An adaptive Cahn-Hilliard equation for enhanced edges in binary image inpainting
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 b...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2020-07-01
|
| Series: | Journal of Algorithms & Computational Technology |
| Online Access: | https://doi.org/10.1177/1748302620941430 |
| Summary: | 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. |
|---|---|
| ISSN: | 1748-3026 |