Digital Image Inpainting Analysis Based on the Cahn-Hilliard Model

Abstract

One of the most important applications in image processing is digital image restoration, which attempts to restore sections of an image that have been lost or damaged. In this paper, we analyze and implement the Cahn-Hilliard model, a fourth-order nonlinear partial differential equation renowned for its efficiency and speed in preserving structural continuity and smoothness in the image. The model is designed to restore regions affected by intentional damage, scratches, or distortions. The model was numerically solved using the implicit finite difference method, which produced a stable and precise reconstruction using the convex partitioning technique. We applied the model to images with deliberate defects within eight different color spaces, including YUV, YCbCr, RGB, NTSC, XYZ, HSV, and others, and evaluated its performance in terms of restoration accuracy and the absence of visual distortions. The effectiveness of the Cahn-Hilliard model outperforms traditional restoration methods in reconstructing missing areas while preserving the original edges and fine details.