• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2001년도 봄 학술발표회 논문집
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• pp.333-338
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• 2001

Fractal geometry is a non-Euclidean geometry which has been developed to quantitative analysis irregular or fractional shapes. Fractal dimension of irregular surface has fractal values ranging from 2 to 3 and of irregular line profile has fractal values ranging from 1 to 2. In this paper, quantitative analysis of crack growth patterns during the fracture processing of fiber-reinforced cement composites based on fractal geometry. The fracture behaviors of fiber reinforced mortar beams subjected to three-point loading in flexure. The beams all had a single notch depth, but varing volume fractions of polypropylene, cellulose fibers. The crack growth behaviors, as observed through the image processing system, and the box counting method was used to determine the fractal dimension, Df. The results showed that the linear correlation exists between fractal dimension and fracture energy of the fiber reinforced cement mortar.

• Geomechanics and Engineering
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• 제4권3호
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• pp.219-227
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• 2012

Pavement management systems require systematic monitoring of pavement surfaces to determine preventive and corrective maintenance. The process involves the accumulation of large amounts of visual data, typically obtained from site visitation. The pavement surface condition is then correlated to a pavement distress index that is based on a scoring system previously established by state or federal agencies. The scoring system determines if the pavement section requires maintenance, overlay or reconstruction. One of the surface distresses forming part of the overall pavement distress index is the Alligator Crack Index (AC Index). The AC Index involves the visual evaluation of the crack severity of a section of a pavement as being low, medium, or high. This evaluation is then integrated into a formula in order to obtain the AC Index. In this study a quantification of the visual evaluation of the severity of alligator cracking is carried out using photographs and the fractal dimension concept from fractal theory. Pavements with low levels of cracking were found to have a fractal dimension equal to 1.051. Pavements with moderate levels of cracking had a fractal dimension equal to 1.1754. Pavements with high degrees of cracking had a fractal dimension that varied between 1.5037 (high) and 1.7111 (very high). Pavements with a level of cracking equal to 1.8976 represented pavements that disintegrated and developed potholes. Thus, the visual evaluation of the state of cracking of a pavement (the AC Index) could be enhanced with the use of the fractal dimension concept from fractal theory.

• Journal of Periodontal and Implant Science
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• 제43권5호
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• pp.209-214
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• 2013

Purpose: To assess bony trabecular changes potentially caused by loading stress around dental implants using fractal dimension analysis. Methods: Fractal dimensions were measured in 48 subjects by comparing radiographs taken immediately after prosthesis delivery with those taken 1 year after functional loading. Regions of interest were isolated, and fractal analysis was performed using the box-counting method with Image J 1.42 software. Wilcoxon signed-rank test was used to analyze the difference in fractal dimension before and after implant loading. Results: The mean fractal dimension before loading ($1.4213{\pm}0.0525$) increased significantly to $1.4329{\pm}0.0479$ at 12 months after loading (P<0.05). Conclusions: Fractal dimension analysis might be helpful in detecting changes in peri-implant alveolar trabecular bone patterns in clinical situations.

• 치과방사선
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• 제28권1호
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• pp.17-26
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• 1998

The purpose of this study was to investigate whether a radiographic estimate of osseous fractal dimension is useful in the characterization of structural changes in bone. Ten specimens of bone were progressively decalcified in fresh 50 ml solutions of 0.1 N hydrochloric acid solution at cummulative timed periods of 5, 10, 20, 30, 60 and 90 minutes, and radiographed from 0 degree projection angle controlled by intraoral parelleling device. The test set of 70 radiographs was digitized and digitally filtered to reduce film -grain noise. I performed one-dimensional variance and fractal analysis of bony profiles or scan lines. Correlation analysis quantified the relationship between variance and fractal dimension. The obtained results were as follow. 1. After the first stage of decalcification variance and fractal dimension of scan line pixel intensities generally decreased with a range of 57.94 to 12.64 and 1.59 to 1.36. 2. Correlation coefficient(r) relating variances to fractal dimensions was consistantly excellent(range r=0.90 to 0.98). 3. Variance and fractal dimension were much alike in ability to discriminate, at leat on a group basis, between control and decalcified specimens.

