• Imaging Science in Dentistry
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• v.41 no.2
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• pp.71-78
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• 2011

Purpose : This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Materials and Methods : Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. Results : The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. Conclusion : The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm.

• Imaging Science in Dentistry
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• v.36 no.4
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• pp.183-188
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• 2006

Purpose: The purpose of this research was to study bone changes after bilateral sagittal split osteotomy through fractal analysis and measurement of mandibular cortical thickness. Materials and Methods: This study included twenty-two prognathic patients who underwent bilateral sagittal split osteotomy. Panoramic radiographs of these patients were taken immediately before operation and at 1 month, 6 months, and 12 months postoperatively. The fractal dimension was measured by the box-counting method in the region of interest centered on both the basal and interdental bones between the first and second mandibular molars. Measurements of mandibular cortical thickness were taken both in the area between the first and second mandibular molars and at the osteotomy site. Changes of fractal dimension and cortical thickness over four stages were statistically analyzed. Results: The fractal dimension of the mandibular basal bone before surgery and after 1 month, 6 months and 12 months were $1.4099{\pm}0.0657,\;1.382{\pm}0.0595,\;1.2995{\pm}0.0949,\;and\;1.4166{\pm}0.0676$, respectively (Repeated-measures ANOVA, P<0.001). However, no statistically significant differences were noted in interdental fractal dimensions among the four stages. Mandibular cortical thickness between the first and second mandibular molars before operation and after 1 month, 6 months and 12 months was $3.74{\pm}0.48mm,\;3.63{\pm}0.47mm,\;3.41{\pm}0.61mm\;and\;3.55{\pm}0.66mm$ (P<0.01), respectively. Mandibular cortical thickness at the osteotomy site at each of the four stages was $3.22{\pm}0.44mm,\;2.87{\pm}0.59mm,\;2.37{\pm}0.61mm\;and\;2.64{\pm}0.62mm$, respectively (P<0.001). Conclusion: This study suggests that the mandibular tissue continued decreasing for 6 months postoperatively and then increased over the subsequent 6 months.

• Geomechanics and Engineering
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• v.1 no.4
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• pp.323-335
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• 2009

Gravels forming part of the base of flexible pavements experience abrasion and crushing as a result of static and dynamic loads. Abrasion takes place when the sharp corners of the particles of gravel are removed as a result of compressive and shear loads. As a result of abrasion, the particles change in shape. Crushing is caused by the fragmentation of the particles into a mixture of many small particles of varying sizes. In this study, the abrasion and crushing of gravels are evaluated experimentally and analytically. The laboratory component of this study involves gravels that were subjected to abrasion and dynamic compression tests. The evaluation of the abrasion and crushing experienced by the gravel was carried out using fractals. In this study, the fractal dimension concept from fractal theory is used to evaluate: (a) the changes in shape, and (b) the crushing (fragmentation) of the original particles of gravel. It was determined that the fractal dimension of the profile of the particles decreased as a result of abrasion. With respect to crushing, the fragmentation fractal dimension was found to increase with the degree of breakage of the gravel. To understand the influence of crushing on the permeability of the gravels, the hydraulic conductivity of the gravels was measured before and after crushing. The hydraulic conductivity of the gravels was found to decrease with an increase in their level of crushing. Also, changes in the angle of friction of the granular materials as a result of abrasion was calculated using the Krumbein's roundness chart. The angle of friction of the granular materials was found to decrease as a result of abrasion.

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.2
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• pp.59-64
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• 2004

Most features of nature and phenomena we encounter in many branches of science are inherently very irregular and have fractal aspects. Thus the analysis of them with the traditional methods such as a differential operator may result in their ill-posed problems. To settle these problems, one may use several type of mean filters which smooth the input signal. However when a given function or data are complex in their nature, there may be loss of some original information during these process. In this paper, we utilized the tangent plane method instead of mean filters for the purpose of less loss of information and more smoothness. After then we attempt to take more accurate edges for the irregular image on the basis of the Otzu threshold. Finally we introduce the effective edge extracting method which use the fractal dimension representing the complexity of the given image.

• Journal of The Korean Society of Agricultural Engineers
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• v.47 no.7
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• pp.37-45
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• 2005

In this study, R/S analysis which was proposed by Mandelbrot & Wallis (1969) was applied to evaluate the presence of the fractal property in the cone tip resistance of in-situ CPT data. Hurst exponents (H) were evaluated in the range of 0.660$\sim$0.990 and the average was 0.875. It was confirmed that a cone tip resistance data had the characteristic of fractals and it was expected that cone tip resistance data sets are well approximated by a fBm process with an Hurst exponent near 0.875. It was also observed that the boundary between layers were obviously identified as a result of R/S analysis and it will be usage in practices.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.48 no.1
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• pp.33-40
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• 2022

