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Fractal Fract
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Methods for Estimation of Fractal Dimension Based on Digital Images
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Methods for Estimation of Fractal Dimension Based on Digital Images

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Numerical and Computational Methods".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 6747

Special Issue Editor

Prof. Dr. Pedro Chamorro Posada

E-Mail Website
Guest Editor
Dpto. de Teoría de la Señal y Comunicaciones e Ingeniería Telemática, Universidad de Valladolid, Paseo Belén 15, 47011 Valladolid, Spain
Interests: nonlinearity; solitons and fractals; photonics; quantum information; optical materials

Special Issue Information

Dear Colleagues,

The analysis of the fractal structure of real-world objects is generally based on digital images. The effective and accurate determination of the fractal dimension from image data is a highly active area of research due to its relevance to applications in medicine, materials science, and to the description of a great variety of processes in the life and physical sciences. Besides their practical applications, the theoretical analyses of the methods themselves are highly valuable to unveil the relations between the structural complexity of phenomena captured as image data and their fractal dimension.

This Special Issue focuses on methods for the estimation of the dimension of fractals stored as digital image files, and related theoretical analyses and applications. Topics that are invited for submission include (but are not limited to):

  • Methods for estimating the fractal dimension of digital images.
  • Theoretical analyses in the estimation of the fractal dimension of image data.
  • Applications in medical imaging.
  • Applications in materials science.
  • Applications to fractals in optical systems.
  • Applications to fractals in physical processes.
  • Applications to fractals in life sciences.

Prof. Dr. Pedro Chamorro Posada
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. Fractal and Fractional 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 2700 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.

Published Papers (4 papers)

