Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 87909 Total View: 1370287
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Article http://dx.doi.org/10.26855/jamc.2023.03.017

An Image Inpainting Model for Grayscale Images Based on TV-H-1 Coupled with Perona-Malik Equation

Rajrup Banerjee1,*, Rohit Kamal Chatterjee2, Avijit Kar1

1Department of Computer Science and Engineering, Jadavpur University, Kolkata, India.

2Department of Computer Science and Engineering, BIT Mesra, Ranchi, India.

*Corresponding author: Rajrup Banerjee

Published: May 6,2023

Abstract

Image inpainting is the interpolation of missing or damaged portions of images employing information from the boundary and adjacent areas. Several fourth order Partial Differential Equation (PDE) based models are available in the literature to solve the inpainting problem, e.g. various Curvature Driven Diffusion methods, Cahn Hilliard Equation, TV-H-1 etc. This paper presents a new fourth order PDE for image inpainting based on TV-H-1 coupled with the Perona Malik equation. Perona and Malik proposed a nonlinear PDE to regulate diffusion by replacing the conductivity term with a function that enhances diffusion in homogenous regions but prohibits diffusion across edges in the image. An explicit- implicit numerical scheme is proposed in this paper based on splitting two convex energy terms, followed by Fourier spectral method on those, to solve the proposed PDE model. The results indicate that the proposed method generates better results in far less computational time than state-of-the-art methods.

References

[1] Bertalmio, M., Sapiro, G., Caselles, V., & Ballester, C. (2000). Image inpainting. Proceedings of the 27th annual conference on Computer graphics and interactive techniques, (pp. 417–424).

[2] Bertalmio, M., Bertozzi, A. L., & Sapiro, G. (2001). Navier-stokes, fluid dynamics, and image and video inpainting. Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, 1, pp. I–I.

[3] Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on pattern analysis and machine intelligence, 12, 629–639.

[4] Rudin, L. I., Osher, S., & Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D: nonlinear phenomena, 60, 259–268.

[5] Chan, T. F., Shen, J., & Zhou, H.-M. (2006). Total variation wavelet inpainting. Journal of Mathematical imaging and Vision, 25, 107–125.

[6] Shen, J., Kang, S. H., & Chan, T. F. (2003). Euler's elastica and curvature-based inpainting. SIAM journal on Applied Mathematics, 63, 564–592.

[7] Chan, T. F., & Shen, J. (2001). Nontexture inpainting by curvature-driven diffusions. Journal of visual communication and image representation, 12, 436–449.

[8] Bertozzi, A. L., Esedoglu, S., & Gillette, A. (2006). Inpainting of binary images using the Cahn–Hilliard equation. IEEE Transactions on image processing, 16, 285–291.

[9] Burger, M., He, L., & Schönlieb, C.-B. (2009). Cahn–Hilliard inpainting and a generalization for grayvalue images. SIAM Journal on Imaging Sciences, 2, 1129–1167.

[10] Zou, Q. (2021). An image inpainting model based on the mixture of Perona–Malik equation and Cahn–Hilliard equation. Journal of Applied Mathematics and Computing, 66, 21–38.

[11] Bertozzi, A., & Schönlieb, C.-B. (2011). Unconditionally stable schemes for higher order inpainting. Communications in Mathematical Sciences, 9, 413–457.

[12] Gillette, A. (2006). Image inpainting using a modified Cahn-Hilliard equation. Ph.D. dissertation, University of California Los Angeles.

[13] Schonlieb, C.-B. (2009). Modern PDE techniques for image inpainting. Ph.D. dissertation, University of Cambridge.

[14] Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13, 600–612.

How to cite this paper

An Image Inpainting Model for Grayscale Images Based on TV-H-1 Coupled with Perona-Malik Equation

How to cite this paper:  Rajrup Banerjee, Rohit Kamal Chatterjee, Avijit Kar. (2023) An Image Inpainting Model for Grayscale Images Based on TV-H-1 Coupled with Perona-Malik EquationJournal of Applied Mathematics and Computation7(1), 152-161.

DOI: http://dx.doi.org/10.26855/jamc.2023.03.017