Mass fractal dimension of soil macropores using computed tomography: from the box-counting to the cube-counting algorithm

2003 ◽  
Vol 54 (3) ◽  
pp. 569-579 ◽  
Author(s):  
J.S. Perret ◽  
S.O. Prasher ◽  
A.R. Kacimov
Keyword(s):  
Computed Tomography ◽  
Fractal Dimension ◽  
Box Counting ◽  
Mass Fractal ◽  
Mass Fractal Dimension ◽  
Counting Algorithm

3D box-counting algorithm for calculating fractal dimension of cities

2010 ◽  
Vol 30 (8) ◽  
pp. 2070-2072
Author(s):  
Le-shan ZHANG ◽  
Ge CHEN ◽  
Yong HAN ◽  
Tao ZHANG
Keyword(s):  
Fractal Dimension ◽  
Box Counting ◽  
Counting Algorithm

ULTRA SMALL-ANGLE X-RAY SCATTERING STUDY OF FLOCCULATION IN SILICA-FILLED RUBBER

2014 ◽  
Vol 87 (2) ◽  
pp. 348-359 ◽  
Author(s):  
Satoshi Mihara ◽  
Rabin N. Datta ◽  
Wilma K. Dierkes ◽  
Jacques W. M. Noordermeer ◽  
Naoya Amino ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Small Angle ◽  
Radius Of Gyration ◽  
X Ray ◽  
X Ray Scattering ◽  
Mass Fractal ◽  
Mass Fractal Dimension ◽  
Lower Mobility ◽  
Low Mass ◽  
Ray Scattering

ABSTRACT The flocculation of silica during vulcanization is monitored using the ultra small-angle X-ray scattering technique for two different types of silica: a highly dispersible silica (HD) and a conventional silica (CV), mixed into a blend of S-SBR and BR rubbers. The cutoff length of the silica aggregate Rss and the mass fractal dimension Dm, which indicate the degree of flocculation of aggregates, are estimated according to the modified unified equation. The aggregate radius Ra is estimated to be related to the lower cutoff length Rss, indicating the radius of gyration of the mass-fractal structure. For both silicas, Ra increases during vulcanization. For the CV silica, an increase of Dm is observed, whereas no significant increase of Dm can be seen for the HD silica. The Ra of CV is relatively high compared with that of HD. On the other hand, the CV silica shows a relatively lower Dm compared with that of HD. These results indicate that CV has a larger size of aggregates and lower degree of agglomeration of its aggregates. The presence of di(tri-ethoxy-silyl-propyl)tetrasulfide (TESPT) as coupling agent between the silica and rubber decreases the aggregate radius of silica. However, in the absence of TESPT, a low mass-fractal dimension, which means a low degree of agglomeration of aggregates, is observed. This results from a lower mobility of silica aggregates, depending on the size of the aggregates. The silica loading also has an influence on the flocculation process. The aggregate radius increases as the silica loading is increased. At the same time, a higher mass-fractal dimension, and therefore also a higher degree of agglomeration, can be seen at higher silica loading.

scholarly journals Identification of emphysema patterns in high resolution computed tomography images

2017 ◽  
Vol 4 (1) ◽  
pp. 16
Author(s):  
Musibau A. Ibrahim ◽  
Oladotun A. Ojo ◽  
Peter A. Oluwafisoye
Keyword(s):  
Computed Tomography ◽  
Fractal Dimension ◽  
High Resolution ◽  
Hölder Exponent ◽  
High Resolution Computed Tomography ◽  
Box Counting ◽  
Computed Tomography Images ◽  
Local Intensity ◽  
Box Counting Method

Fractal dimension (FD) is a very useful metric for the analysis of image structures with statistically self-similar properties. It has applications in areas such as texture segmentation, shape classification and analysis of medical images. Several approaches can be used for calculating the fractal dimension of digital images; the most popular method is the box-counting method. It is also very challenging and difficult to classify patterns in high resolution computed tomography images (HRCT) using this important descriptor. This paper applied the Holder exponent computation of the local intensity values for detecting the emphysema patterns in HRCT images. The absolute differences between the normal and the abnormal regions in the images are the key for a successful classification of emphysema patterns using the statistical analysis. The results obtained in this paper demonstrated the effectiveness of the predictive power of the features extracted from the Holder exponent in the analysis and classification of HRCT images. The overall classification accuracy achieved in lung tissue layers is greater than 90%, which is an evidence to prove the effectiveness of the methods investigated in this paper.

