Garcke, Harald and Lam, Kei Fong and Styles, Vanessa (2018) Cahn-Hilliard Inpainting with the Double Obstacle Potential. SIAM JOURNAL ON IMAGING SCIENCES, 11 (3). pp. 2064-2089. ISSN 1936-4954,
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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 |
|---|---|
| Uncontrolled Keywords: | IMAGE; EQUATION; MODEL; DECOMPOSITION; RESTORATION; DYNAMICS; inpainting; Cahn-Hilliard model; double obstacle potential; binary and grayvalue images |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 24 Mar 2020 08:28 |
| Last Modified: | 24 Mar 2020 08:28 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15334 |
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