Professional paper

https://doi.org/10.31896/k.28.6

The application of the Cahn-Hilliard equation for digital image inpainting

Andrej Novak ; Faculty of Science, University of Zagreb, Zagreb, Croatia *
Martina Armanda ; Faculty of Science, University of Zagreb, Zagreb, Croatia

* Corresponding author.

Abstract

We investigate the application of the Cahn-Hilliard (CH) equation for digital image inpainting, focusing on various choices of nonlinear potential, including the double well potential and classiers based on shock filters. These potentials are crucial in shaping the inpainting results, and their selection depends on the characteristics of specific images and the desired properties of reconstruction. Additionally, we present a numerical scheme based on the principle of convexity splitting, and we demonstrate the results of inpainting simple binary shapes. Throughout the text, we emphasize the fundamental features of the Cahn-Hilliard equation to enable a better understanding of the role of partial differential equations in image processing.

Keywords

Cahn-Hilliard equation; digital image inpainting; numerical methods; image processing

Hrčak ID:

324096

URI

https://hrcak.srce.hr/324096

Publication date:

20.12.2024.

Article data in other languages: croatian

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