Fractal and Multifractal Analysis in Environmental, Medical and Technical Fields: Pattern Recognition, Analysis and Processing of Images

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Life Science, Biophysics".

Deadline for manuscript submissions: closed (30 June 2025) | Viewed by 5220

Special Issue Editors


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Guest Editor
Amazonian Materials Group, Department of Physics, Federal University of Amapá, Macapá 68903-419, Brazil
Interests: fractal analysis; fractal features; image processing; surface physical biotechnology; materials science; surface architecture; monofractal and multifractal approach; 3D spatial analysis
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Guest Editor
Division of Technologies, Federal University of Alagoa, Delmiro Gouveia 57480-000, Brazil
Interests: statistical physics and its interdisciplinary applications
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Guest Editor
Department of Physics, Federal University of Sergipe, São Cristóvão 49100-000, Brazil
Interests: solid surfaces; interfaces and thin films; nanomaterials; material characterization; magnetism
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Special Issue Information

Dear Colleagues,

Pattern recognition techniques applied to image processing and analysis have continually evolved over the years, mainly due to the significant increase in studies involving mathematical morphology, neural networks and image analysis systems based on machine learning. Texture analysis, for example, has been extensively employed for automatic pattern recognition in images, as an alternative to human cognitive capacity. The application of this technique directly benefits areas such as control theory, manufacturing, biomedicine and taxonomy, among others. In this context, the use of fractal descriptors, such as fractal dimension, succolarity, lacunarity and the multifractal spectrum, deserve attention because they can appropriately measure complex shapes, particularly those found in nature. Considering this, we encourage our colleagues to contribute to our multidisciplinary Special Issue.

The aim of this Special Issue is to advance research on topics relating to Fractal and Multifractal Analysis in Environmental, Medical and Technical Fields: Pattern Recognition, Analysis and Processing of Images. Potential topics include (but are not limited to) the following:

  • Fractal and/or multifractal analysis of images using scanning probe microscopy (SPM);
  • fractal and/or multifractal analysis of images using scanning and/or transmission electron microscopy;
  • pattern recognition using fractal descriptors in medical images;
  • pattern recognition using fractal descriptors in images of environmental interest;
  • fractal descriptors combined with neural networks;
  • mathematical morphology and fractal descriptors;
  • fractal descriptors and machine learning.

Dr. Erveton Pinheiro Pinto
Dr. Marcelo Amanajás Pires
Dr. Nilson dos Santos Ferreira
Guest Editors

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Keywords

  • fractal analysis
  • multifractal spectrum
  • lacunarity spectrum
  • pattern recognition
  • neural networks
  • mathematical morphology
  • machine learning
  • medical images
  • nature textures
  • surfaces
  • scanning probe microscopy (SPM)
  • transmission electron microscopy (TEM)
  • scanning electron microscopy (SEM)

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Published Papers (4 papers)

