• Imaging Science in Dentistry
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• v.35 no.1
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• pp.33-40
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• 2005

Purpose : (1) To analyse the effect of exposure time, ROI size and one impact factor in the image processing procedure on estimates of fractal dimension; and (2) to analyse the correlated relationship between the fractal dimension and the Cu-Eq value (bone density). Materials and Methods : The cylindric bone phantoms of 6 large and 5 small diameter having different bone densities respectively and human dry mandible segment with copper step wedge were radiographed at 1.0 and 1.2 sec esposure (70 kVp, 7 mA) using one occlusal film and digitized. Eleven rectangular ROIs from 11 cylindric bone phantoms and 4 rectan-gular ROIs from cortical, middle, periodontal regions, and socket of bone were selected. Gaussian blurred Image was subtracted from original image of each ROI and multiplied respectively by 1, 0.8, and 0.5, and then the image was made binary, eroded and dilated once, and skeletonized. The fractal dimension was calculated by means of a box counting method in the software ImageJ. Results : The fractal dimension was decreased gradually with continued bone density decrease showing strong correlations (bone phantom; r> 0.87, bone; r> 0.68) under 70 kVp 1.0 sec M = 0.8. Fractal dimensions showed the significant differerence (p < 0.05) between two different exposure times on the same small ROI of bone phantom. Fractal dimensions between two different sizes of ROI on bone phantom showed the significant differerence (p < 0.05) under 1.2 sec exposure, but did not show it (p > 0.05) under 1.0 sec exposure. Conclusions : Exposure time, ROI size, and modifying factor during subtracting could become impacting on the results of fractal dimension. Fractal analysis with thoroughly evaluated method considering the various impacting factors on the results could be useful in assessing the bone density in dental radiography.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.24 no.1
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• pp.124-129
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• 2010

When a phenolic resin is carbonized by the leakage current flowing along its surface, the carbonization pattern is one of the most important factors to determine its carbonization characteristics. However, the typical carbonization pattern of a phenolic resin is too complicated to be analyzed by conventional Euclidean geometry. In most cases, such a complicated shape shows a fractal structure. It is possible, therefore, to examine the characteristics of the carbonization pattern regarding a given phenolic resin. In order to quantitatively investigate the carbonization pattern of the phenolic resin carbonized by a leakage current, in this paper, the fractal dimension of the carbonization pattern has been calculated as a function of the magnitude of a leakage current and the distance between two electrodes. For reliability of calculation, the correlation function as well as the box counting method has been used to calculate the fractal dimension. According to the result of calculation, the fractal dimension increases as the current increases at the constant electrode gap distance. However, there is no significant relation between the fractal dimension and the electrode gap distance at a constant current.

• Tunnel and Underground Space
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• v.16 no.1 s.60
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• pp.26-37
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• 2006

This study addresses the applicability of box fractal dimension, $D_B$, as an index of statistical homogeneity of fractured rock mass. The box-count method's capability in quantifying the combined effect of fracture density and size distribution is examined systematically. Total of 129 two-dimensional fracture configurations were generated based on different combinations of fracture size distribution and fracture density. $D_B$was calculated for the generated fracture network systems using the box-counting method. It was found that was standard deviation of trace length and fracture orientation have no effect on calculated $D_B$. The estimated $D_B$ was found to increase with increasing total density and/or mean trace length. To explore the field applicability of this study, the statistical homogeneity of fractured rock mass was investigated at the rock slope and the underground facility using the box-counting method as well as conventional contingency table analysis. The results obtained in this study clearly show that the methodologies given in this paper have the capability of determining the statistical homogeneity of fractured rock mass.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.135-140
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• 2000

The characteristics of mechanical behavior were estimated for Ti-6Al-4V alloy with four kinds of microstructure prepared with heat treatments. For this study, impact test, tensile test and fatigue crack growth test were performed, and then compared mechanical properties on the four microstructures. Furthermore, for quantitative evaluation, fractal dimensions of crack pass were obtained using the box counting method. The main results obtained are summarized as follows. (1) The microstructures exhibited equiaxed microstructure, bimodal-microstructure and lamellar microstructure by heat treatment. (2) The impact absorbed energy and elongation is superior in the bimodal-microstructure, and the hardness and tensile strength are superior in the lamellar microstructure. (3) The fatigue crack growth rate is similar to all microstructures in the low ${\Delta}K$ region. The fatigue crack growth rate of equiaxed microstructure is fastest, and that of lamellar microstructure is lowest in the high ${\Delta}K$ region. (4) The fractal dimension D of lamellar microstructure is higher then that of the equiaxed microstructure and bimodal microstructure.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.4
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• pp.609-616
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• 2002

The characteristics of mechanical behavior are investigated for Ti-6Al-4V alloy. Four kinds of the specimens are prepared under different heat treatments in order to produce different microstructures. In the present investigations, impact, tensile and fatigue crack growth tests are performed for each test specimen. The results obtained through the investigations are compared. Additionally fr actal dimensions of crack pass are obtained using the box counting method. The results are, 1) the microstructures shows as equiaxed, bimodal and Widmanstatten microstructures respectively, 2) the impact energy and elongation are superior fur the bimodal microstructure, and the hardness and tensile strength are superior fur the Widmanstatten microstructure, 3) the fatigue crack growth rate is similar to all microstructures in low ΔK region while that of equiaxed microstructure is the largest, and that of Widmanstatten microstructure is the lowest in high ΔK region respectively, 4) the fractal dimension D of Widmanstatten microstructure shows higher value than that of the equiaxed and bimodal microstructures under 200 magnification view of the SEM micrographs.

