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Mathematics
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Advances in Mathematical Methods for Image Processing and Pattern Recognition
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Advances in Mathematical Methods for Image Processing and Pattern Recognition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 13238

Special Issue Editor

Prof. Dr. Huafeng Li

E-Mail Website
Guest Editor
Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China
Interests: image processing; image recognition and retrieval; machine learning

Special Issue Information

Dear Colleagues,

Image processing and pattern recognition span multiple industries, including transportation, manufacturing, healthcare, military, and others. The related techniques cover medical imaging, remote sensing, autonomous driving, intelligent monitoring, road-condition and traffic-flow analysis, and more, providing people with a smarter living environment. The relevance of artificial intelligence has attracted much attention, and has also sparked great interest in the development of image-processing and pattern-recognition algorithms to solve a wide variety of real-world problems using mathematical skills such as low-rank sparse modeling theory, statistical learning, singular value decomposition, graph theory, information theory, and fuzzy theory.

This Special Issue is intended as a forum aimed at encouraging new mathematical methods in the fields of image processing and pattern recognition. Specifically, from the perspective of the fields of mathematics relevant to modern applications, research topics have discovered key correlations between the two, with mathematical methods including, but not limited to, the design of nonlinear classifiers, optimization under specific conditions, or feature selection based on probabilistic latent graphs.

Papers of both theoretical and applied nature are welcome, as well as original contributions to the theories, methods, discoveries, and applications of image processing and pattern recognition. Papers with mathematical analysis and practical applications are particularly welcome.

Potential topics include, but are not limited to, the following:

  • Low-rank and sparse representation for image processing and pattern recognition;
  • Optimization in deep learning;
  • Optimization and learning methods;
  • Basic theory of computer vision;
  • Mathematical problems in object detection;
  • Mathematical Problems in object recognition;
  • Regression methods for image processing and pattern recognition;
  • Mathematical problems in classification;
  • Mathematical problems in subspace learning;
  • Feature extraction and feature selection;
  • Graph theory in graph neural networks;
  • Information theory in deep neural networks;
  • Inverse problems in image processing and pattern recognition;
  • Fuzzy logic application;
  • Objective evaluation for image processing and pattern recognition tasks;
  • Interpretability of deep learning;
  • Deep learning theory and application;
  • Mathematical methods for medical image processing and recognition.

Prof. Dr. Huafeng Li
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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.

Keywords

  • image processing
  • image recognition and retrieval
  • medical imaging
  • medical image segmentation
  • machine learning
  • deep learning

Published Papers (6 papers)

