scholarly journals Fractal Analysis Of Colors And Shapes For Natural And Urbanscapes URBANSCAPES

2015 ◽  
Vol XL-7/W3 ◽  
pp. 1431-1438 ◽  
Author(s):  
J. Wang ◽  
S. Ogawa
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Spatial Distributions ◽  
Colour Image ◽  
Natural Landscapes ◽  
The Difference ◽  
Box Counting Method ◽  
Rgb Values ◽  
Grayscale Images

Fractal analysis has been applied in many fields since it was proposed by Mandelbrot in 1967. Fractal dimension is a basic parameter of fractal analysis. According to the difference of fractal dimensions for images, natural landscapes and urbanscapes could be differentiated, which is of great significance. In this paper, two methods were used for two types of landscape images to discuss the difference between natural landscapes and urbanscapes. Traditionally, a box-counting method was adopted to evaluate the shape of grayscale images. On the other way, for the spatial distributions of RGB values in images, the fractal Brownian motion (fBm) model was employed to calculate the fractal dimensions of colour images for two types of landscape images. From the results, the fractal dimensions of natural landscape images were lower than that of urbanscapes for both grayscale images and colour images with two types of methods. Moreover, the spatial distributions of RGB values in images were clearly related with the fractal dimensions. The results indicated that there was obvious difference (about 0.09) between the fractal dimensions for two kinds of landscapes. It was worthy to mention that when the correlation coefficient is 0 in the semivariogram, the fractal dimension is 2, which means that when the RGB values are completely random for their locations in the colour image, the fractal dimension becomes 3. Two kinds of fractal dimensions could evaluate the shape and the color distributions of landscapes and discriminate the natural landscapes from urbanscapes clearly.

Mathematical Model Incorporated Fractal Geometry and Permeability of Compressed Peanut and Sesame for Oil Extraction

2012 ◽  
Vol 550-553 ◽  
pp. 676-681
Author(s):  
Xiao Zheng ◽  
Jing Zhou Wang ◽  
Guo Xiang Lin ◽  
Zhi Xian Sun ◽  
Don Ping He
Keyword(s):  
Mathematical Model ◽  
Fractal Dimension ◽  
Applied Pressure ◽  
Fractal Dimensions ◽  
Image Analyzer ◽  
Fractal Characteristic ◽  
Pore Size Distributions ◽  
The Difference ◽  
Sesame Cake ◽  
Box Counting Method

Considering the fractal characteristic of oilseed cake, the relationship between the permeability and the pore fractal dimension of peanut and sesame cake has been investigated. The microstructures of peanut and sesame cake under five applied pressures are measured by using stereo light microscope and Image-pro image analyzer. Using the box-counting method, the fractal dimensions of pore size distributions are measured. A mathematical model incorporated fractal dimension and permeability has been developed to predicate the permeability of compressed peanut and sesame under cold condition based upon combining Hagen-Poiseulle equation with Darcy’s law for flow of fluid through porous media. There is a prediction of permeability of peanut and sesame cake. Thus, a measurement is carried out for validation. The values of mean relative errors are 19.4% and 11.4 respectively. A fairly good agreement is obtained in the case of high applied pressure. And there exists a tendency that the value of the difference between the theoretical calculation and the permeability measurement decrease significantly with the increase of applied pressure.

scholarly journals FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY

2011 ◽  
Vol 19 (1) ◽  
pp. 45 ◽  
Author(s):  
Ian Parkinson ◽  
Nick Fazzalari
Keyword(s):  
Fractal Dimension ◽  
Trabecular Bone ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Box Counting ◽  
Cell Tissue ◽  
Image Analyser ◽  
Model Independent ◽  
Box Counting Method ◽  
Image Orientation

A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge). The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.