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Research

12 pages, 3901 KiB  
Article
Water Detection in Satellite Images Based on Fractal Dimension
by Javier Del-Pozo-Velázquez, Pedro Chamorro-Posada, Javier Manuel Aguiar-Pérez, María Ángeles Pérez-Juárez and Pablo Casaseca-De-La-Higuera
Fractal Fract. 2022, 6(11), 657; https://doi.org/10.3390/fractalfract6110657 - 7 Nov 2022
Cited by 3 | Viewed by 1898
Abstract
Identification and monitoring of existing surface water bodies on the Earth are important in many scientific disciplines and for different industrial uses. This can be performed with the help of high-resolution satellite images that are processed afterwards using data-driven techniques to obtain the [...] Read more.
Identification and monitoring of existing surface water bodies on the Earth are important in many scientific disciplines and for different industrial uses. This can be performed with the help of high-resolution satellite images that are processed afterwards using data-driven techniques to obtain the desired information. The objective of this study is to establish and validate a method to distinguish efficiently between water and land zones, i.e., an efficient method for surface water detection. In the context of this work, the method used for processing the high-resolution satellite images to detect surface water is based on image segmentation, using the Quadtree algorithm, and fractal dimension. The method was validated using high-resolution satellite images freely available at the OpenAerialMap website. The results show that, when the fractal dimensions of the tiles in which the image is divided after completing the segmentation phase are calculated, there is a clear threshold where water and land can be distinguished. The proposed scheme is particularly simple and computationally efficient compared with heavy artificial-intelligence-based methods, avoiding having any special requirements regarding the source images. Moreover, the average accuracy obtained in the case study developed for surface water detection was 96.03%, which suggests that the adopted method based on fractal dimension is able to detect surface water with a high level of accuracy. Full article
(This article belongs to the Special Issue Methods for Estimation of Fractal Dimension Based on Digital Images)
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21 pages, 12436 KiB  
Article
Fractal Characteristics of Deep Shales in Southern China by Small-Angle Neutron Scattering and Low-Pressure Nitrogen Adsorption
by Hongming Zhan, Xizhe Li, Zhiming Hu, Xianggang Duan, Wei Wu, Wei Guo and Wei Lin
Fractal Fract. 2022, 6(9), 484; https://doi.org/10.3390/fractalfract6090484 - 30 Aug 2022
Cited by 5 | Viewed by 1384
Abstract
The occurrence and flow of shale gas are substantially impacted by nanopore structures. The fractal dimension provides a new way to explore the pore structures of shale reservoirs. In this study, eight deep shale samples from Longmaxi Formation to Wufeng Formation in Southern [...] Read more.
The occurrence and flow of shale gas are substantially impacted by nanopore structures. The fractal dimension provides a new way to explore the pore structures of shale reservoirs. In this study, eight deep shale samples from Longmaxi Formation to Wufeng Formation in Southern Sichuan were selected to perform a series of analysis tests, which consisted of small-angle neutron scattering, low-pressure nitrogen adsorption, XRD diffraction, and large-scale scanning electron microscopy splicing. The elements that influence the shale fractal dimension were discussed from two levels of mineral composition and pore structures, and the relationship between the mass fractal dimension and surface fractal dimension was focused on during a comparative analysis. The results revealed that the deep shale samples both had mass fractal characteristics and surface fractal characteristics. The mass fractal dimension ranged from 2.499 to 2.991, whereas the surface fractal dimension ranged from 2.814 to 2.831. The mass fractal dimension was negatively correlated with the surface fractal dimension. The mass fractal dimension and the surface fractal dimension are controlled by organic matter pores, and their development degree significantly affects the fractal dimension. The mass fractal dimension increases with the decrease of a specific surface area and pore volume and increases with the increase of the average pore diameter. The permeability and surface fractal dimension are negatively correlated, but no significant correlation exists between the permeability and mass fractal dimension, and the internal reason is the dual control effect of organic matter on shale pores. This study comprehensively analyses the mass fractal characteristics and surface fractal characteristics, which helps in a better understanding of the pore structure and development characteristics of shale gas reservoirs. Full article
(This article belongs to the Special Issue Methods for Estimation of Fractal Dimension Based on Digital Images)
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10 pages, 1098 KiB  
Article
Monofractal Dimension in Quantifying the Image of Neurons in the Plane: Analysis of Image Features of Multipolar Neurons from the Principal Olivary Nucleus in Humans with Age
by Nebojša Milošević
Fractal Fract. 2022, 6(8), 408; https://doi.org/10.3390/fractalfract6080408 - 25 Jul 2022
Viewed by 1248
Abstract
The existing study examines four features of 2D images from the principal olivary nucleus of the adult human. The main goal of the research is to investigate the relationship between monofractal and computational parameters that quantify three features of neuronal images. An additional [...] Read more.
The existing study examines four features of 2D images from the principal olivary nucleus of the adult human. The main goal of the research is to investigate the relationship between monofractal and computational parameters that quantify three features of neuronal images. An additional goal of the research is to examine the change in the four features of the image with age. The samples belonged to the histological collection from the Department of Anatomy of the University of Novi Sad. From the pool of binary images, a sample of medium-sized neurons was selected and further processed. A public computer program (Image J with FracLac plugin) with standard commands that calculate computational and monofractal parameters analyzed all images. The relationship between parameters or between parameters with age was performed by statistical evaluation of Pearson’s correlation coefficient. The monofractal dimension of corresponding images can qualitatively represent image properties and some features decrease with age, while some do not. This study confirms the previous conclusions according to which the monofractal dimension of neuronal image reliably quantifies three features of the image. On the other hand, the study shows the distribution of four features with age. Full article
(This article belongs to the Special Issue Methods for Estimation of Fractal Dimension Based on Digital Images)
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14 pages, 2022 KiB  
Article
Volume of Interest-Based Fractal Analysis of Huffaz’s Brain
by Iqbal Jamaludin, Mohd Zulfaezal Che Azemin, Mohd Izzuddin Mohd Tamrin and Abdul Halim Sapuan
Fractal Fract. 2022, 6(7), 396; https://doi.org/10.3390/fractalfract6070396 - 19 Jul 2022
Cited by 2 | Viewed by 1357
Abstract
The robust process in memorising the Quran is expected to cause neuroplasticity changes in the brain. To date, the analysis of neuroplasticity is limited in binary images because greyscale analysis requires the usage of more robust processing techniques. This research work aims to [...] Read more.
The robust process in memorising the Quran is expected to cause neuroplasticity changes in the brain. To date, the analysis of neuroplasticity is limited in binary images because greyscale analysis requires the usage of more robust processing techniques. This research work aims to explore and characterise the complexity of textual memorisation brain structures using fractal analysis between huffaz and non-huffaz applying global box-counting, global Fourier fractal dimension (FFD), and volume of interest (VOI)-based analysis. The study recruited 47 participants from IIUM Kuantan Campus. The huffaz group had their 18 months of systematic memorisation training. The brain images were acquired by using MRI. Global box-counting and FFD analysis were conducted on the brain. Magnetic resonance imaging (MRI) found no significant statistical difference between brains of huffaz and non-huffaz. VOI-based analysis found nine significant areas: two for box-counting analysis (angular gyrus and medial temporal gyrus), six for FFD analysis (BA20, BA30, anterior cingulate, fusiform gyrus, inferior temporal gyrus, and frontal lobe), and only a single area (BA33) showed significant volume differences between huffaz and non-huffaz. The results have highlighted the sensitivity of VOI-based analysis because of its local nature, as compared to the global analysis by box-counting and FFD. Full article
(This article belongs to the Special Issue Methods for Estimation of Fractal Dimension Based on Digital Images)
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