Shock filter as the classifier for image inpainting problem using the Cahn-Hilliard equation. (1st October 2022)

• Record Type: Journal Article
• Authors: Novak, Andrej; Reinić, Nora
• Is Part Of: Computers & mathematics with applications. Volume 123(2022)
• Page Start: 105
• Page End: 114
• Publication Date: 2022-10-01
• Subjects: Image inpainting -- Cahn-Hilliard equation -- Shock filter; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.07.021
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We consider a problem of digital image inpainting using the modified Cahn-Hilliard equation, where the standard double well potential is replaced by the shock filter. Using fixed point arguments and Aubin-Lions lemma we prove the existence and uniqueness of the solution. In addition, we introduce a numerical method based on the convexity splitting idea to approximate the solutions of the considered problem. We apply this method to several binary images and demonstrate that this approach naturally extends image features and preserves their edges.