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Research

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16 pages, 3838 KiB  
Article
Potato Blight Detection Using Fine-Tuned CNN Architecture
by Mosleh Hmoud Al-Adhaileh, Amit Verma, Theyazn H. H. Aldhyani and Deepika Koundal
Mathematics 2023, 11(6), 1516; https://doi.org/10.3390/math11061516 - 21 Mar 2023
Cited by 11 | Viewed by 4846
Abstract
Potato is one of the major cultivated crops and provides occupations and livelihoods for numerous people across the globe. It also contributes to the economic growth of developing and underdeveloped countries. However, potato blight is one of the major destroyers of potato crops [...] Read more.
Potato is one of the major cultivated crops and provides occupations and livelihoods for numerous people across the globe. It also contributes to the economic growth of developing and underdeveloped countries. However, potato blight is one of the major destroyers of potato crops worldwide. With the introduction of neural networks to agriculture, many researchers have contributed to the early detection of potato blight using various machine and deep learning algorithms. However, accuracy and computation time remain serious issues. Therefore, considering these challenges, we customised a convolutional neural network (CNN) to improve accuracy with fewer trainable parameters, less computation time, and reduced information loss. We compared the performance of the proposed model with various machine and deep learning algorithms used for potato blight classification. The proposed model outperformed the others with an overall accuracy of 99% using 839,203 trainable parameters in 183 s of training time. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods for Image Processing and Pattern Recognition)
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19 pages, 5871 KiB  
Article
Multi-Layer Decomposition and Synthesis of HDR Images to Improve High-Saturation Boundaries
by Hyuk-Ju Kwon and Sung-Hak Lee
Mathematics 2023, 11(3), 785; https://doi.org/10.3390/math11030785 - 03 Feb 2023
Cited by 2 | Viewed by 1264
Abstract
Recently, high dynamic range (HDR) imaging has been used in many fields such as display, computer graphics, and digital cameras. Various tone mapping operators (TMOs) are used for effective HDR imaging. TMOs aim to express HDR images without loss of information and natural [...] Read more.
Recently, high dynamic range (HDR) imaging has been used in many fields such as display, computer graphics, and digital cameras. Various tone mapping operators (TMOs) are used for effective HDR imaging. TMOs aim to express HDR images without loss of information and natural images on existing display equipment. In this paper, to improve the color distortion that occurs during tone mapping, multi-layer decomposition-based color compensation and global color enhancement of the boundary region are proposed. Multi-layer decomposition is used to preserve the color information of the input image and to find the area where color distortion occurs. Color compensation and enhancement are especially used to improve the color saturation of the border area, which is degraded due to color distortion and tone processing. Color compensation and enhancement are processed in IPT color space with excellent hue linearity to improve effective performance by reducing interference between luminance and chrominance components. The performance of the proposed method was compared to the existing methods using naturalness, distortion, and tone-mapped image quality metrics. The results show that the proposed method is superior to the existing methods. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods for Image Processing and Pattern Recognition)
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17 pages, 12163 KiB  
Article
Single Image Super-Resolution Reconstruction with Preservation of Structure and Texture Details
by Yafei Zhang, Yuqing Huang, Kaizheng Wang, Guanqiu Qi and Jinting Zhu
Mathematics 2023, 11(1), 216; https://doi.org/10.3390/math11010216 - 01 Jan 2023
Cited by 3 | Viewed by 1839
Abstract
In recent years, deep-learning-based single image super-resolution reconstruction has achieved good performance. However, most existing methods pursue a high peak signal-to-noise ratio (PSNR), while ignoring the quality of the structure and texture details, resulting in unsatisfactory performance of the reconstruction results in terms [...] Read more.
In recent years, deep-learning-based single image super-resolution reconstruction has achieved good performance. However, most existing methods pursue a high peak signal-to-noise ratio (PSNR), while ignoring the quality of the structure and texture details, resulting in unsatisfactory performance of the reconstruction results in terms of human subjective perception. To solve this issue, this paper proposes a structure- and texture-preserving image super-resolution reconstruction method. Specifically, two different network branches are used to extract features for image structure and texture details. A dual-coordinate direction perception attention (DCDPA) mechanism is designed to highlight structure and texture features. The attention mechanism fully considers the complementarity and directionality of multi-scale image features and effectively avoids information loss and possible distortion of image structure and texture details during image reconstruction. Additionally, a cross-fusion mechanism is designed to comprehensively utilize structure and texture information for super-resolution image reconstruction, which effectively integrates the structure and texture details extracted by the two branch networks. Extensive experiments verify the effectiveness of the proposed method and its superiority over existing methods. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods for Image Processing and Pattern Recognition)
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17 pages, 444 KiB  
Article
Resource- and Time-Efficient Computation Offloading in Vehicular Edge Computing: A Max-Min Fairness Oriented Approach
by Shujuan Wang, Hao Peng and Dongchao Guo
Mathematics 2022, 10(20), 3735; https://doi.org/10.3390/math10203735 - 11 Oct 2022
Cited by 3 | Viewed by 1060
Abstract
Nowadays, computation offloading has become a research focus since it has the potential to solve the challenges faced when dealing with computation-intensive applications in the Internet of Vehicles (IoVs), especially in the 5G or future network environment. However, major issues still exist and [...] Read more.
Nowadays, computation offloading has become a research focus since it has the potential to solve the challenges faced when dealing with computation-intensive applications in the Internet of Vehicles (IoVs), especially in the 5G or future network environment. However, major issues still exist and the performance of main metrics can be improved to better adapt to the practical scenarios. This paper focuses on achieving resource- and time-efficient computation offloading in IoVs by boosting the cooperation efficiency of vehicles. Firstly, a fuzzy logic-based pricing strategy is designed to evaluate the cooperation tendency and capability of each vehicle from multiple aspects. Vehicles are encouraged to participate in the offloading process even if they are in a disadvantageous position compared to other vehicles. Secondly, a Max-Min fairness-oriented approach is proposed to find the most suitable offloading decision, and vehicles with poor cooperation capabilities are guaranteed to be treated equally in the offloading. Finally, two heuristic algorithms are presented to solve the problem with applicable complexity and to suit the practical IoV environment. Extensive simulation results prove that the proposed approach achieves remarkable performance improvements in terms of delay, service cost and the resource utilization ratios of vehicles. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods for Image Processing and Pattern Recognition)
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13 pages, 1821 KiB  
Article
A Primal–Dual Fixed-Point Algorithm for TVL1 Wavelet Inpainting Based on Moreau Envelope
by Zemin Ren, Qifeng Zhang and Yuxing Yuan
Mathematics 2022, 10(14), 2470; https://doi.org/10.3390/math10142470 - 15 Jul 2022
Cited by 1 | Viewed by 1126
Abstract
In this paper, we present a novel variational wavelet inpainting based on the total variation (TV) regularization and the l1-norm fitting term. The goal of this model is to recover incomplete wavelet coefficients in the presence of impulsive noise. By incorporating the Moreau [...] Read more.
In this paper, we present a novel variational wavelet inpainting based on the total variation (TV) regularization and the l1-norm fitting term. The goal of this model is to recover incomplete wavelet coefficients in the presence of impulsive noise. By incorporating the Moreau envelope, the proposed model for wavelet inpainting can better handle the non-differentiability of the l1-norm fitting term. A modified primal dual fixed-point algorithm is developed based on the proximity operator to solve the proposed variational model. Moreover, we consider the existence of solution for the proposed model and the convergence analysis of the developed iterative scheme in this paper. Numerical experiments show the desirable performance of our method. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods for Image Processing and Pattern Recognition)
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Review

