An image inpainting model based on the mixture of Perona-Malik equation and Cahn-Hilliard equation

被引：5
|
作者：
Zou, Qing [1 ,2 ]
机构：
[1] Univ Iowa, Appl Math & Computat Sci, Iowa City, IA 52242 USA
[2] Univ Iowa, Computat Biomed Imaging Grp, Iowa City, IA 52242 USA
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2021年 / 66卷 / 1-2期
关键词：
Image inpainting; Perona-Malik equation; Cahn-Hilliard equation; Fourier spectral method;
D O I：
10.1007/s12190-020-01422-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a fourth-order PDE model is proposed for image inpainting. This model is based on the mixture of Perona-Malik equation and Cahn-Hilliard equation. Using the idea of energy splitting, a numerical scheme is introduced for solving the proposed PDE model. Numerical experiments for testing the proposed model are provided at the end of the paper. The numerical results indicate that the proposed model can provide better inpainting performance with less computational time comparing to the classical PDE based inpainting models.
引用
收藏
页码：21 / 38
页数：18
相关论文
共 50 条
  • [1] An image inpainting model based on the mixture of Perona–Malik equation and Cahn–Hilliard equation
    Qing Zou
    [J]. Journal of Applied Mathematics and Computing, 2021, 66 : 21 - 38
  • [2] Generalized Perona-Malik equation for image restoration
    Wei, GW
    [J]. IEEE SIGNAL PROCESSING LETTERS, 1999, 6 (07) : 165 - 167
  • [3] IMAGE RESTORATION USING A NOVEL MODEL COMBINING THE PERONA-MALIK EQUATION AND THE HEAT EQUATION
    Lecheheb, Samira
    Maouni, Messaoud
    Lakhal, Hakim
    [J]. INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2021, 19 (02): : 228 - 238
  • [4] An adaptive Cahn-Hilliard equation for enhanced edges in binary image inpainting
    Theljani, Anis
    Houichet, Hamdi
    Mohamed, Anis
    [J]. JOURNAL OF ALGORITHMS & COMPUTATIONAL TECHNOLOGY, 2020, 14
  • [5] A Fractional Inpainting Model Based on the Vector-Valued Cahn-Hilliard Equation
    Bosch, Jessica
    Stoll, Martin
    [J]. SIAM JOURNAL ON IMAGING SCIENCES, 2015, 8 (04): : 2352 - 2382
  • [6] Strong solutions for the generalized Perona-Malik equation for image restoration
    Jin, Zhengmeng
    Yang, Xiaoping
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (04) : 1077 - 1084
  • [7] Gradient estimates for the Perona-Malik equation
    Ghisi, Marina
    Gobbino, Massimo
    [J]. MATHEMATISCHE ANNALEN, 2007, 337 (03) : 557 - 590
  • [8] Inpainting of binary images using the Cahn-Hilliard equation
    Bertozzi, Andrea L.
    Esedoglu, Selim
    Gillette, Alan
    [J]. IEEE TRANSACTIONS ON IMAGE PROCESSING, 2007, 16 (01) : 285 - 291
  • [9] Modified Perona-Malik equation and computer simulation for image denoising
    Feng, Zheng Jian
    Chengwei, Huang
    Ji, Zhang
    [J]. Open Mechanical Engineering Journal, 2014, 8 (01): : 37 - 41
  • [10] Shock filter as the classifier for image inpainting problem using the Cahn-Hilliard equation
    Novak, Andrej
    Reinic, Nora
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2022, 123 : 105 - 114
12345