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Estimating fractal dimension of lineaments using box counting method for the Indian landmass

GEOCARTO INTERNATIONAL 2014年第3期29卷 314-331页

作者： Jaya, V. Raghukanth, S. T. G. Mohan, S. Sonika Univ Kerala Coll Engn Dept Civil Engn Trivandrum 695001 Kerala India Indian Inst Technol Dept Civil Engn Madras 600036 Tamil Nadu India

A fractal in general is a scale-invariant object that has an underlying power-law equation and is characterized by a positive fractal dimension. The fractal dimension of the Indian landmass is evaluated from the lineament map by utilizing the MATLAB programme for box counting method. The lineament map of India is divided into grids. The fractal dimension of each grid is obtained and the values are mapped. Most of the regions of India has fractal dimension in the range 1-1.25. The fractal values are compared with b-value in Gutenberg-Richter equation which gives a relationship between frequency of occurrence of earthquake and its magnitude. The estimation of b-value requires a complete earthquake dataset. In regions where the complete earthquake data are not available, the fractal dimension evaluated from the study can be used as a parameter to assess the seismic hazard of the region.

关键词： fractal dimension lineament box counting method Gutenberg-Richter equation

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Application of box counting method-based fractal geometry technique for disturbance detection in power systems

Application of box counting method-based fractal geometry te...

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IEEE-Power-Engineering-Society General Meeting

作者： Huang, SH Lin, JM Natl Cheng Kung Univ Dept Elect Engn Tainan 70101 Taiwan

ISBN: (纸本)0780379896

In this paper, the box counting method-based fractal geometry technique is proposed to detect the power quality disturbances in power systems. In the proposed approach, the fractional dimension computation is embedded into the detection procedure. Thanks to its quantization capability of disordered dynamics, the proposed method becomes highly effective to monitor the power quality. This proposed approach has been tested on various disturbances and the test results reveal the feasibility of the method for the detection of power quality.

关键词： power quality disturbance box counting method

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Fractal Dimension of Turing Instability in the Fractional Lengyel-Epstein Model

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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 2025年第3期35卷

作者： Yun, Ana Lee, Dongsun Korea Aerosp Univ Liberal Arts & Sci Goyang Si 10540 Gyeonggi Do South Korea Incheon Natl Univ Dept Math Educ Incheon 21999 South Korea

We investigate pattern formation driven by Turing instability in the Lengyel-Epstein model incorporating the fractional Laplacian operator. This approach simulates anomalous superdiffusion, where particle clouds spread more rapidly than predicted by the classical diffusion models. Such phase phenomena are often observed in viruses or biochemical substances that require unusually rapid diffusion. Our study allows for the estimation of superdiffusion effects in biochemistry or thermodynamics by analyzing temporal changes in fractional dimensions that exhibit abnormal patterns. Specifically, we employ the fractal dimension to quantify the complexity of these patterns using the box-counting method. Since this method is based on examining neighboring patterns, that is self-similarity, we observe that the formation of patterns varies with the bifurcations induced by Turing instability. Interestingly, despite these instabilities and variations, the fractal dimension stabilizes to a certain value once the patterns are formed. We also investigate how fractional diffusion affects the fractal dimension. Numerical experiments were performed with various initial conditions, including random values and circles centered with a fixed distance. The fractal dimension was calculated for Turing instability of the Lengyel-Epstein model, and is analyzed for both classical and fractional diffusion following a L & eacute;vy process. These tests revealed the formation of different patterns under the Turing instability by varying parameters, including a time variable t, and mass-conserving the chemical concentrations of the activator iodide u and the inhibitor chlorite v. Then, we analyzed these results in terms of the fractal dimension of the patterns. Furthermore, we analyze the consistency with the mesh refinement numerically and examine parameter sensitivity. Our numerical simulation of the fractional-Lengyel-Epstein model examined the relationship between the fractal dimension and the p

关键词： Fractal dimension turing instability box counting method Lengyel-Epstein model

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Tracking of Defects in Reinforced Concrete Bridges Using Digital Images

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JOURNAL OF COMPUTING IN CIVIL ENGINEERING 2016年第5期30卷 1-15页

作者： Adhikari, R. S. Moselhi, O. Bagchi, A. Rahmatian, A. Concordia Univ Dept Bldg Civil & Environm Engn Montreal PQ H3G 1M8 Canada Univ Houston Downtown Dept Comp Sci & Engn Technol Houston TX 77002 USA

This paper proposes a novel approach for the periodic detection of defects in concrete bridges based on a set of dimensionless metrics pertinent to fractal analysis of digital images. Visual inspection and image subtraction methods are generally used for the periodic comparison of structural conditions. However, such approaches, such as visual inspections, have been identified with several limitations, but they are time consuming processes and decisions are influenced by individual experiences. Likewise, image subtraction method requires image registration, which is a difficult process in achieving precise image registration for reliable outputs. This research uses fractal analysis of digital images to track surface defects by estimating their fractal dimensions. The results of the fractal analysis of concrete beams are compared with the results of spectral analysis which requires images to be translated from spatial domain to frequency domain. The proposed method successfully generates unique metrics necessary for change quantification which overcomes the limitation of the existing approaches. (C) 2016 American Society of Civil Engineers.

