Finite difference method for Perona-Malik model with fractional derivative and its application in image processing

Sayah, Achraf; Moussaid, Noureddine; Gouasnouane, Omar

doi:10.1109/tst52996.2021.00024

2021 Third International Conference on Transportation and Smart Technologies (TST) 2021

DOI: 10.1109/tst52996.2021.00024

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Finite difference method for Perona-Malik model with fractional derivative and its application in image processing

Achraf Sayah

Noureddine Moussaid

Omar Gouasnouane

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2024

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Cited by 2 publications

References 10 publications

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A nonlinear fractional partial differential equation for image inpainting

Gouasnouane¹,

Moussaid²,

Boujena³

et al. 2022

Math. Model. Comput.

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Image inpainting is an important research area in image processing. Its main purpose is to supplement missing or damaged domains of images using information from surrounding areas. This step can be performed by using nonlinear diffusive filters requiring a resolution of partial differential evolution equations. In this paper, we propose a filter defined by a partial differential nonlinear evolution equation with spatial fractional derivatives. Due to this, we were able to improve the performance obtained by known inpainting models based on partial differential equations and extend certain existing results in image processing. The discretization of the fractional partial differential equation of the proposed model is carried out using the shifted Grünwald–Letnikov formula, which allows us to build stable numerical schemes. The comparative analysis shows that the proposed model produces an improved image quality better or comparable to that obtained by various other efficient models known from the literature.

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A nonlinear fractional partial differential equation for image inpainting

Gouasnouane¹,

Moussaid²,

Boujena³

et al. 2022

Math. Model. Comput.

View full text Add to dashboard Cite

show abstract

Total fractional-order variation and bilateral filter for image denoising

Addouch,

Moussaid,

Gouasnouane

et al. 2024

Math. Model. Comput.

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Image denoising stands out as a primary goal in image processing. However, many existing methods encounter challenges in preserving features such as corners and edges of an image while deleting the noise. This study investigates and evaluates a fractional-order derivative based on the total α-order variation (TV) model and the bilateral total variation (BTV) model. This choice is motivated by the proven effectiveness of the TV model in noise removal and edge preservation, with the BTV model further utilized to enhance the restoration of fine and intricate details. The experimental results affirm the efficacy of the proposed model, supported by objective quantitative metrics and subjective assessments of visual appearance.

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Finite difference method for Perona-Malik model with fractional derivative and its application in image processing

Cited by 2 publications

References 10 publications

A nonlinear fractional partial differential equation for image inpainting

A nonlinear fractional partial differential equation for image inpainting

Total fractional-order variation and bilateral filter for image denoising

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