scholarly journals Experimental Study on the Riverbed Coarsening Process and Changes in the Flow Structure and Resistance in the Gravel Riverbed Downstream of Dams

2021 ◽  
Vol 9 ◽  
Author(s):  
Yinjun Zhou ◽  
Jinyou Lu ◽  
Zhongwu Jin ◽  
Yuan Li ◽  
Yu Gao ◽  
...  
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Flow Structure ◽  
Turbulence Intensity ◽  
Coarse Grained ◽  
Adjustment Process ◽  
Bed Sediment ◽  
Sandy Gravel ◽  
Mass Fractal ◽  
Mass Fractal Dimension

Following the construction of a reservoir, sediment is intercepted, which greatly reduces the sediment concentration in the discharged flow. This reduction causes riverbed scouring and flow structure adjustments downstream, thereby impacting the river habitat. This study used the generalized flume test with different bed sand compositions and discharge rates to simulate the scouring adjustment process of a sand pebble riverbed channel downstream of a reservoir. The results show that the bed sediment composition affects the water surface gradient, scour depth, turbulence intensity, and sand resistance directly after final scouring. Coarse-grained bed sediment demonstrated the greatest final turbulence intensity and sand resistance, while bed sediments with reduced coarseness exhibited a greater scouring degree; the resistance for sand grains of moderate coarseness showed the greatest change. Sand resistance was exponentially and positively correlated with the median grain size and the fractal dimension of bed sediment mass. The mass fractal dimension expression was suitable for the analysis of bed sand grain-size distribution; it contributed to the calculation of grain resistance with fewer hydraulic parameters. The relationship between the mass fractal dimension and the adjusted grain resistance was also established, which can aid the calculation of the resistance changes in sandy gravel-bed river reaches downstream of reservoirs, enabling the prediction of their effects on aquatic habitats.

scholarly journals Asymmetry of Information in the Analysis of Socio-Economic Processes

Vestnik NSUEM ◽  
2020 ◽  
pp. 64-75
Author(s):  
A. N. Kislyakov
Keyword(s):  
Fractal Dimension ◽  
Shannon Entropy ◽  
The State ◽  
Actual Problem ◽  
Asymmetry Of Information ◽  
Market Participants ◽  
Box Counting ◽  
Cosine Distance ◽  
Minkowski Fractal ◽  
Counting Algorithm

The work is aimed at solving the actual problem of analyzing the interaction of market participants. The degree of unpredictability of market participant’s behavior determines economic risks and manifests itself as a violation of information symmetry. Asymmetry is expressed in different degrees of awareness of groups of sellers and groups of buyers-users of the product about the state of the market, which determines the different behavioral moods and intentions of market participants. The possibility of using the Shannon entropy and fractal dimension indicators to assess the degree of ordering of relationships between groups of buyers and the results of their behavior is considered.This allows us to draw conclusions about the logic of relationships between the behavior of different clients. An iterative box-counting algorithm is used to determine the approximate value of the Minkowski fractal dimension.As a metric of distances between the signs of transactions of pairs of clients, the cosine distance can be used for the case of sparse data.It is shown how the fractal dimension will change in the case of observation of more stable relationships between groups of clients.

Fractal Estimation Using Extended Triangularisation and Box Counting Algorithm for any Geo-Referenced Point Data in GIS

2013 ◽  
pp. 1988-2005 ◽  
Author(s):  
R. Sridhar ◽  
S. Balasubramaniam
Keyword(s):  
Fractal Dimension ◽  
Linear Model ◽  
Crime Data ◽  
Cancer Data ◽  
Box Counting ◽  
Point Event ◽  
Point Data ◽  
Counting Algorithm

Fractal dimension is often used as a measure of how fast length, area, or volume increases or decreases with increase or decrease in scale, or as a measure of complexity of a system. In this paper, input depends only on the Geo-referenced point data where the point event has occurred. An Extended Triangularisation Algorithm is developed to cover the area of point data as a polygon and its perimeter is calculated. Box Counting Algorithm is applied on those point data to calculate the Fractal values, which in turn work as an input to Prediction Plot Linear Model, to show that fractal value increases or decreases as perimeter of Polygon increases or decreases. To validate this model, Crime data was used and its results were analyzed. It provides information to police officials about the intensity of crime, area of patrolling and deputation of police in the sensitivity area. This model could be applied for any Geo-referenced point data such as cancer data, hypertension data and so on.

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