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Symmetry
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Novel Symmetry Analysis and Numerical Methods for Solving Nonlinear Differential...
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Novel Symmetry Analysis and Numerical Methods for Solving Nonlinear Differential and Integral Equations

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 15 August 2024 | Viewed by 2917

Special Issue Editor

Dr. Behzad Ghanbari

E-Mail Website
Guest Editor
Associate Professor, Applied Mathematics, Kermanshah University of Technology, Imam Khomeyni Highway, Kermanshah 83GW+3H3, Iran
Interests: numerical analysis; computational

Special Issue Information

Dear Colleagues,

Over the years, it has been apparent that the application of classical concepts in differential integral and calculus equations and symmetry analysis in describing new applied problems requires a kind of general and fundamental overhaul. This Special Issue is so important that it may introduce new and various definitions into these fields. The Special Issue on “Novel symmetry analysis and numerical methods for solving nonlinear differential and integral equations” invites original manuscripts and review articles that deal with the new basic concepts, materials, experimental, and applied aspects of solving nonlinear differential and integral equations in one or more of the following areas:

  • Analytical methods;
  • Exact solutions;
  • Chaos and bifurcation;
  • Meshfree methods;
  • Fractional differential equations;
  • Modified fractional reduced differential transform method;
  • Wavelet analysis;
  • Operational matrices with function approximation;
  • Different methods in image processing.

Dr. Behzad Ghanbari
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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Research

24 pages, 18470 KiB  
Article
On Edge Detection Algorithms for Water-Repellent Images of Insulators Taking into Account Efficient Approaches
by Yizhuo Ding and Xiaofei Nan
Symmetry 2023, 15(7), 1418; https://doi.org/10.3390/sym15071418 - 14 Jul 2023
Cited by 1 | Viewed by 896
Abstract
Computer vision has become an essential interdisciplinary field that aims to extract valuable information from digital images or videos. To develop novel concepts in this area, researchers have employed powerful tools from both pure and applied mathematics. Recently, the use of fractional differential [...] Read more.
Computer vision has become an essential interdisciplinary field that aims to extract valuable information from digital images or videos. To develop novel concepts in this area, researchers have employed powerful tools from both pure and applied mathematics. Recently, the use of fractional differential equations has gained popularity in practical applications. Moreover, symmetry is a critical concept in digital image processing that can significantly improve edge detection. Investing in symmetry-based techniques, such as the Hough transform and Gabor filter, can enhance the accuracy and robustness of edge detection algorithms. Additionally, CNNs are incredibly useful in leveraging symmetry for image edge detection by identifying symmetrical patterns for improved accuracy. As a result, symmetry reveals promising applications in enhancing image analysis tasks and improving edge detection accuracy. This article focuses on one of the practical aspects of research in computer vision, namely, edge determination in image segmentation for water-repellent images of insulators. The article proposes two general structures for creating fractional masks, which are then calculated using the Atangana–Baleanu–Caputo fractional integral. Numerical simulations are utilized to showcase the performance and effectiveness of the suggested designs. The simulations’ outcomes reveal that the fractional masks proposed in the study exhibit superior accuracy and efficiency compared to various widely used masks documented in the literature. This is a significant achievement of this study, as it introduces new masks that have not been previously used in edge detection algorithms for water-repellent images of insulators. In addition, the computational cost of the suggested fractional masks is equivalent to that of traditional masks. The novel structures employed in this article can serve as suitable and efficient alternative masks for detecting image edges as opposed to the commonly used traditional kernels. Finally, this article sheds light on the potential of fractional differential equations in computer vision research and the benefits of developing new approaches to improve edge detection. Full article
(This article belongs to the Special Issue Novel Symmetry Analysis and Numerical Methods for Solving Nonlinear Differential and Integral Equations)
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24 pages, 7526 KiB  
Article
Image Denoising Method Relying on Iterative Adaptive Weight-Mean Filtering
by Meixia Wang, Susu Wang, Xiaoqin Ju and Yanhong Wang
Symmetry 2023, 15(6), 1181; https://doi.org/10.3390/sym15061181 - 1 Jun 2023
Cited by 2 | Viewed by 1314
Abstract
Salt-and-pepper noise (SPN) is a common type of image noise that appears as randomly distributed white and black pixels in an image. It is also known as impulse noise or random noise. This paper aims to introduce a new weighted average based on [...] Read more.
Salt-and-pepper noise (SPN) is a common type of image noise that appears as randomly distributed white and black pixels in an image. It is also known as impulse noise or random noise. This paper aims to introduce a new weighted average based on the Atangana–Baleanu fractional integral operator, which is a well-known idea in fractional calculus. Our proposed method also incorporates the concept of symmetry in the window mask structures, resulting in efficient and easily implementable filters for real-time applications. The distinguishing point of these techniques compared to similar methods is that we employ a novel idea for calculating the mean of regular pixels rather than the existing used mean formula along with the median. An iterative procedure has also been provided to integrate the power of removing high-density noise. Moreover, we will explore the different approaches to image denoising and their effectiveness in removing noise from images. The symmetrical structure of this tool will help in the ease and efficiency of these techniques. The outputs are compared in terms of peak signal-to-noise ratio, the mean-square error and structural similarity values. It was found that our proposed methodologies outperform some well-known compared methods. Moreover, they boast several advantages over alternative denoising techniques, including computational efficiency, the ability to eliminate noise while preserving image features, and real-time applicability. Full article
(This article belongs to the Special Issue Novel Symmetry Analysis and Numerical Methods for Solving Nonlinear Differential and Integral Equations)
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