Journal of Applied Mathematics and Computation

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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


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.


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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.