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25 pages, 1407 KiB  
Review
Survey of Cross-Modal Person Re-Identification from a Mathematical Perspective
by Minghui Liu, Yafei Zhang and Huafeng Li
Mathematics 2023, 11(3), 654; https://doi.org/10.3390/math11030654 - 28 Jan 2023
Cited by 1 | Viewed by 1598
Abstract
Person re-identification (Re-ID) aims to retrieve a particular pedestrian’s identification from a surveillance system consisting of non-overlapping cameras. In recent years, researchers have begun to focus on open-world person Re-ID tasks based on non-ideal situations. One of the most representative of these is [...] Read more.
Person re-identification (Re-ID) aims to retrieve a particular pedestrian’s identification from a surveillance system consisting of non-overlapping cameras. In recent years, researchers have begun to focus on open-world person Re-ID tasks based on non-ideal situations. One of the most representative of these is cross-modal person Re-ID, which aims to match probe data with target data from different modalities. According to the modalities of probe and target data, we divided cross-modal person Re-ID into visible–infrared, visible–depth, visible–sketch, and visible–text person Re-ID. In cross-modal person Re-ID, the most challenging problem is the modal gap. According to the different methods of narrowing the modal gap, we classified the existing works into picture-based style conversion methods, feature-based modality-invariant embedding mapping methods, and modality-unrelated auxiliary information mining methods. In addition, by generalizing the aforementioned works, we find that although deep-learning-based models perform well, the black-box-like learning process makes these models less interpretable and generalized. Therefore, we attempted to interpret different cross-modal person Re-ID models from a mathematical perspective. Through the above work, we attempt to compensate for the lack of mathematical interpretation of models in previous person Re-ID reviews and hope that our work will bring new inspiration to researchers. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods for Image Processing and Pattern Recognition)
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