• Journal of Electrochemical Science and Technology
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• v.14 no.2
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• pp.194-204
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• 2023

Models based on diffusion-limited aggregation (DLA) have been extensively used to explore the mechanisms of dendritic particle aggregation phenomena. The physical and chemical properties of systems in which DLA aggregates emerge are given in their fractal. In this paper, we present a comprehensive study of the growth of electrodeposited copper dendrites in flat plate electrochemical cells from a fractal perspective. The effects of growth time, applied voltage, copper ion concentration, and electrolyte acidity on the morphology and fractal dimension of deposited copper were examined. 'Phase diagram' set out the variety of electrodeposited copper fractal morphology analysed by metallographic microscopy. The box counting method confirms that the electrodeposited dendritic structures manifestly exhibit fractal character. It was found that with the increase of the voltage and copper ion concentration. The fractal copper size becomes larger and its morphology shifts towards a dendritic structure, with the fractal dimension fluctuating around 1.60-1.70. In addition, the morphology of the deposited copper is significantly affected by the acidity of the electrolyte. The increase in acidity from 0.01 to 1.00 mol/L intensifies the hydrogen precipitation side reactions and the overflow path of hydrogen bubbles affects the fractal growth of copper dendrites.

• Journal of the Korean Society of Safety
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• v.16 no.1
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• pp.31-36
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• 2001

Surface crack growth characteristics and influence of the stress amplitude in rotary bending fatigue test were evaluated for annealed S35C steel, and than fractal dimensions of fatigue crack paths estimated using the box counting method. The following results that will be helpful to understand the fatigue crack growth mechanism were obtained. (1) Crack growth rate ds/dN and db/dN (s : half crack length at the surface crack, b : crack depth) depended on stress amplitude (${\Delta}{\sigma}/2$), stress intensity factor range (${\Delta}K_A, {\Delta}K_C$) and crack length. (2) At the effect area of 0.3 mm hole notch (s＜0.5 mm) crack growth rate did not depend on these factors. (3) The fractal dimensions (D) increased with stress amplitude (${\Delta}{\sigma}/2$) but decreased with cyclic number.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.38
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• pp.1-7
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• 1996

프랙탈이란 말은 라틴어 Fractus(부서진 상태를 뜻함)에서 유래되었으며, 1975년 Mandelbrot가 수학 및 자연계의 비정규적 패턴들에 대한 체계적 고찰을 담은 자신의 에세이의 표제를 주기 위해서 만들었다 (〔6〕). 프랙탈을 기술하는데 있어서 가장 중요한 양은 차원(dimension)으로 프랙탈 차원은 정수차원이 아닌 실수 차원을 갖는다. 이 논문에서는 box counting 차원, Hausdorff 차원, s-potential 및 s-energy등에 대한 정의를 하고 정리 2.8, 정리 3.1및 정리 3.2을 증명하고자 한다.

• Economic and Environmental Geology
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• v.29 no.4
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• pp.523-528
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• 1996

In Korean topography the behaviors of random fractals and multifractality are analytically and numerically studied on the mountain heights shown between $128{\sim}129^{\circ}E$ and $37{\sim}38^{\circ}N$. The phase transitions on the fractal structure are approximately found at the critical length $N_c=2000m$ from the values of standard deviations that it varies with both the longitudinal and latitudinal lengths. In the multifractal structure we assume that the mountain heights divided by the intervals of 20 m are located on the horizontal plane in two dimensional square lattice, and estimate the values of the generalized dimension and the scaling exponents by using the the box counting method for the three cases of square area ($1{\times}1km^2$, $2{\times}2km^2$, $4{\times}4km^2$).

• Journal of Korea Multimedia Society
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• v.7 no.2
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• pp.173-186
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• 2004

This paper proposed the content-based retrieval system as a method for performing image retrieval through the effective feature extraction of the object of significant meaning based on the characteristics of man's visual system. To allow the object region of interest to be primarily detected, the region, being comparatively large size, greatly different from the background color and located in the middle of the image, was judged as the major object with a meaning. To get the original features of the image, the cumulative sum of tile declination difference vector the segment of the object contour had and the signature of the bipartite object were extracted and used in the form of being applied to the rotation of the object and the change of the size after partition of the total length of the object contour of the image into the normalized segment. Starting with this form feature, it was possible to make a retrieval robust to any change in translation, rotation and scaling by combining information on the texture sample, color and eccentricity and measuring the degree of similarity. It responded less sensitively to the phenomenon of distortion of the object feature due to the partial change or damage of the region. Also, the method of imposing a different weight of similarity on the image feature based on the relationship of complexity between measured objects using the fractal dimension by the Boxing-Counting Dimension minimized the wrong retrieval and showed more efficient retrieval rate.