Mathematical Methods for Image Processing and Computer Vision

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

Deadline for manuscript submissions: 12 October 2025 | Viewed by 2198

Special Issue Editors


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Guest Editor
Center for Research in Mathematics (CIMAT), Apartado Postal 402, Guanajuato CP 36000, Mexico
Interests: image processing; chaotic security; computer networking

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Guest Editor
Centro de Investigación en Matemáticas, A.C., Jalisco S/N, Col. Valenciana, Guanajuato CP 36023, Mexico
Interests: numerical optimization; machine learning and image processing
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Special Issue Information

Dear Colleagues,

Advances in the field of digital Image Processing and Computer Vision (IPCV) have contributed to the development of virtually every branch of science for which imaging technologies are applicable. This collaboration has led to the realization of unimaginable problem-solving capabilities that closely resemble (up to a certain level) common human vision tasks and behaviors. Typical applications include object recognition and tracking, autonomous navigation, accident prevention, face detection and recognition, security and surveillance, medical diagnoses, the remote sensing of the environment, and many more. IPVC has empowered digital machines to manipulate, transform, enhance, extract, and analyze image semantics by using both classical mathematical models and artificial intelligence schemes, such as Deep Neural Networks. These IPVC systems represent a valuable asset for the automation of image and vision-related tasks in various domains, enhancing their accuracy, efficiency, and decision-making capabilities in real-time.

This Special Issue welcomes the submission of original research and review articles on the development and advancement of mathematical and artificial intelligence approaches, techniques, and models in the field of image processing and computer vision.

The scope of this Special Issue includes, but is not limited to, the following topics:

  • Mathematical and statistical models;
  • Low-level vision;
  • Filtering, enhancement, and restoration (denoising, deblurring, error concealment, etc.);
  • Stereo vision and Super-resolution;
  • Segmentation, grouping, and shape analysis;
  • Biomedical diagnostic and imaging;
  • Remote sensing;
  • Image and video synthesis and generation;
  • Multimodal Learning;
  • Security and surveillance;
  • Industrial automation;
  • Multi-scale analysis and decomposition;
  • Mathematical morphology and topology;
  • Machine learning and deep learning.

Dr. Rogelio Hasimoto-Beltran
Dr. Oscar Susano Dalmau Cedeño
Guest Editors

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Keywords

  • image processing
  • computer vision
  • mathematical morphology and topology
  • machine learning and deep learning

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Published Papers (2 papers)

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Research

18 pages, 2692 KiB  
Article
Unit Size Determination for Exploratory Brain Imaging Analysis: A Quest for a Resolution-Invariant Metric
by Jihnhee Yu, HyunAh Lee and Zohi Sternberg
Mathematics 2025, 13(7), 1195; https://doi.org/10.3390/math13071195 - 4 Apr 2025
Viewed by 232
Abstract
Defining an adequate unit size is often crucial in brain imaging analysis, where datasets are complex, high-dimensional, and computationally demanding. Unit size refers to the spatial resolution at which brain data is aggregated for analysis. Optimizing unit size in data aggregation requires balancing [...] Read more.
Defining an adequate unit size is often crucial in brain imaging analysis, where datasets are complex, high-dimensional, and computationally demanding. Unit size refers to the spatial resolution at which brain data is aggregated for analysis. Optimizing unit size in data aggregation requires balancing computational efficiency in handling large-scale data sets with the preservation of brain activity patterns, minimizing signal dilution. We propose using the Calinski–Harabasz index, demonstrating its invariance to sample size changes due to varying image resolutions when no distributional differences are present, while the index effectively identifies an appropriate unit size for detecting suspected regions in image comparisons. The resolution-independent metric can be used for unit size evaluation, ensuring adaptability across different imaging protocols and modalities. This study enhances the scalability and efficiency of brain imaging research by providing a robust framework for unit size optimization, ultimately strengthening analytical tools for investigating brain function and structure. Full article
(This article belongs to the Special Issue Mathematical Methods for Image Processing and Computer Vision)
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16 pages, 1852 KiB  
Article
Universal Network for Image Registration and Generation Using Denoising Diffusion Probability Model
by Huizhong Ji, Peng Xue and Enqing Dong
Mathematics 2024, 12(16), 2462; https://doi.org/10.3390/math12162462 - 9 Aug 2024
Cited by 1 | Viewed by 1472
Abstract
Classical diffusion model-based image registration approaches require separate diffusion and deformation networks to learn the reverse Gaussian transitions and predict deformations between paired images, respectively. However, such cascaded architectures introduce noisy inputs in the registration, leading to excessive computational complexity and issues with [...] Read more.
Classical diffusion model-based image registration approaches require separate diffusion and deformation networks to learn the reverse Gaussian transitions and predict deformations between paired images, respectively. However, such cascaded architectures introduce noisy inputs in the registration, leading to excessive computational complexity and issues with low registration accuracy. To overcome these limitations, a diffusion model-based universal network for image registration and generation (UNIRG) is proposed. Specifically, the training process of the diffusion model is generalized as a process of matching the posterior mean of the forward process to the modified mean. Subsequently, the equivalence between the training process for image generation and that for image registration is verified by incorporating the deformation information of the paired images to obtain the modified mean. In this manner, UNIRG integrates image registration and generation within a unified network, achieving shared training parameters. Experimental results on 2D facial and 3D cardiac medical images demonstrate that the proposed approach integrates the capabilities of image registration and guided image generation. Meanwhile, UNIRG achieves registration performance with NMSE of 0.0049, SSIM of 0.859, and PSNR of 27.28 on the 2D facial dataset, along with Dice of 0.795 and PSNR of 12.05 on the 3D cardiac dataset. Full article
(This article belongs to the Special Issue Mathematical Methods for Image Processing and Computer Vision)
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