基于偏微分方程的图像修复数值模型
Numerical Model of Image Inpainting Based on Partial Differential Equation
DOI: 10.12677/CSA.2021.118208, PDF,   
作者: 霍俊蓉：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；图像处理；TV模型；偏微分方程；Image Inpainting； Image Processing； TV Model； Partial Differential Equation
摘要: 图像修复是图像处理的一个分支，是利用周围区域的信息填充图像的缺失或损坏区域。本文为今后能够更好地对破损图像进行修复与技术处理，进而针对图像修复中常见的边缘问题总结了几类基于偏微分方程进行图像修复的数值模型，这几种数值模型能够在保证修复效果较好且稳定的同时减少计算量，并提高修复效率，进一步完善修复效果，能够更好地为图像修复发展研究提供理论与数值模型基础。
Abstract: Image inpainting is a branch of image processing, which uses the information of the surrounding area to fill in the missing or damaged area of the image. In order to better repair and process the damaged image in the future, this paper summarizes several kinds of numerical models based on partial differential equation for image restoration, aiming at the common edge problems in image restoration. These numerical models can ensure the good and stable repair effect, reduce the amount of calculation, improve the repair efficiency, and further improve the repair effect, it can provide a theoretical and numerical model foundation for the development of image inpainting.
文章引用：霍俊蓉. 基于偏微分方程的图像修复数值模型[J]. 计算机科学与应用, 2021, 11(8): 2035-2041. https://doi.org/10.12677/CSA.2021.118208

参考文献

[1] 谷伊, 韩军. 基于样本的图像修补方法在视频修复中的应用[J]. 应用科学学报, 2010, 28(2): 163-169.
[2] Gu, J., Zhang, L., Yu, G., et al. (2006) X-Ray CT Metal Artifacts Reduction through Curvature Based Sinogram Inpainting. Journal of X-Ray Science and Technology, 14, 73-82.
[3] Chen, X., Yang, S., Wang, X., et al. (2010) Satellite Image Blind Restoration Based on Surface Fitting and Iterative Multishrinkage Method in Redundant Wavelet Domain. Optik, 121, 1909-1911. [Google Scholar] [CrossRef] 
[4] 李凯. 基于纹理特征的图像修复算法研究[D]: [硕士学位论文]. 重庆: 重庆邮电大学, 2017.
[5] 王鑫, 朱行成, 宁晨, 等. 基于冗余字典学习的图像修补算法[J]. 计算机工程与应用, 2018, 54(6): 198-204. [Google Scholar] [CrossRef] 
[6] Shen, J.H. and Chan, T.F. (2002) Mathematical Models for Local Nontexture Inpaintings. SIAM Journal on Applied Mathematics, 62, 1019-1043. [Google Scholar] [CrossRef] 
[7] 赵颜伟, 李象霖. 基于CDD模型的快速图像修复算法[J]. 计算机仿真, 2008, 25(10): 223-227.
[8] Greer, J.B., Bertozzi, A.L. and Sapiro, G. (2006) Fourth Order Partial Dif-ferential Equations on General Geometries. Journal of Computational Physics, 216, 216-246. [Google Scholar] [CrossRef] 
[9] Bertozzi, A., Esedoglu, S. and Gillette, A. (2007) Analysis of a Two-Scale Cahn-Hilliard Model for Binary Image Inpainting. Multiscale Modeling & Simulation, 6, 913-936. [Google Scholar] [CrossRef] 
[10] 郑精灵, 王树根. 整体变分算法在图像修补中的应用研究[J]. 计算机辅助设计与图形学学报, 2003, 15(10): 1218-1223.
[11] 林云莉, 赵俊红, 朱学峰, 等. 改进的TV模型图像修复算法[J]. 计算机工程与设计, 2010(4): 776-779.
[12] Bertalmio, M., Sapiro, G., Caselles, V., et al. (2000) Image Inpainting. Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, New Orleans, 23-28 July 2000, 417-424. [Google Scholar] [CrossRef] 
[13] 谢正伟, 王创新. 基于全变分模型改进的图像修复算法应用[J]. 电子科技, 2017(1): 61-64.
[14] 苗晓, 张新东, 唐泉, 杨思渊. 基于偏微分方程的图像修复方法研究[J]. 山东科学, 2021, 34(2): 90-95.
[15] 邱俊, 胡晓, 王汉权. 数字图像修复的变分方法与实现过程[J]. 数值计算与计算机应用, 2016, 37(4): 273-286.
[16] 王世强. 基于偏微分方程的图像修复技术研究[D]: [硕士学位论文]. 大连: 大连理工大学, 2014.
[17] 王大凯. 图像处理的偏微分方程方法[M]. 北京: 北京科技出版社, 2008.
[18] Easley, G., Labate, D. and Lim, W.Q. (2008) Sparse Directional Image Representations Using the Discrete Shearlet Transform. Ap-plied and Computational Harmonic Analysis, 25, 25-46. [Google Scholar] [CrossRef] 
[19] Li, Y., Jeong, D., Choi, J.I., et al. (2015) Fast Local Image Inpainting Based on the Allen-Cahn Model. Digital Signal Pro-cessing, 37, 65-74. [Google Scholar] [CrossRef] 
[20] Qiao, Y.Y., Zhai, S.Y. and Feng, X.L. (2018) An Operator Splitting Method for Image Inpainting Based on the Allen-Cahn Equation. Chinese Journal of Engineering Mathematics, 35, 722-732.