关键词： Periodic detection of defects Fractal analysis box counting method Image subtraction Non-Euclidean Concrete bridges

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Generation of fractal dimension images and its application to automatic edge detection in brain MRI

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COMPUTERIZED MEDICAL IMAGING AND GRAPHICS 2000年第2期24卷 73-85页

作者： Uemura, K Toyama, H Baba, S Kimura, Y Senda, M Uchiyama, A Waseda Univ Sch Sci & Engn Dept Elect Informat & Commun Engn Tokyo Japan

We have developed four methods to generate a fractal dimension image and have applied them to the brain MRI. We have adopted four types of scanning methods, "CONVENTIONAL", "OVERLAPPING", "SYMMETRIC" and "FOLDED" to estimate the fractal dimension. The first three methods show almost the same fractal dimension images and their values were between two and three. In the "FOLDED" method, we were able to obtain the images in which the edge of a narrow region including dura and scalp surrounding the brain was selectively enhanced in the T1-weighted MRI, This is found to be a new edge-enhancing filter. We could remove the surrounding structure of the brain by using these filtered images and detect the edge of the brain surface automatically. The brain surface data can be used for various applications such as three-dimensional surface display and registration of inter-modal brain images. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： fractal dimension box counting method edge enhance filter brain MRI edge detection

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CAN THE ARTIFICIAL-HEART MAKE THE CIRCULATION BECOME FRACTAL

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INTERNATIONAL JOURNAL OF ARTIFICIAL ORGANS 1995年第4期18卷 190-196页

作者： YAMBE, T NANKA, S NAGANUMA, S KOBAYASHI, S AKIHO, H KAKINUMA, Y OHSAWA, N NITTA, S FUKUJU, T MIURA, M UCHIDA, N TABAYASHI, K TANAKA, A YOSHIZUMI, N ABE, K TAKAYASU, M TAKAYASU, H YOSHIZAWA, M TAKEDA, H TOHOKU UNIV SCH MED DEPT CARDIOVASC & THORAC SURG SENDAI MIYAGI JAPAN TOHOKU UNIV FAC ENGN DEPT ELECT ENGN SENDAI MIYAGI 980 JAPAN TOHOKU UNIV FAC ENGN FRACTURE TECHNOL RES INST SENDAI MIYAGI 980 JAPAN TOHOKU UNIV GRAD SCH INFORMAT SCI SENDAI MIYAGI JAPAN TOHOKU GAKUIN UNIV FAC ENGN SENDAI MIYAGI JAPAN

In order to analyze the hemodynamic parameters in prosthetic circulation as an entity and not as decomposed parts, non linear mathematical analyzing techniques, including the fractal dimension analyzing theory, were utilized. Two pneumatically actuated ventricular assist devices were implanted, as biventricular bypasses (BVB), in chronic animal experiments, using four healthy adult goats. For the comparison between the natural and prosthetic circulation in the same animals, the BVB type complete prosthetic circulation model with ventricular fibrillation, was adopted. All hemodynamic parameters with natural and prosthetic circulation were recorded under awake conditions, and calculated with a personal computer system. Using the non-linear mathematical technique, the arterial blood pressure waveform was embedded into the return map as the beat-to-beat time series data and fractal dimension analysis were performed to analyze the reconstructed attractor. By the use of the box counting method, fractal dimension analysis of the hemodynamics was performed. Return map of the hemodynamics during natural and artificial circulation showed fractal characteristics, and fractal dimension analysis of the arterial blood pressure revealed the fact that lower dimensional fractal dynamics were evident during prosthetic circulation. Fractal time series data is suggested to have robustness and error resistance, thus our results suggest that the circulatory regulatory system with an artificial heart may have these desired characteristics.

关键词： CHAOS FRACTAL FRACTAL DIMENSION TOTAL ARTIFICIAL HEART box counting method DETERMINISTIC CHAOS

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Three-dimensional fractal analysis of real electrical trees in polyethylene

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JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS BRIEF COMMUNICATIONS & REVIEW PAPERS 1999年第6A期38卷 3604-3610页

作者： Uehara, H Kudo, K Meiji Univ Dept Elect Engn Sch Sci & Technol Tama Ku Kawasaki Kanagawa 2140033 Japan

In this paper, real electrical trees in polymeric insulating materials were discussed from the viewpoint of their fractal characteristics. Experiments on real electrical trees were carried out in the needle to plane electrode geometry under ac voltage application. Samples in this investigation were made of cross-linked polyethylene (XLPE). Two methods of reconstructing three-dimensional (3D) patterns of real electrical trees were developed. One is the computerized tomography method (CTM) and the other is the serial sectioning method (SSM). The relationship between tree. characteristics and 3D fractal dimensions of tree patterns was studied. The experimental results showed that the spatial tree patterns have a fractal characteristics and that the tree characteristics can be characterized by fractal dimensions.

