose and implement a practical numerical scheme for both models and investigate their use in applications, alongside some other models from literature. We investigate various real digital image examples and compare the resulting inpaintings for these competing models, considering their suitability for real-world applications.

Item Type: Thesis (Doctoral)
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: T Technology > TA Engineering (General). Civil engineering (General) > TA0329 Engineering mathematics. Engineering analysis > TA0347.A-Z Other specific mathematical aids in the solution of engineering problems, A-Z > TA0347.F5 Finite element method
Depositing User: Library Cataloguing
Date Deposited: 15 Feb 2017 13:51
Last Modified: 15 Feb 2017 13:51
URI: http://sro.sussex.ac.uk/id/eprint/66783

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