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Mathematics
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Applications of Mathematical Models in Image Processing and Algorithm Theory
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Applications of Mathematical Models in Image Processing and Algorithm Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 824

Special Issue Editors

Prof. Dr. Fernando Fausto

E-Mail Website
Guest Editor
Departamento de Innovación Basada en la Información y el Conocimiento, Universidad de Guadalajara (CUCEI), Blvd. Marcelino García Barragán #1421, Guadalajara 44430, Mexico
Interests: computer graphics; computing in mathematics, natural science, engineering and medicine, and artificial intelligence; evolutionary algorithms; soft computing; bio-inspired computing; global optimization; machine learning; swarm intelligence
Prof. Dr. Primitivo Diaz

E-Mail Website
Guest Editor
Department of Electro-Photonics, Universidad de Guadalajara, Guadalajara 44430, México
Interests: energy management systems; optimal power flow; machine learning; power system control; distribution network reconfiguration
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We extend to you an invitation to participate in our Special Issue titled Applications of Mathematical Models in Image Processing and Algorithm Theory for the Mathematics journal. This Special Issue aims to present high-impact scientific contributions related to the development, analysis, and application of mathematical models in the field of image processing and computer vision. We invite the academic community, as well as industry professionals, to submit works that address current challenges and propose innovative solutions from a mathematical and computational perspective.

This Special Issue is set to include papers ranging from fundamental theoretical research to practical applications in various domains, as well as review articles and case studies that provide a comprehensive overview of the state of the art. Particular value will be given to contributions that stand out for their originality, methodological rigor, and potential for real-world implementation.

This collection seeks to strengthen interdisciplinary dialogue among applied mathematics, engineering, computer science, and cognitive sciences, thereby advancing knowledge in modern techniques for image analysis and processing, pattern recognition, segmentation, 3D reconstruction, deep learning, and computer vision.

Prof. Dr. Fernando Fausto
Prof. Dr. Primitivo Diaz
Guest Editors

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 250 words) can be sent to the Editorial Office for assessment.

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

  • mathematical modeling
  • image processing
  • pattern recognition
  • computer vision
  • interdisciplinary applications

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Published Papers (1 paper)

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38 pages, 2287 KB  
Article
Universal Comparison Methodology for Hough Transform Approaches
by Danil Kazimirov, Vitalii Gulevskii, Alexey Kroshnin, Ekaterina Rybakova, Arseniy Terekhin, Elena Limonova and Dmitry Nikolaev
Mathematics 2026, 14(7), 1136; https://doi.org/10.3390/math14071136 - 28 Mar 2026
Viewed by 422
Abstract
The Hough transform (HT) is widely used in computer vision, tomography, and neural networks. Numerous algorithms for HT computation have been proposed, making their systematic comparison essential. However, existing comparative methodologies are either non-universal and limited to certain HT formulations or task-oriented, relying [...] Read more.
The Hough transform (HT) is widely used in computer vision, tomography, and neural networks. Numerous algorithms for HT computation have been proposed, making their systematic comparison essential. However, existing comparative methodologies are either non-universal and limited to certain HT formulations or task-oriented, relying on application-specific criteria that do not fully capture algorithmic properties. This paper introduces a novel unified methodology for the systematic comparison of HT algorithms. It evaluates key characteristics, including computational complexity, accuracy, and auxiliary space complexity, while explicitly accounting for the property of self-adjointness. The methodology integrates both implementation-level and theoretical considerations related to the interpretation of HT as a discrete approximation of the Radon transform. A set of mathematically justified evaluation functions, not previously described in the literature, is proposed to support our methodology. Importantly, the methodology is universal, applicable across diverse HT paradigms, encompasses pattern-based and Fourier-based fast HT (FHT) algorithms, and offers a comprehensive alternative to existing task-specific methodologies. Its application to several state-of-the-art FHT algorithms (FHT2DT, FHT2SP, ASD2, KHM, and Fast Slant Stack) yields new experimentally confirmed theoretical insights, identifies ASD2 as the most balanced algorithm, and provides practical guidelines for algorithm selection. In particular, the methodology reveals that for image sizes up to 3000, the maximum normalized computational complexity increases as follows: FHT2DT (1.1), ASD2 (15.3), and KHM (30.6), while the remaining algorithms exhibit at least 1.1 times higher values. The maximum orthotropic approximation error equals 0.5 for ASD2, KHM, and Fast Slant Stack; lies between 0.5 and 1.5 for FHT2SP; and reaches 2.1 for FHT2DT. In terms of worst-case normalized auxiliary space complexity, the lowest values are achieved by FHT2DT (2.0), Fast Slant Stack (4.0, lower bound), and ASD2 (6.8), with all other algorithms requiring at least 8.2 times more memory. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Image Processing and Algorithm Theory)
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