• Imaging Science in Dentistry
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• 제41권2호
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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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• 제36권4호
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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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• 제1권4호
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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.

• 한국산업정보학회논문지
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• 제9권2호
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• pp.59-64
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• 2004

우리가 일반적으로 다루는 많은 대상들은 대부분 복잡하고 불규칙적인 형태를 지니고 있다. 이로 인해 보통 사용하는 미분연산자와 같은 전통의 수학적 기법들은 경우에 따라 심각한 불량문제(ill-posed problem)를 야기하여 부정확한 결과를 나타내기도 한다. 이의 해결을 위해 전처리 과정으로 평활화를 위한 여러 가지 mean filter를 사용하기도 한다. 그렇지만 원 자료가 근본적으로 복잡한 경우 위 과정으로 오히려 중요 정보가 소실될 수도 있다. 이에 본 논문에서는 먼저 전처리로서 흔히 사용되는 각종 평균필터 대신 손실을 최소화하면서 곡면의 부드러움(smoothness)을 유도할 수 있는 접평면 접근 방식을 이용하고, 아울러 대상 영상의 복잡도에 연동한 프랙탈 차원을 적용하여 보다 효과적으로 영상의 경계를 추출하고자 했다.

• 한국농공학회논문집
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• 제47권7호
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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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• 제48권1호
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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.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2002년도 춘계학술대회 논문집 센서 박막재료 반도체재료 기술교육
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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.

• 한국대기환경학회지
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• 제15권2호
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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.

• 콘크리트학회논문집
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• 제29권1호
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• pp.101-107
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• 2017

본 연구는 시멘트계 재료의 프랙탈 특성에 관한 기초적 연구로써, 고로슬래그 미분말 혼입 시멘트 페이스트의 공극 구조를 수은압입법을 이용하여 측정하였고, 측정된 결과를 프랙탈 모델에 적용하여 그 특성을 분석하였다. 분석 결과, 고로슬래그미분말 혼입 시멘트 페이스트의 공극 구조는 그 범위가 나노미터부터 밀리미터 단위까지 다양하게 분포하는 불규칙한 조직이기 때문에, 전체 영역에 대한 프랙탈 차원을 산정했을 때 각 공극 영역의 특성을 반영할 수 없다. 따라서 프랙탈 차원 산정 시 공극 영역을 나누어서 분석하였다. Zhang and Li (1995) model을 적용했을 때, 시멘트와 GGBFS의 수화반응 결과 생성된 C-S-H 내의 gel pores 및 small capillary pores에 해당하는 micro 영역과 large capillary pores에 해당하는 macro 영역에서 각각 프랙탈 특성이 나타나는 결과를 보였다. 또한 macro 영역보다 micro 영역의 공극 표면이 더 불규칙한 형상을 나타내었다. Ji et al. (1997) model을 적용할 경우, micro 영역이 C-S-H 내의 gel pores에 해당하는 micro I과 small capillary pores에 해당하는 micro II로 구분되었으며, 각각의 프랙탈 특성이 산정되었다. 또한 Zhang and Li (1995) model을 결과와 유사하게, macro, micro II, micro I의 순서대로 공극 크기가 작아질수록 VFD 결과 값이 감소하였으며, 이는 곧 공극의 복잡성이 증가함을 나타낸다.

• 물과 미래
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• 제28권5호
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• pp.117-127
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• 1995

해상도를 고려하는 GIUH 모형에 대한 적용과 분석을 평창강 유역의 소유역인 이목정유역에 대하여 수행하였다. 모형의 적용과 Fractal 분석을 위해 1:25,000, 1:50,000 그리고 1:100,000 축척의 지도를 이용하였다. 따라서 축척간의 비율이 일정한 값을 갖는다. 링크의 길이는 해상도 1mm의 구장기를 이용하였고 Fractal 차원은 Richardson 방법을 사용하였다. 지도의 축척에 따라 매개변수들의 현저한 변화를 발견하였으며 이러한 경향은 매개변수의 물리적 의미를 상실하게 한다. 그런데 Fractal 변환과 의 Melton지형법칙은 이러한 규모문제를 효과적으로 조정해주는 역할을 할 수 있다. 그리고 이 방법은 하도망과 유역간의 연관성을 모형에 반영할 수 있는 장점이 있다. 이 연구에서 제안한 GIUH의 적용성을 검증하기 위해 지수형 GIUH 모형과 비교하였다. 그 결과 제안된 2모수 gamma GIUH 모형이 좋은 재현성을 보였다. 따라서 Fractal 이론을 도입한 2모수 gamma GIUH 모형은 축척을 고려하는 IUH를 유도하는데 있어서 적절하다고 할 수 있다.