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Axioms
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Developments of Mathematical Methods in Image Processing
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Developments of Mathematical Methods in Image Processing

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (20 March 2024) | Viewed by 3275

Special Issue Editor

Dr. Domingo López-Rodríguez

E-Mail Website
Guest Editor
Departamento Matemática Aplicada, Universidad de Málaga, 29071 Málaga, Spain
Interests: formal concept analysis; machine learning; image processing; neural networks; applied mathematics

Special Issue Information

Dear Colleagues,

The development of mathematical methods in image processing has been an active area of research for several decades. The aim of these methods is to extract useful information from images and to process them for various applications, such as computer vision, medical or satellite image processing, security, and so on. The mathematical methods used in image processing also originate from different areas, for instance, algebraic methods, Fourier analysis, optimization, machine learning, differential equations, logic, formal methods and languages, fuzzy transforms, graph theory, and Bayesian analysis, among many others. This Special Issue of Axioms focuses on recent advances in the mathematical foundations of image processing methods and their applications. The guest editors aim to provide a platform to present the latest research related to the development of mathematical methods (as mentioned above) in topics that may include, but are not limited to, the following:

  • image segmentation;
  • feature extraction, edge detection, and pattern recognition;
  • image enhancement: denoising, contrast adjustment, sharpening, and super-resolution;
  • image registration;
  • image compression;
  • object recognition;
  • image classification;
  • motion estimation;
  • image restoration;
  • image analysis;
  • image generation;
  • image-to-image translation: style transfer and semantic segmentation;
  • applications: medical imaging, satellite imaging, etc.

We hope that this Special Issue will be attractive to researchers specializing in the above-mentioned fields. Contributions may be submitted on a continuous basis until the deadline. After a peer-review process, submissions will be selected for publication based on their quality and relevance.

Dr. Domingo López-Rodríguez
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. Axioms 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.

Keywords

  • image processing
  • segmentation
  • mathematical methods
  • classification
  • registration
  • enhancement

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Published Papers (2 papers)

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Research

15 pages, 273 KiB  
Article
Digital h-Fibrations and Some New Results on Digital Fibrations
by Talip Can Termen and Ozgur Ege
Axioms 2024, 13(3), 180; https://doi.org/10.3390/axioms13030180 - 8 Mar 2024
Viewed by 1015
Abstract
In this work, the notion of digital fiber homotopy is defined and its properties are given. We present some new results on digital fibrations. Moreover, we introduce digital h-fibrations. We prove some of the properties of these digital h-fibrations. We show [...] Read more.
In this work, the notion of digital fiber homotopy is defined and its properties are given. We present some new results on digital fibrations. Moreover, we introduce digital h-fibrations. We prove some of the properties of these digital h-fibrations. We show that a digital fibration and a digital map p are fiber homotopic equivalent if and only if p is a digital h-fibration. Finally, we explore a relation between digital fibrations and digital h-fibrations. Full article
(This article belongs to the Special Issue Developments of Mathematical Methods in Image Processing)
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30 pages, 2235 KiB  
Article
Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit
by Rosa Maza-Quiroga, Karl Thurnhofer-Hemsi, Domingo López-Rodríguez and Ezequiel López-Rubio
Axioms 2023, 12(12), 1117; https://doi.org/10.3390/axioms12121117 - 13 Dec 2023
Viewed by 1504
Abstract
This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first [...] Read more.
This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first digit distribution is examined, which causes deviations from the ideal distribution. A novel methodology is proposed for noise level estimation, employing metrics such as the Bhattacharyya distance, Kullback–Leibler divergence, total variation distance, Hellinger distance, and Jensen–Shannon divergence. Supervised learning techniques utilize these metrics as regressors. Evaluations on MRI scans from several datasets coming from a wide range of different acquisition devices of 1.5 T and 3 T, comprising hundreds of patients, validate the adherence of noiseless T1 MRI frequency domain coefficients to Benford’s law. Through rigorous experimentation, our methodology has demonstrated competitiveness with established noise estimation techniques, even surpassing them in numerous conducted experiments. This research empirically supports the application of Benford’s law in transforms, offering a reliable approach for noise estimation in denoising algorithms and advancing image quality assessment. Full article
(This article belongs to the Special Issue Developments of Mathematical Methods in Image Processing)
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