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Mathematics
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Mathematical Methods for Image Processing and Understanding
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Mathematical Methods for Image Processing and Understanding

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

Deadline for manuscript submissions: 10 May 2025 | Viewed by 1819

Special Issue Editors

Prof. Dr. Gianluca Vinti

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy
Interests: real analysis, theory of integral operators, approximation theory, and their applications to signal and image processing and reconstruction
Prof. Dr. Ivan Gerace

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Perugia, I-06123 Perugia, Italy
Interests: image processing; numerical linear algebra; computational complexity
Arianna Travaglini

E-Mail Website
Guest Editor Assistant
Department of Mathematics and Computer Science “U.Dini”-DIMAI, University of Florence, 67/a, Viale Giovanni Battista Morgagni, 50134 Firenze, Italy
Interests: real analysis; theory of integral operators; approximation theory and their applications to signal and image processing and reconstruction

Special Issue Information

Dear Colleagues,

We are very happy to announce that The Workshop on Mathematical Methods for Image Processing and Understanding (https://sites.google.com/view/mmipu-2023/home-page) will be held in conjunction with the 2023 International Conference on Computational Science and its Applications (ICCSA 2023) in Athens, Greece, on July 3‒6, 2023.

The Workshop is focused on the analysis of mathematical methods to solve the theoretical and computational problems that are typical in image processing and understanding. The themes and topics include but are not limited to:

  • Theoretical and numerical approximation for image processing;
  • Filter theory;
  • Space color definition;
  • Regularization techniques;
  • MAP estimation for image processing;
  • Image reconstruction;
  • Image enhancement;
  • Image rescaling;
  • Image segmentation;
  • Image registration;
  • Image clustering;
  • Image compactification;
  • Image demosaicing;
  • Medical imaging;
  • Digital tomography;
  • Mathematical methods for virtual document restoration;
  • Pattern recognition;
  • Stereoscopic and optical flow.

Moreover, applications of digital image processing in different fields will be also considered.

We would like to invite authors to submit an extended version of their conference papers for this Special Issue. All papers accepted in this Special Issue will meet the usual standards for publication in Mathematics.

Prof. Dr. Gianluca Vinti
Prof. Dr. Ivan Gerace
Guest Editors

Arianna Travaglini
Guest Editor Assistant

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
  • feature extraction and selection
  • pattern recognition
  • mathematical methods
  • regularization techniques
  • inverse problems in imaging

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Published Papers (2 papers)

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Research

13 pages, 4727 KiB  
Article
Mathematical Data Models and Context-Based Features for Enhancing Historical Degraded Manuscripts Using Neural Network Classification
by Pasquale Savino and Anna Tonazzini
Mathematics 2024, 12(21), 3402; https://doi.org/10.3390/math12213402 - 30 Oct 2024
Viewed by 472
Abstract
A common cause of deterioration in historic manuscripts is ink transparency or bleeding from the opposite page. Philologists and paleographers can significantly benefit from minimizing these interferences when attempting to decipher the original text. Additionally, computer-aided text analysis can also gain from such [...] Read more.
A common cause of deterioration in historic manuscripts is ink transparency or bleeding from the opposite page. Philologists and paleographers can significantly benefit from minimizing these interferences when attempting to decipher the original text. Additionally, computer-aided text analysis can also gain from such text enhancement. In previous work, we proposed the use of neural networks (NNs) in combination with a data model that characterizes the damage when both sides of a page have been digitized. This approach offers the distinct advantage of allowing the creation of an artificial training set that teaches the NN to differentiate between clean and damaged pixels. We tested this concept using a shallow NN, which proved effective in categorizing texts with varying levels of deterioration. In this study, we adapt the NN design to tackling remaining classification uncertainties caused by areas of text overlap, inhomogeneity, and peaks of degradation. Specifically, we introduce a new output class for pixels within overlapping text areas and incorporate additional features related to the pixel context information to promote the same classification for pixels adjacent to each other. Our experiments demonstrate that these enhancements significantly improve the classification accuracy. This improvement is evident in the quality of both binarization, which aids in text analysis, and virtual restoration, aimed at recovering the manuscript’s original appearance. Tests conducted on a public dataset, using standard quality indices, reveal that the proposed method outperforms both our previous proposals and other notable methods found in the literature. Full article
(This article belongs to the Special Issue Mathematical Methods for Image Processing and Understanding)
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21 pages, 507 KiB  
Article
A Note on the Convergence of Multigrid Methods for the Riesz–Space Equation and an Application to Image Deblurring
by Danyal Ahmad, Marco Donatelli, Mariarosa Mazza, Stefano Serra-Capizzano and Ken Trotti
Mathematics 2024, 12(12), 1916; https://doi.org/10.3390/math12121916 - 20 Jun 2024
Cited by 1 | Viewed by 772
Abstract
In recent decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on multigrid methods for a Riesz–Space FDE whose theoretical [...] Read more.
In recent decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on multigrid methods for a Riesz–Space FDE whose theoretical convergence analysis of such multigrid methods is currently limited in the relevant literature to the two-grid method. Here we provide a detailed theoretical convergence study in the multilevel setting. Moreover, we discuss its use combined with a band approximation and we compare the result with both τ and circulant preconditionings. The numerical tests include 2D problems as well as the extension to the case of a Riesz–FDE with variable coefficients. Finally, we investigate the use of a Riesz–Space FDE in a variational model for image deblurring, comparing the performance of specific preconditioning strategies. Full article
(This article belongs to the Special Issue Mathematical Methods for Image Processing and Understanding)
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