Image inpainting is the process of restoring damaged areas in an image using information available from neighboring regions. In this paper, we present a novel, efficient, and simple local image inpainting algorithm based on the Allen–Cahn (AC) equation with a fidelity term. We utilize the phase separation property of the AC equation and introduce a new phase-dependent fidelity parameter to preserve the original values in the neighboring regions of an inpainting region. The governing partial differential equation is solved using the finite difference method, with the values of the neighboring cells serving as the Dirichlet boundary condition. The proposed algorithm is both local and explicit, making it is fast and easy to implement. We demonstrate the performance of the proposed model through several numerical experiments. Furthermore, comparing this method to other image inpainting methods demonstrates its superiority in image inpainting.

图像修复是使用邻近区域的可用信息恢复图像中受损区域的过程。在本文中，我们提出了一种新颖、高效且​​简单的局部图像修复算法，该算法基于具有保真度项的 Allen–Cahn (AC) 方程。我们利用 AC 方程的相分离特性，并引入一种新的与相位相关的保真度参数来保留修复区域的相邻区域中的原始值。使用有限差分法求解控制偏微分方程，以相邻单元的值作为狄利克雷边界条件。所提出的算法既是局部的又是显式的，使其快速且易于实现。我们通过几个数值实验证明了所提出模型的性能。此外，将该方法与其他图像修复方法进行比较，证明了其在图像修复方面的优越性。