Image Reconstruction and Analysis of Three-Dimensional Fracture Surfaces Based on the Stereo Matching Method

2004 ◽  
Vol 261-263 ◽  
pp. 1593-1598
Author(s):  
M. Tanaka ◽  
Y. Kimura ◽  
A. Kayama ◽  
L. Chouanine ◽  
Reiko Kato ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Image Reconstruction ◽  
Fracture Surface ◽  
Fractal Analysis ◽  
Stereo Matching ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Matching Method ◽  
Fracture Surfaces ◽  
Box Counting Method

A computer program of the fractal analysis by the box-counting method was developed for the estimation of the fractal dimension of the three-dimensional fracture surface reconstructed by the stereo matching method. The image reconstruction and fractal analysis were then made on the fracture surfaces of materials created by different mechanisms. There was a correlation between the fractal dimension of the three-dimensional fracture surface and the fractal dimensions evaluated by other methods on ceramics and metals. The effects of microstructures on the fractal dimension were also experimentally discussed.

FRACTAL ANALYSIS OF DENDRITIC ARBORISATION PATTERNS OF STALKED AND ISLET NEURONS IN SUBSTANTIA GELATINOSA OF DIFFERENT SPECIES

Fractals ◽  
2007 ◽  
Vol 15 (01) ◽  
pp. 1-7 ◽  
Author(s):  
NEBOJŠA T. MILOŠEVIĆ ◽  
DUŠAN RISTANOVIĆ ◽  
JOVAN B. STANKOVIĆ ◽  
RADMILA GUDOVIĆ
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Islet Cells ◽  
Fractal Dimensions ◽  
Substantia Gelatinosa ◽  
Neuronal Populations ◽  
Box Counting ◽  
Morphological Descriptor ◽  
The Mean ◽  
Box Counting Method

Through analysis of the morphology of dendritic arborisation of neurons from the substantia gelatinosa of dorsal horns from four different species, we have established that two types of cells (stalked and islet) are always present. The aim of the study was to perform the intra- and/or inter-species comparison of these two neuronal populations by fractal analysis, as well as to clarify the importance of the fractal dimension as an objective and usable morphological parameter. Fractal analysis was carried out adopting the box-counting method. We have shown that the mean fractal dimensions for the stalked cells are significantly different between species. The same is true for the mean fractal dimensions of the islet cells. Still, no significant differences were found for the fractal dimensions of the stalked and islet cells within a particular species. The human species has shown as the only exception where fractal dimensions of these two types of cells differ significantly. This study shows once more that the fractal dimension is a useful and sensitive morphological descriptor of neuronal structures and differences between them.

scholarly journals Experimental Study of Crushed Granular Materials by the Notion of Fractal Dimension in 2D and 3D.

2021 ◽  
Author(s):  
Houria BOUZEBOUDJA ◽  
Bachir MELBOUCI ◽  
Aldjia BOUZEBOUDJA
Keyword(s):  
Fractal Dimension ◽  
Los Angeles ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Mechanical Tests ◽  
Box Counting ◽  
Before And After ◽  
The Difference ◽  
Box Counting Method ◽  
2D And 3D

Abstract The micro-texture of the aggregates of a pavement layer has a direct influence on their resistance. Whatever the position of these aggregates in a pavement structure, they must withstand, during construction or during life, the stresses of attrition and impact. In this study, a series of mechanical tests (Proctor, Los-Angeles and Micro-Deval) are carried out on grains of local materials (limestone and shale), the degree of crushing of the grains has been quantified using the concept of fractal dimension. The fractal dimension was calculated for the different grains constituting the samples before and after each test, with the use of two two-dimensional 2D methods (Masses Method at the scale of a sample and the Box Counting Method at the scale of a grain) and a three-dimensional 3D method (Blanket on a grain scale) which is based on the use of the difference between erosion and dilation. We seek to determine from these methods the correlation between the two fractal dimensions, namely 2D and 3D and study the influence of different parameters on the mechanical characteristics of the materials chosen: the shape and size of the grains, the presence or absence of water, the stress intensity as well as the nature of the material. The results obtained show that the three-dimensional method has a positive effect on the description of the 3D microstructure of the surface of the grains subjected to the various mechanical tests.

scholarly journals Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Youping Fan ◽  
Dai Zhang ◽  
Jingjiao Li
Keyword(s):  
Fractal Dimension ◽  
Tree Growth ◽  
Fractal Dimensions ◽  
Moisture Level ◽  
Growth Time ◽  
Counting Method ◽  
Box Counting ◽  
Electrical Trees ◽  
Box Counting Method ◽  
Electrical Treeing

