• Journal of Navigation and Port Research
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• v.40 no.4
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• pp.207-212
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• 2016

The box-counting(BC) method is one of the most commonly used methods for fractal dimension calculation of binary images in the fields of Engineering, Science, Medical Science, Geology, etc due to its simplicity and reliability. It deals with only square images with each size equal to the power of 2 to prevent it from discarding unused pixels for images of arbitrary size. In this paper, we presents a more efficient BC method based on the original one, which is applicable to images of arbitrary size. The proposed approach allows the number of the counting boxes to be real to improve the estimation accuracy. The mean absolute error performance is computed on two deterministic fractal images whose theoretical dimensions are well known to compare with those of the existing BC method and triangular BC method. The experimental results show that the proposed method can outperform the two methods and assess the complexity of coastline images of Korea and Chodo island taken from the Google map.

• Journal of the Korean association of regional geographers
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• v.16 no.4
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• pp.387-399
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• 2010

This study, using Fractal theory, aims to examine the meaning in the aspect of urban spatial structure by reflecting the characteristics of elements organizing the urban space and at the same time measuring the urban form quantitatively. By calculating Fractal Dimension to Cheongju as a target, it conducted comparison and analysis by dividing building and road which are internal element of a space into the whole city and urbanized area to compare and analyze validity of the theory application and the inside of an actual urban space. For the method of an analysis, it calculated Fractal Dimension by linking a digital map including the property of building and road with GIS program and using box counting. An analysis result showed that the result value of Fractal Dimension by structure and road is all high and similar. It drew a similar result value from the whole Cheongju and the urbanized area as well, but commercial and industrial area showed low result value from the partial viewpoint. However, it is correct to regard these spaces as one space because they are intimately connected with a residential area. From the general viewpoint, it could be said that Cheongju's Fractal Dimension grows in the context of a urbanized area.

• Journal of the Korea Concrete Institute
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• v.13 no.2
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• pp.146-152
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• 2001

The fractal geometry is a non-Euclidean geometry which discribes the naturally irregular or fragmented shaps, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cemposite composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is appearent.ent.

• The Journal of Engineering Geology
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• v.9 no.2
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• pp.119-134
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• 1999

Joints developed around the Moryang fault were investigated by traverse and inventory methods in order to characterize their orientation, spacing and density. The results of the traverse method show that the orientation of the dominant joint sets of the study area is NNE and EW, and that joint spacing distribution is a negative exponential distribution to the center of the fault and a log-normal distribution to the margin of the fault. The results of the inventory method show that the orientation of the dominant joint sets on joint map is NW and NE, and that joint density tends to increase toward the center of the fault. Fractal dimension was determined by using Box-counting method and Cantor's dust method to quantify the distribution of joint network and to evaluate the dimension around the fault. The dimension determined by Box-counting method ranges from 1.31 to 1.70 and shows the tendency of increasing value toward the center of the fault. Comparing fractal dimension by Box-counting method with joint density, fractal dimension is directly proportional to joint density. Nevertheless, fractal dimension could be varied due to the different distribution patterns of the joints with same density. The dimensions determined by Cantor's dust method show different values with respect to the orientation of scan lines. This results form the anisotropy of joint distribution.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.1083-1087
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• 1997

End milling is available for machining the variable shape of products and has brrn widely applied in many Manufacturing industries. The surface finish of machined parts determines quality and functionality of products. Surface roughness causes friction,noise,fracture, glossiness and seizure, so many research had been performed to precisely. In particular an experimental analysis was carried out to investigate the influence ofsurface roughness on the fractal dimension. This parameter was assumed to contain not only information of roughness but also extra meaning. Experiments which were performed under various cutting conditions to compare fractal dimension with surface roughness R /sab a/ show fractal dimension to be useful parameter for determining of roughness.

• Journal of Advanced Marine Engineering and Technology
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• v.22 no.4
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• pp.522-528
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• 1998

This paper presents a fundamental fractal characteristics of the growing crack that has an irregularity producing a zigzag crack contour. This irregularity is analysed by a fractal geometry in a box counting method that is a very simple technique. First the fractal dimensions and actual fractal extensive crack length are obtained. Also a fractal fracture energy relation with a fractal dimension is found so as to get fractal crack behaviors. Thus it can be shown that the fractal dimension has a possibility as a fracture parameter in a real crack growth length meaning.

• Journal of the Korean GEO-environmental Society
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• v.18 no.8
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• pp.23-32
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• 2017

For exposed slopes, the weathering degree over time has a major effect on the engineering properties of rocks and the slope stability. Rocks are gradually changed by weathering into soil over time, and the resulting physical, chemical and mechanical changes of rocks affect the engineering stability of the slope. However, there are not many ways to objectively evaluate the weathering degree of a slope. In this study, therefore, to investigate the weathering characteristics of rocks, granite, gneiss and shale distributed in the Chungbuk region were sampled by weathering stage and changes in their component minerals and tissues were investigated. Furthermore, artificial weathering was induced using the freezing and thawing test and quantitatively investigated through porosity and absorption rate. In addition, the changes of microcracks due to artificial weathering were evaluated through box fractal dimension ($D_B$). Through mineralogical study the phase change of constituting minerals, the growth of secondary minerals, the development of micro-cracks and the fabric changes due to weathering were observed. The mineralogical, chemical and engineering evaluations of the weathering degree through the experimental results in this study are expected to be useful for analyzing the weathering characteristics and causes by rock type and for proposing a methodology to evaluate the degradation of physical properties comparatively and quantitatively.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.251-254
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• 1995

The quality and functionality of machined products is determined by surface finish. The surface roughness is characterized by roughness parameters such as R $_{a}$ and R $_{max}$. While such parameters are useful to define the quality of surface, they are nor sufficiently descriptive characteristics of surface. The fractal dimension which can describe characteristics od surface roughness than conventional roughness parameters has been applied. In this work, Relation between fractal dimension and surface roughness will be examined as a means of characterizing surface roughness.s.s.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.9
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• pp.710-715
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• 2016

Due to its simplicity and high reliability, the box-counting(BC) method is one of the most frequently used techniques to estimate the fractal dimensions of a binary image with a self-similarity property. The fractal calculation requires data sampling that determines the size of boxes to be sampled from the given image and directly affects the accuracy of the fractal dimension estimation. There are three non-overlapping regular grid methods: geometric-step method, arithmetic-step method and divisor-step method. These methods have some drawbacks when the image size M becomes large. This paper presents a BC algorithm for enhancing the accuracy of the fractal dimension estimation based on a new sampling method. Instead of using the geometric-step method, the new sampling method, called the coverage ratio-step method, selects the number of steps according to the coverage ratio. A set of experiments using well-known fractal images showed that the proposed method outperforms the existing BC method and the triangular BC method.