scholarly journals Fingerprints Authentication Using Grayscale Fractal Dimension

2019 ◽  
Vol 29 (3) ◽  
pp. 106
Author(s):  
Nadia. M. G. Alsaidi ◽  
Arkan J. Mohammed ◽  
Wael J. Abdulaal
Keyword(s):  
Pattern Recognition ◽  
Fractal Dimension ◽  
Shape Analysis ◽  
Relevant Information ◽  
The Self ◽  
Fingerprint Recognition ◽  
Self Similarity ◽  
Visual Objects ◽  
Box Counting ◽  
Box Counting Dimension

Characterizing of visual objects is an important role in pattern recognition that can be performed through shape analysis. Several approaches have been introduced to extract relevant information of a shape. The complexity of the shape is the most widely used approach for this purpose where fractal dimension and generalized fractal dimension are methodologies used to estimate the complexity of the shapes. The box counting dimension is one of the methods that used to estimate fractal dimension. It is estimated basically to describe the self-similarity in objects. A lot of objects have the self-similarity; fingerprint is one of those objects where the generalized box counting dimension is used for recognizing of the fingerprints to be utilized for authentication process. A new fractal dimension method is proposed in this paper. It is verified by the experiment on a set of natural texture images to show its efficiency and accuracy, and a satisfactory result is found. It also offers promising performance when it is applied for fingerprint recognition.

A Modified Box-Counting Method to Estimate the Fractal Dimensions

2011 ◽  
Vol 58-60 ◽  
pp. 1756-1761 ◽  
Author(s):  
Jie Xu ◽  
Giusepe Lacidogna
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
The Self ◽  
Whole Body ◽  
Counting Method ◽  
Border Effect ◽  
Self Similarity ◽  
Box Counting ◽  
Self Similar ◽  
Box Counting Method

A fractal is a property of self-similarity, each small part of the fractal object is similar to the whole body. The traditional box-counting method (TBCM) to estimate fractal dimension can not reflect the self-similar property of the fractal and leads to two major problems, the border effect and noninteger values of box size. The modified box-counting method (MBCM), proposed in this study, not only eliminate the shortcomings of the TBCM, but also reflects the physical meaning about the self-similar of the fractal. The applications of MBCM shows a good estimation compared with the theoretical ones, which the biggest difference is smaller than 5%.

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

scholarly journals A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters

2021 ◽  
Vol 35 (4) ◽  
pp. 1197-1210
Author(s):  
C. Giudicianni ◽  
A. Di Nardo ◽  
R. Greco ◽  
A. Scala
Keyword(s):  
Fractal Dimension ◽  
Community Structure ◽  
Distribution Systems ◽  
Water Distribution ◽  
Scaling Law ◽  
Vulnerability Index ◽  
The Self ◽  
Node Degree ◽  
Specific Response ◽  
Self Similarity

AbstractMost real-world networks, from the World-Wide-Web to biological systems, are known to have common structural properties. A remarkable point is fractality, which suggests the self-similarity across scales of the network structure of these complex systems. Managing the computational complexity for detecting the self-similarity of big-sized systems represents a crucial problem. In this paper, a novel algorithm for revealing the fractality, that exploits the community structure principle, is proposed and then applied to several water distribution systems (WDSs) of different size, unveiling a self-similar feature of their layouts. A scaling-law relationship, linking the number of clusters necessary for covering the network and their average size is defined, the exponent of which represents the fractal dimension. The self-similarity is then investigated as a proxy of recurrent and specific response to multiple random pipe failures – like during natural disasters – pointing out a specific global vulnerability for each WDS. A novel vulnerability index, called Cut-Vulnerability is introduced as the ratio between the fractal dimension and the average node degree, and its relationships with the number of randomly removed pipes necessary to disconnect the network and with some topological metrics are investigated. The analysis shows the effectiveness of the novel index in describing the global vulnerability of WDSs.

Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

2021 ◽  
Author(s):  
Nicholas Dudu ◽  
Arturo Rodriguez ◽  
Gael Moran ◽  
Jose Terrazas ◽  
Richard Adansi ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Atmospheric Turbulence ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Counting Method ◽  
Data Set ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Self Similar ◽  
Box Counting Method

Abstract Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.

ON THE MENDÈS FRANCE FRACTAL DIMENSION OF STRANGE ATTRACTORS: THE HÉNON CASE

2002 ◽  
Vol 12 (07) ◽  
pp. 1549-1563 ◽  
Author(s):  
M. PIACQUADIO ◽  
R. HANSEN ◽  
F. PONTA
Keyword(s):  
Fractal Dimension ◽  
Hausdorff Dimension ◽  
Strange Attractors ◽  
Planar Curves ◽  
Box Counting ◽  
Box Counting Dimension

We consider the Hénon attractor ℋ as a curve limit of continuous planar curves H(n), as n → ∞. We describe a set of tools for studying the Hausdorff dimension dim H of a certain family of such curves, and we adapt these tools to the particular case of the Hénon attractor, estimating its Hausdorff dimension dim H (ℋ) to be about 1.258, a number smaller than the usual estimates for the box-counting dimension of the attractor. We interpret this discrepancy.

scholarly journals Rock Mechanical Property Influenced by Inhomogeneity

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yunliang Tan ◽  
Dongmei Huang ◽  
Ze Zhang
Keyword(s):  
Mechanical Property ◽  
Fractal Dimension ◽  
Rock Type ◽  
Fractal Dimensions ◽  
Rock Material ◽  
The Self ◽  
Self Similarity ◽  
Red Sandstone ◽  
Variation Patterns ◽  
Rock Microstructure

