Cahn--Hilliard inpainting with the double obstacle potential

Garcke, Harald, Lam, Kei Fong and Styles, Vanessa (2018) Cahn--Hilliard inpainting with the double obstacle potential. SIAM Review, 11 (3). pp. 2064-2089. ISSN 0036-1445

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Abstract

The inpainting of damaged images has a wide range of applications, and many different mathematical methods have been proposed to solve this problem. Inpainting with the help of Cahn{Hilliard models has been particularly successful, and it turns out that Cahn{Hilliard inpainting with the double obstacle potential can lead to better results compared to inpainting with a smooth double well
potential. However, a mathematical analysis of this approach is missing so far. In this paper we give first analytical results for a Cahn{Hilliard double obstacle inpainting model regarding existence of global solutions to the time-dependent problem and stationary solutions to the time-independent problem without constraints on the parameters involved. With the help of numerical results we show the effectiveness of the approach for binary and grayscale images.

Item Type: Article
Keywords: inpainting, Cahn{Hilliard model, double obstacle potential, binary and grayvalue images
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Jodie Bacon
Date Deposited: 12 Oct 2018 11:31
Last Modified: 12 Oct 2018 11:32
URI: http://srodev.sussex.ac.uk/id/eprint/79377

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