基于Cahn-Hilliard方程的二值图像修复方法
Binary Image Inpainting Method Based on Cahn-Hilliard Equation
DOI: 10.12677/AAM.2021.103073, PDF,    科研立项经费支持
作者: 霍俊蓉, 张荣培, 刘 昊：沈阳师范大学，数学与系统科学学院，辽宁 沈阳
关键词: 图像修复；Cahn-Hilliard方程；二值图像；有限差分法；Image Inpainting； Cahn-Hilliard Equation； Binary Image； Finite Difference Method
摘要: 图像修复作为图像处理的一个分支，在计算机视觉、天文学、生物学等领域中有广泛的应用。本文使用修正Cahn-Hilliard方程进行二值图像修复，采用二阶有限差分方法将含有非线性项的方程在空间上进行离散，采用Crank-Nicolson方法将其在时间上进行离散，应用快速离散余弦变换结合不动点迭代法求解全离散格式下的方程组。基于该模型的图像修复数值方法具有参数少、存储量小、计算效率高等优点。最后，给出数值实验，数值结果验证该数值方法能有效地进行图像修复与去噪。
Abstract: As a branch of image processing, image inpainting is widely used in computer vision, astronomy, biology and other fields. In this paper, the modified Cahn-Hilliard equation is used for binary image inpainting. The second-order finite difference method is used to discretize the equation with nonlinear term in space, and the Crank-Nicolson method is used to discretize it in time. The fast discrete cosine transform combined with fixed point iteration method is used to solve the equations in the fully discrete scheme. The numerical method of image inpainting based on this model has the advantages of few parameters, small storage and high computational efficiency. Finally, numerical experiments are given to verify the effectiveness of the proposed method.
文章引用：霍俊蓉, 张荣培, 刘昊. 基于Cahn-Hilliard方程的二值图像修复方法[J]. 应用数学进展, 2021, 10(3): 674-679. https://doi.org/10.12677/AAM.2021.103073

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