In order to identify the microstructure inhomogeneity influence on rock mechanical property, SEM scanning test and fractal dimension estimation were adopted. The investigations showed that the self-similarity of rock microstructure markedly changes with the scanned microscale. Different rocks behave in different fractal dimension variation patterns with the scanned magnification, so it is conditional to adopt fractal dimension to describe rock material. Grey diabase and black diabase have high suitability; red sandstone has low suitability. The suitability of fractal-dimension-describing method for rocks depends on both investigating scale and rock type. The homogeneities of grey diabase, black diabase, grey sandstone, and red sandstone are 7.8, 5.7, 4.4, and 3.4, separately; their average fractal dimensions of microstructure are 2.06, 2.03, 1.72, and 1.40 correspondingly, so the homogeneity is well consistent with fractal dimension. For rock material, the stronger brittleness is, the less profile fractal dimension is. In a sense, brittleness is an image of rock inhomogeneity in macroscale, while profile fractal dimension is an image of rock inhomogeneity in microscale. To combine the test of brittleness with the estimation of fractal dimension with condition will be an effective approach for understanding rock failure mechanism, patterns, and behaviours.

scholarly journals Classification of texture using random box counting and binarization methods

2021 ◽  
Vol 10 (1) ◽  
pp. 533-540
Author(s):  
Wijdan Jaber AL-kubaisy ◽  
Maha Mahmood
Keyword(s):  
Image Processing ◽  
Fractal Dimension ◽  
Blood Cells ◽  
Multifractal Analysis ◽  
Vision System ◽  
White Blood Cells ◽  
Real Life ◽  
Self Similarity ◽  
Box Counting

The heterogeneous texture classifications with the complexity of structures provide variety of possibilities in image processing, as an example of the multifractal analysis features. The task of texture analysis is a highly significant field of study in the field of machine vision. Most of the real-life surfaces exhibit textures and an efficiently modelled vision system must have the ability to deal with this variety of surfaces. A considerable number of surfaces maintain a self-similarity quality as well as statistical roughness at different scales. Fractals could provide a great deal of advantages; also, they are popular in the process of modelling these properties in the tasks related to the field of image processing. With two distinct methods, this paper presents classification of texture using random box counting and binarization methods calculate the estimation measures of the fractal dimension BCM. There methods are the banalization and random selecting boxes. The classification of the white blood cells is presented in this paper based on the texture if it is normal or abnormal with the use of a number of various methods.

scholarly journals An Analysis of COVID-19 in Europe Based on Fractal Dimension and Meteorological Data

2021 ◽  
Author(s):  
Cristina Maria Pacurar ◽  
Victor Dan Păcurar ◽  
Marius Paun
Keyword(s):  
Fractal Dimension ◽  
Meteorological Parameters ◽  
Prediction Models ◽  
Meteorological Data ◽  
Global Radiation ◽  
Reproduction Rate ◽  
Box Counting ◽  
Box Counting Dimension ◽  
First Choice ◽  
Research Efficiency

The present paper proposes a fractal analysis of the Covid-19 dynamics in 45 European countries. We introduce a new idea of using the box-counting dimension of the epidemiologic curves as a means of classifying the Covid-19 pandemic in the countries taken into consideration. The classification can be a useful tool in deciding upon the quality and accuracy of the data available. We also investigated the reproduction rate, which proves to have significant fractal features, thus enabling another perspective on this epidemic characteristic. Moreover, we studied the correlation between two meteorological parameters: global radiation and daily mean temperature and two Covid-19 indicators: daily new cases and reproduction rate. The fractal dimension differences between the analysed time series graphs could represent a preliminary analysis criterion, increasing research efficiency. Daily global radiation was found to be stronger linked with Covid-19 new cases than air temperature (with a greater correlation coefficient -0.386, as compared with -0.318), and consequently it is recommended as the first-choice meteorological variable for prediction models.

scholarly journals The linkage between box-counting and geomorphic fractal dimensions in the fractal structure of river networks: the junction angle

2020 ◽  
Vol 51 (6) ◽  
pp. 1397-1408
Author(s):  
Xianmeng Meng ◽  
Pengju Zhang ◽  
Jing Li ◽  
Chuanming Ma ◽  
Dengfeng Liu
Keyword(s):  
Fractal Dimension ◽  
Fractal Structure ◽  
Fractal Dimensions ◽  
River Networks ◽  
Stream Length ◽  
Box Counting ◽  
Linear Relationships ◽  
Box Counting Dimension ◽  
Junction Angle

Abstract In the past, a great deal of research has been conducted to determine the fractal properties of river networks, and there are many kinds of methods calculating their fractal dimensions. In this paper, we compare two most common methods: one is geomorphic fractal dimension obtained from the bifurcation ratio and the stream length ratio, and the other is box-counting method. Firstly, synthetic fractal trees are used to explain the role of the junction angle on the relation between two kinds of fractal dimensions. The obtained relationship curves indicate that box-counting dimension is decreasing with the increase of the junction angle when geomorphic fractal dimension keeps constant. This relationship presents continuous and smooth convex curves with junction angle from 60° to 120° and concave curves from 30° to 45°. Then 70 river networks in China are investigated in terms of their two kinds of fractal dimensions. The results confirm the fractal structure of river networks. Geomorphic fractal dimensions of river networks are larger than box-counting dimensions and there is no obvious relationship between these two kinds of fractal dimensions. Relatively good non-linear relationships between geomorphic fractal dimensions and box-counting dimensions are obtained by considering the role of the junction angle.

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