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Research

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28 pages, 3276 KB  
Article
Fractal-Inspired Region-Weighted Optimization and Enhanced MobileNet for Medical Image Classification
by Yichuan Shao, Jiapeng Yang, Wen Zhou, Haijing Sun and Qian Gao
Fractal Fract. 2025, 9(8), 511; https://doi.org/10.3390/fractalfract9080511 - 5 Aug 2025
Viewed by 458
Abstract
In the field of deep learning, the design of optimization algorithms and neural network structures is crucial for improving model performance. Recent advances in medical image analysis have revealed that many pathological features exhibit fractal-like characteristics in their spatial distribution and morphological patterns. [...] Read more.
In the field of deep learning, the design of optimization algorithms and neural network structures is crucial for improving model performance. Recent advances in medical image analysis have revealed that many pathological features exhibit fractal-like characteristics in their spatial distribution and morphological patterns. This observation has opened new possibilities for developing fractal-inspired deep learning approaches. In this study, we propose the following: (1) a novel Region-Module Adam (RMA) optimizer that incorporates fractal-inspired region-weighting to prioritize areas with higher fractal dimensionality, and (2) an ECA-Enhanced Shuffle MobileNet (ESM) architecture designed to capture multi-scale fractal patterns through its enhanced feature extraction modules. Our experiments demonstrate that this fractal-informed approach significantly improves classification accuracy compared to conventional methods. On gastrointestinal image datasets, the RMA algorithm achieved accuracies of 83.60%, 81.60%, and 87.30% with MobileNetV2, ShuffleNetV2, and ESM networks, respectively. For glaucoma fundus images, the corresponding accuracies reached 84.90%, 83.60%, and 92.73%. These results suggest that explicitly considering fractal properties in medical image analysis can lead to more effective diagnostic tools. Full article
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21 pages, 7529 KB  
Article
Multifractal Detrended Fluctuation Analysis Combined with Allen–Cahn Equation for Image Segmentation
by Minzhen Wang, Yanshan Wang, Renkang Xu, Runqiao Peng, Jian Wang and Junseok Kim
Fractal Fract. 2025, 9(5), 310; https://doi.org/10.3390/fractalfract9050310 - 12 May 2025
Viewed by 607
Abstract
This study proposes a novel image segmentation method, MF-DFA combined with the Allen–Cahn equation (MF-AC-DFA). By utilizing the Allen–Cahn equation instead of the least squares method employed in traditional MF-DFA for fitting, the accuracy and robustness of image segmentation are significantly improved. The [...] Read more.
This study proposes a novel image segmentation method, MF-DFA combined with the Allen–Cahn equation (MF-AC-DFA). By utilizing the Allen–Cahn equation instead of the least squares method employed in traditional MF-DFA for fitting, the accuracy and robustness of image segmentation are significantly improved. The article first conducts segmentation experiments under various conditions, including different target shapes, image backgrounds, and resolutions, to verify the feasibility of MF-AC-DFA. It then compares the proposed method with gradient segmentation methods and demonstrates the superiority of MF-AC-DFA. Finally, real-life wire diagrams and transmission tower diagrams are used for segmentation, which shows the application potential of MF-AC-DFA in complex scenes. This method is expected to be applied to the real-time state monitoring and analysis of power facilities, and it is anticipated to improve the safety and reliability of the power grid. Full article
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Review

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15 pages, 2740 KB  
Review
Statistical Insights into Spatial Patterns: A Panorama About Lacunarity
by Erveton P. Pinto, Marcelo A. Pires, Thiago B. F. Antunes, Rone N. da Silva and Sílvio M. Duarte Queirós
Fractal Fract. 2025, 9(9), 570; https://doi.org/10.3390/fractalfract9090570 - 29 Aug 2025
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Abstract
This overview is designed to illuminate the concept and utility of lacunarity. We first establish a strong foundation with a pedagogical introduction to the lacunarity measure applied to images, detailing analytical examples and a general approach. In the second part, we compare the [...] Read more.
This overview is designed to illuminate the concept and utility of lacunarity. We first establish a strong foundation with a pedagogical introduction to the lacunarity measure applied to images, detailing analytical examples and a general approach. In the second part, we compare the available software for estimating the lacunarity of images. Related to this goal, we also provide an open-source code in R and Python. The third part then synthesizes these theoretical and computational aspects by presenting an analysis of the diverse applications of lacunarity across various scientific disciplines, utilizing VOSviewer networks to visually organize research topics into distinct clusters. We identify distinct thematic clusters in materials science, biological systems, and medical imaging. Full article
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15 pages, 5564 KB  
Review
Morphological Features of Mathematical and Real-World Fractals: A Survey
by Miguel Patiño-Ortiz, Julián Patiño-Ortiz, Miguel Ángel Martínez-Cruz, Fernando René Esquivel-Patiño and Alexander S. Balankin
Fractal Fract. 2024, 8(8), 440; https://doi.org/10.3390/fractalfract8080440 - 26 Jul 2024
Cited by 3 | Viewed by 2376
Abstract
The aim of this review paper is to survey the fractal morphology of scale-invariant patterns. We are particularly focusing on the scale and conformal invariance, as well as on the fractal non-uniformity (multifractality), inhomogeneity (lacunarity), and anisotropy (succolarity). We argue that these features [...] Read more.
The aim of this review paper is to survey the fractal morphology of scale-invariant patterns. We are particularly focusing on the scale and conformal invariance, as well as on the fractal non-uniformity (multifractality), inhomogeneity (lacunarity), and anisotropy (succolarity). We argue that these features can be properly quantified by the following six adimensional numbers: the fractal (e.g., similarity, box-counting, or Assouad) dimension, conformal dimension, degree of multifractal non-uniformity, coefficient of multifractal asymmetry, index of lacunarity, and index of fractal anisotropy. The difference between morphological properties of mathematical and real-world fractals is especially outlined in this review paper. Full article
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