2022
DOI: 10.23939/mmc2022.03.536
|View full text |Cite
|
Sign up to set email alerts
|

A nonlinear fractional partial differential equation for image inpainting

Abstract: 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 b… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1

Citation Types

0
3
0

Year Published

2022
2022
2023
2023

Publication Types

Select...
4
1

Relationship

0
5

Authors

Journals

citations
Cited by 6 publications
(3 citation statements)
references
References 15 publications
0
3
0
Order By: Relevance
“…However, the algorithm can be computationally intensive and requires good initialization of the known parts of the image to produce good results. It should be noted that there are several other mathematical models by nonlinear partial differential equations for image processing which have recently been derived from that of Perona and Malik and which have made it possible to improve their performance [4][5][6]. We will focus in the following on one of these models to build our powerful algorithm.…”
Section: Perona-malik Equationmentioning
confidence: 99%
“…However, the algorithm can be computationally intensive and requires good initialization of the known parts of the image to produce good results. It should be noted that there are several other mathematical models by nonlinear partial differential equations for image processing which have recently been derived from that of Perona and Malik and which have made it possible to improve their performance [4][5][6]. We will focus in the following on one of these models to build our powerful algorithm.…”
Section: Perona-malik Equationmentioning
confidence: 99%
“…Many authors have introduced fractional calculus in many works, fractional operators can more accurately express the natural phenomena than their traditional counterpart in [25][26][27][28][29][30][31][32].…”
Section: Fractional Order Modelmentioning
confidence: 99%
“…It is inspired by a very old technique performed by professionals to repair damaged photographs or paintings with defects such as spots, scratches, dust and cracks in order to maintain the best possible quality. There is a wide variety of literature papers that handle the problem of Image Inpainting such as [13][14][15][16][17][18][19].…”
Section: Introductionmentioning
confidence: 99%