Objectives: Prolotherapy is a method that has gained popularity in recent years and has been reported to have positive short-term and long-term clinical results in maxillofacial surgery, especially temporomandibular joint (TMJ) hypermobility. This study aimed to evaluate the changes in the trabecular structure of mandibular condyles in patients who underwent prolotherapy due to TMJ hypermobility using the fractal analysis method. Materials and Methods: Forty-five patients who received dextrose prolotherapy at a concentration of 20% and fifteen control patients were included in the study. All patients had panoramic radiographs just before (T0) and six months after treatment (T1). The patients who received treatment were divided into three groups according to the number of prolotherapy injections. The regions of interest were selected from bone areas close to the articular surfaces of the condyles. The fractal dimension (FD) values were calculated. Results: The main effect of time on the FD value was significant [F (1, 56)=86.176, P<0.001]. This effect was qualified by a significant time×group interaction effect [F (3, 56)=9.023, P<0.001]. The decreases in FD values in all treatment groups between T0 and T1 times were significant (P=0.004). However, changes in FD values were not significant in the control group (P=0.728). Conclusion: Dextrose prolotherapy without the effect of the number of injections caused a decrease in FD values in the mandibular condyles over time.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.05b
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• pp.107-110
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• 2002

The optical memory devices of BST thin films to composite $(Ba_{0.7}\;Sr_{0.3})TiO_{3}$ using sol-gel method were fabricated by changing of the depositing layer number on $Pt/Ti/SiO_{2}/Si$ substrate. The structural properties of optical memory devices to be ferroelectric was investigated by fractal analysis and 3-dimension image processing. The thickness of BST thin films at each coating numbers 3, 4 and 5 times was $2500[\AA]$, $3500[\AA]$ and $3800[\AA]$. BST thin films exhibited the most pronounced grain growth. The surface morphology image was roughness with coating numbers. The thin films increasing with coating numbers shows a more textured and complex configuration.

• Journal of Korean Society for Atmospheric Environment
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• v.15 no.2
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• pp.175-182
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• 1999

Scanning electron microscopy (SEM) has played an important role in receptor modeling area because it is a powerful tool for characterizing individual particles. The purpose of the study was to classify individual diesel particles base on statistical analysis and image analysis by SEM/EDX (energy dispersive x-ray analyser). The diesel particles were sampled by both a modified CVS 75 mode and a high speed mode with a chassis dynamometer. The SEM/EDX system provides various physical parameters including particle's particle diameter and chemical information. Thus density and mass of the diesel particle were estimated cased on its chemical composition and further fractal dimensions of the diesel particle were obtained by the Hurst exponent method. The fractal dimension in the sample of modified CVS 75 mode was higher than the high speed mode. Finally, mass fractions for a diesel vehicle as a source profile were estimated cased on a particle class concept.

• Journal of the Korea Concrete Institute
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• v.29 no.1
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• pp.101-107
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• 2017

This study aimed to conduct the basic analysis on the fractal characteristics of cementitious materials. The pore structure of cement paste incorporating ground granulated blast furnace slag (GGBFS) was measured using mercury intrusion porosimetry (MIP) and the fractal characteristics were investigated using different models. Because the pore structure of GGBFS-blended cement paste is an irregular system in the various range from nanometer to millimeter, the characteristics of pore region in the different scale may not be adequately described when the fractal dimension was calculated over the whole scale range. While Zhang and Li model enabled analyzing the fraction dimension of pore structure over the three divided scale ranges of micro, small capillary and macro regions, Ji el al. model refined analysis on the fractal characteristics of micro pore region consisting of micro I region corresponding to gel pores and micro II region corresponding to small capillary pores. As the pore size decreased, both models suggested that the pore surface of micro region became more irregular than macro region and the complexity of pores increased.

• Water for future
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• v.28 no.5
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• pp.117-127
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• 1995

The application and analysis for the scale considering GIUH model proposed by the authors in this issue have been performed for the leemokjung sub-basin in the Pyungchang basin one of IHP representative basin in Korea. Scales of topographic maps for model application and fractal analysis are 1:25,000, 1:50,000 and 1:100,000. The ratio between successive scales is therefore constant. Link lengths were measured using a curvimeter with the resolution of 1 mm. Richardson's method was employed to have fractal dimension of streams. Apparent alternations of parameters were found in accordance with variations of map scale. And this tendency could mislead physical meanings of parameters because model parameters had to preserve their own value in spite of map scale change. It was found that uses of fractal transform and Melton's law could help to control the scale problem effectively. This methodlogy also could emphasize the relationship between network and basin to the model. To verify the applicability of GIUH proposed in this research, the model was compared with the exponential GIUH model. It is proven that proposed 2-parameter gamma GIUH model can better simulate the corresponding runoff from any given flood events than exponential GIUH model. The result showed that 2-parameter gamma GIUH model and fractal theory could be used for deriving scale considered IUH of the basin.