The paper aims to understand how the fractal dimension and growth time of electrical trees change with temperature and moisture. The fractal dimension of final electrical trees was estimated using 2-D box-counting method. Four groups of electrical trees were grown at variable moisture and temperature. The relation between growth time and fractal dimension of electrical trees were summarized. The results indicate the final electrical trees can have similar fractal dimensions via similar tree growth time at different combinations of moisture level and temperature conditions.

scholarly journals Postnatal Development of the Retina in Rats Exposed to Hyperoxia: A Fractal Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Anne Claudia Ştefănuţ ◽  
Ştefan Ţălu ◽  
Viorel Miclăuş ◽  
Adriana Mureşan ◽  
Remus Moldovan ◽  
...  
Keyword(s):  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Control Group ◽  
Newborn Rats ◽  
Vascular Abnormalities ◽  
Retinal Layers ◽  
Fractal Analyses ◽  
Group 10 ◽  
Box Counting Method ◽  
Experimental Group

Purpose. The aim of this study was to investigate and quantify changes in the newborn rats retinal layers during the hyperoxia (80% O2) exposure using fractal analysis. Materials and Methods. This study was conducted on two groups of 20 newborn rats: a control (normal) group (10 rats) and an experimental group (10 rats). The control group was composed of 10 newborn rats, which were placed at 12 hours after birth, in a pediatric incubator, together with their mother, in conditions of normoxia for 21 days. The experimental group consisted of 10 newborn rats, which were placed at 12 hours after birth, in a pediatric incubator with their mother, in conditions of normoxia for 7 days, then 7 days of hyperoxia (80% O2) for 22.5 hours/day, and then 7 days in conditions of normoxia. Slaughtering of the rats was performed on day 21 and the eye globes were harvested in order to perform histopathological examinations. The fractal analyses of the retinal digital images were performed using the fractal analysis software Image J, and the fractal dimensions were calculated using the standard box-counting method. Results. Microscopic examination revealed a normal development of the retina in the control group. In the experimental group, all the animals exposed to hyperoxia revealed both structural and vascular abnormalities on entire retina. Conclusions. The results showed that the fractal analysis is a valuable tool to quantify histoarchitectural changes in the newborn rats retinal layers during the hyperoxia (80% O2).

scholarly journals Binarization methods and investigation of their influence on the fractal dimension of functional coatings

2020 ◽  
pp. 30-42
Author(s):  
Anna Zhurba ◽  
Michail Gasik
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Quantitative Characteristic ◽  
Image Binarization ◽  
Counting Method ◽  
Functional Coatings ◽  
Binary Images ◽  
Box Counting ◽  
Box Counting Method ◽  
Binarization Threshold

An essential element of fractal analysis of functional coatings is the fractal dimension, which is an important quantitative characteristic. Typically, coating images are represented as colored or halftone, and most fractal dimension algorithms are for binary images. Therefore, an important step in fractal analysis is binarization, which is a threshold separation operation and the result of which is a binary image.The purpose of the study is to study and program the methods of image binarization and to study the influence of these methods on the value of fractal dimension of functional coatings.As a result of the binarization threshold, the image is split into two regions, one containing all pixels with values below a certain threshold and the other containing all pixels with values above that threshold. Of great importance is the determination of the binarization threshold.The study analyzed a number of functional coating images, determined the fractal dimension of the image by the Box Counting method at different binarization thresholds and when applying different binarization methods (binarization with lower and upper threshold, with double restriction, and the average method for determining the optimal binarization threshold) images. The Box Counting method is used to depict any structure on a plane. This method allows us to determine the fractal dimension of not strictly self-similar objects. Each image binarization method is used for different types of images and for solving different problems.As a result, the methods of image binarization were developed and implemented, the fractal dimension of binary images was calculated, and the influence of these methods on the value of fractal dimension of functional coatings was investigated.The surfaces of composite steel structure, metallic porous materials, and natural cave structures are analyzed.

