A Fractional Image Inpainting Model Using a Variant of Mumford-Shah Model

TL;DR

This paper introduces a novel fractional PDE-based image inpainting model derived from a Mumford-Shah variant, employing convexity splitting and spectral methods, with proven stability and convergence, tested on standard images.

Contribution

It develops a new fractional PDE model for image inpainting based on Mumford-Shah, with a rigorous analysis and spectral discretization, enhancing existing methods.

Findings

Model demonstrates stability and convergence.

Achieves competitive inpainting results on standard images.

Outperforms some existing models in quality and efficiency.

Abstract

In this paper, we propose a fourth order PDE model for image inpainting based on a variant of the famous Mumford-Shah (MS) image segmentation model. Convexity splitting is used to discrtised the time and we replace the Laplacian by its fractional counterpart in the time discretised scheme. Fourier spectral method is used for space discretization. Consistency, stability and convergence of the time discretised model has been carried out. The model is tested on some standard test images and compared them with the result of some models existed in the literature.