An adaptive Cahn-Hilliard equation for enhanced edges in binary image inpainting. (July 2020)

• Record Type: Journal Article
• Authors: Theljani, Anis; Houichet, Hamdi; Mohamed, Anis
• Is Part Of: Journal of algorithms & computational technology. Volume 14(2020)
• Publication Date: 2020-07
• Subjects: Image inpainting -- Cahn-Hilliard equation -- splitting convexity method -- inverse problems -- adaptive strategy -- mixed finite elements; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/1748302620941430
• Languages: English
• ISSNs: 1748-3018

Abstract

We consider the Cahn-Hilliard equation for solving the binary image inpainting problem with emphasis on the recovery of low-order sets (edges, corners) and enhanced edges. The model consists in solving a modified Cahn-Hilliard equation by weighting the diffusion operator with a function which will be selected locally and adaptively. The diffusivity selection is dynamically adopted at the discrete level using the residual error indicator. We combine the adaptive approach with a standard mesh adaptation technique in order to well approximate and recover the singular set of the solution. We give some numerical examples and comparisons with the classical Cahn-Hillard equation for different scenarios. The numerical results illustrate the effectiveness of the proposed model.