关键词： fractal dimension electrical tree cross-linked polyethylene computerized tomography method serial sectioning method box counting method

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Measuring fractal dimension and complexity - An alternative approach with an application

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JOURNAL OF MICROSCOPY-OXFORD 1997年第2期186卷 164-176页

作者： Sandau, K Kurz, H UNIV FREIBURG INST ANATD-79110 FREIBURGGERMANY

Fractal dimension has often been applied as a parameter of complexity, related to, for example, surface roughness, or for classifying textures or line patterns. Fractal dimension can be estimated statistically, if the pattern is known to be self-similar. However, the fractal dimension of more general patterns cannot be estimated, even though the concept may be retained to characterize complexity. We here show that the usual statistical methods, e.g. the box counting method, are not appropriate to measure complexity. A recently developed approach, the extended counting method, whose properties are closer to what fractal dimension means, is considered here in more detail. The methods are applied to geometric and to blood vessel patterns. The weak assumptions about the structure, and the lower variance of the estimate, suggest that the extended counting method has beneficial properties for comparing complexity of naturally occurring patterns.

关键词： angiogenesis blood vessel pattern box counting method extended counting method maximum property self-similarity VEGF

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Quantification of damage due to surface tracking

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IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION 2007年第5期14卷 1224-1231页

作者： Rajini, V. Kumar, K. Udaya SSN Coll Engn SSN Nagar India Anna Univ Dept High Voltage Engn Madras 600025 Tamil Nadu India

Fractals have been very successfully used to address the problem of modeling and to provide a description of naturally occurring phenomena and shapes, wherein conventional and existing mathematical models were found to be inadequate. The geometrical patterns of dielectric breakdown like electrical trees, surface discharges, and lightning are known to be of fractal in nature. These fractal patterns can be analyzed numerically using fractal dimensions and lacunarity. Surface tracking occurring in HV insulation systems is a very complex phenomenon and more so are the shapes of tracking patterns. It has been fairly well established that the shapes and the underlying parameters causing tracking have a 1:1 correspondence and therefore methods to describe and quantify these patterns must be explored. This contribution reports preliminary results of such a study wherein 2-D tracking patterns of gamma irradiated Ethylene Propylene Diene monomer (EPDM) were analyzed and found to posses' fairly reasonable pattern discriminating abilities.

关键词： EPDM surface tracking fractal dimensions box counting method

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Analysing roughness of surface through fractal dimension: A review

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IMAGE AND VISION COMPUTING 2019年 89卷 21-34页

作者： Nayak, Soumya Ranjan Mishra, Jibitesh Palai, Gopinath Chitkara Univ Inst Engn & Technol Rajpura 140401 Punjab India Coll Engn & Technol Techno Campus Bhubaneswar 751029 Odisha India Gandhi Inst Technol Adv Dept Elect & Commun Engn Bhubaneswar India

In last three decades, fractal geometry (FG) has been the focus of attention by several researchers owing to it exhibiting excellent properties and robust application with respect to current research scenario. Fractal Dimension (FD) plays a vital role in order to analyse complex objects that are found in nature which was failed to be analysed by Euclidian geometry. FD is an imperative aspect of FG to provide indicative application in different areas of research including image processing, pattern recognition, computer graphics and many more. Analysis of an image is an important technique of image processing to describe image features like texture, roughness, smoothness etc., and is only possible through FG. Due to this reason many more technique were evolved to estimate the fractal dimension. The main aim of this article is to give a comprehensive review, which summarizes recent research progress on analysis of surface roughness and an overview of different concepts, and the way they work and their benefits and their limitations, and also we deliver how the different concepts taken into consideration to estimate FD depend upon different algorithms. This article also discusses several factors affecting FD estimation;types of similarity property, spatial resolution, sampling process, region of interest, spectral band and box-height criteria are discussed. Furthermore, we have tried to present the application area oriented versus core area of FG. There are several contradictory results found in many kinds of literature on the influence of different parameters while conducting FD analysis. Mainly it has been observed that the FD estimation will be affected by texture property, gray scale range, color property, color distance and the other parameters which are already mentioned. Hence this article will be beneficial for researchers in order to select precise FD estimation. However different algorithms lead to different results even with the use of the same kind of databa

关键词： Fractal dimension box counting method Dividers method Probability density function Color fractal dimension

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