Brkić Antun Lovro, Mitrović Darko, Novak Andrej
Institute of Physics, Bijenička cesta 46, 10000 Zagreb, Croatia.
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
J Adv Res. 2020 May 15;25:67-76. doi: 10.1016/j.jare.2020.04.015. eCollection 2020 Sep.
Motivated by the fact that the fractional Laplacean generates a wider choice of the interpolation curves than the Laplacean or bi-Laplacean, we propose a new non-local partial differential equation inspired by the Cahn-Hilliard model for recovering damaged parts of an image. We also note that our model is linear and that the computational costs are lower than those for the standard Cahn-Hilliard equation, while the inpainting results remain of high quality. We develop a numerical scheme for solving the resulting equations and provide an example of inpainting showing the potential of our method.
鉴于分数阶拉普拉斯算子比拉普拉斯算子或双拉普拉斯算子能生成更多样的插值曲线，我们受Cahn-Hilliard模型启发，提出了一种新的非局部偏微分方程，用于修复图像的受损部分。我们还注意到，我们的模型是线性的，计算成本低于标准Cahn-Hilliard方程，同时修复结果仍保持高质量。我们开发了一种数值格式来求解所得方程，并给出了一个修复示例，展示了我们方法的潜力。