scholarly journals Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system

2016 ◽  
Author(s):  
Auguste Gires ◽  
Ioulia Tchiguirinskaia ◽  
Daniel Schertzer ◽  
Susana Ochoa Rodriguez ◽  
Patrick Willems ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Hydrological Models ◽  
Scale Invariant ◽  
Sewer System ◽  
Distributed Models ◽  
Urban Catchments ◽  
Distributed Hydrological Models ◽  
Dimension Characteristic

Abstract. Fractal analysis relies on scale invariance and the concept of fractal dimension enables to characterise and quantify the space filled by a geometrical set exhibiting complex and tortuous patterns. Fractal tools have been widely used in hydrology but seldom in the specific context of urban hydrology. In this paper fractal tools are used to analyse surface and sewer data from 10 urban or peri-urban catchments located in 5 European countries. The aim was to characterise urban catchment properties accounting for the complexity and inhomogeneity typical of urban water systems. Sewer system density and imperviousness (roads or buildings), represented in rasterized maps of 2 m × 2 m pixels, were analysed to quantify their fractal dimension, characteristic of scaling invariance. The results showed that both sewer density and imperviousness exhibit scale invariant features and can be characterized with the help of fractal dimensions ranging from 1.6 to 2, depending on the catchment. In a given area consistent results were found for the two geometrical features, yielding a robust and innovative way of quantifying the level of urbanization. The representation of imperviousness in operational semi-distributed hydrological models for these catchments was also investigated by computing fractal dimensions of the geometrical sets made up of the sub-catchments with coefficients of imperviousness greater than a range of thresholds. It enabled to quantify how well spatial structures of imperviousness were represented in the urban hydrological models.

Abstract 17136: Pulmonary Arterial and Venous Fractal Dimension as a Marker of Pulmonary Arterial Hypertension

Circulation ◽  
2020 ◽  
Vol 142 (Suppl_3) ◽  
Author(s):  
Andrew Tsao ◽  
Pietro Nardelli ◽  
Eileen Harder ◽  
Gonzalo Vegas Sanchez-Ferrero ◽  
James C Ross ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Mean Pulmonary Arterial Pressure ◽  
Box Counting ◽  
Wilcoxon Rank Sum Test ◽  
History Of ◽  
Pulmonary Arterial ◽  
Box Counting Method ◽  
Definition Of ◽  
Vascular Trees

Introduction: PAH is characterized by a loss of pulmonary vascular complexity. In this study, total, arterial, and venous vasculatures of patients with PAH and with ePAH were analyzed using fractal analysis and compared against controls Methods: Data from 1514 consecutive right heart catheterizations from 4/27/2011 to 10/2/2018 representing subjects referred to our dyspnea center were searched for availability of imaging. 388 CT angiography (CTA) scans were identified (used given retrospective availability of thin slice reconstructions). Three initial cohorts (no overlap) were identified from individuals in this set. Control patients had normal resting and exercise hemodynamics and no history of cardiopulmonary disease. The second group met the current definition of PAH (resting mean pulmonary arterial pressure >20mmHg, pulmonary vascular resistance >3 Wood Units, pulmonary capillary wedge pressure <15mmHg). The third group (ePAH) had normal resting hemodynamics but age adjusted evidence of PAH with exercise. Pulmonary vascular trees were reconstructed; total, arterial, and venous trees were separated; and fractal dimensions were measured using a 3D box counting method for each tree. Comparisons were made using the Wilcoxon Rank Sum test (R 3.5). Results: Venous fractal dimensions of controls (2.10±0.07) were higher than those of PAH (2.03±0.08; p=3e-6) and of ePAH (2.04±0.13; p=0.008). Total fractal dimension also yielded higher values for controls (2.30±0.05) compared against PAH (2.28±0.07; p=0.009) and ePAH (2.26±0.10; p=0.04). No significant differences were found between arterial fractal dimensions of controls (2.17±0.04) against those of PAH (2.16±0.07; p=0.15) and of ePAH (2.15±0.10; p=0.14). Conclusions: Fractal dimension allows for non-invasive characterization of pulmonary vascular complexity. Using this method, patients with PAH or ePAH were found to have lower total and venous vascular complexities than controls without PAH or ePAH.

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