• Imaging Science in Dentistry
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• 제52권1호
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• pp.33-41
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• 2022

Purpose: This study aimed to evaluate the structural complexity of craniofacial trabecular bone in multiple myeloma by fractal analysis of panoramic and lateral skull radiography, and to compare the fractal dimension values of healthy patients (HPs), pre-treatment patients (PTPs), and patients during bisphosphonate treatment (DTPs). Materials and Methods: Pairs of digital panoramic and lateral skull radiographs of 84 PTPs and 72 DTPs were selected. After application of exclusion criteria, 43 panoramic and 84 lateral skull radiographs of PTPs, 56 panoramic and 72 lateral skull radiographs of DTPs, and 99 panoramic radiographs of age- and sex-matched HPs were selected. The fractal dimension values from panoramic radiographs were compared among HPs, PTPs, and DTPs and between anatomical locations within patient groups using analysis of variance with the Tukey test. Fractal dimension values from lateral skull radiographs were compared between PTPs and DTPs using the Student t-test. Pearson correlation coefficients were used to assess the relationship between the mandible from panoramic radiographs and the skull from lateral skull radiographs. Intra-examiner agreement was assessed using intraclass correlation coefficients (α=0.05). Results: The fractal dimension values were not significantly different among HPs, PTPs, and DTPs on panoramic radiographs or between PTPs and DTPs on lateral skull radiographs (P>0.05). The mandibular body presented the highest fractal dimension values (P≤0.05). The fractal dimension values of the mandible and skull in PTPs and DTPs were not correlated. Conclusion: Fractal analysis was not sensitive for distinguishing craniofacial trabecular bone complexity in multiple myeloma patients using panoramic and lateral skull radiography.

• 한국농공학회:학술대회논문집
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• 한국농공학회 2005년도 학술발표논문집
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• pp.387-392
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• 2005

The research was performed to predict the potential landslide with roughness index. It was known that fractal dimension and surface area index can be represented the topography, specially when the natural slopes were rough or rugged. A test site was selected and fractal dimension and surface area index were calculated from the irregular triangle network. Fractal dimension were ranged between $2.016{\sim}2.046$ and surface area index $1.56E+07{\sim}2.59E+07$. Surface area index increased as fractal dimension increased. Slope stability was calculated by infinite slope stability analysis model and was compared to slope stability by fractal and surface area index. In the result, unsafe zones where slope stability is under 1.1 were $5.11{\sim}6.25%$ for the test site. It can be said that fractal dimension and surface area index are a good index to evaluate the slope stability because when fractal dimension and surface area index are greater, then stability of the site is more unsafe.

• 자원환경지질
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• 제27권1호
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• pp.81-91
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• 1994

There has been considerable research dealing with the influence of surface roughness along surfaces of rock discontinuities in relation to the peak shear strength of rock masses. Concepts accepted recently for measuring such strength include estimation of a roughness coefficient such as developed by Barton's studies. The method for estimation the Joint Roughness Coefficient (JRC) value of a measured roughness profile is subjective. The aim of this research is to estimate the JRC value of the roughness of a surface profile in a rock mass system using an objective method. The study of roughness of surfaces has included measurement of fractal geometric characteristics. Once the irregularity of the surface has been described by the fractal dimension, the spatial variation of the surface irregularities can be described using variogram and drift analysis. An empirical relationships between the roughness profiles of selected JRC ranges and their fractal dimension with variogram and drift were derived. The application of analyses of fractal dimension, variogram and drift was novel for the analysis of roughness profiles. Also, an empirical equation was applied to experimental data.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2009년도 IWAIT
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• pp.655-658
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• 2009

Fractal dimension has been used for texture analysis as it is highly correlated with human perception of surface roughness and applied to quantifying the structures of wide range of objects in biology and medicine. On the other hand, the evaluation of the human skin state is based solely on the subjective assessment of clinicians; this assessment may vary from moment to moment and from rater to rater. Therefore we attempt to analysis of skin texture image using fractal dimension and discuss its application to evaluating human skin state. It can be helpful for extracting human features and also can be useful for detection of many human skin diseases. This paper presents a method to calculate fractal dimension of skin with use of camera lens magnification. We take multiple pictures frequently from skin with different camera lens magnification as a magnification factor of fractal set, and counting the number of objects (cells) in each picture as a number of self similar pieces of fractal set.

• 한국지역지리학회지
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• 제11권6호
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• pp.530-542
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• 2005

본 연구에서는 지형이 위치별로 자기 상사성을 가진다는 전제하에 프랙탈 차원을 이용한 지형의 복잡성을 표현해 보고자 한다. 특히 수치지도 분석기법에서 표면적요소를 산정하여 프랙탈 차원을 산정하도록 한다. 또한 프랙탈 차원과 지형 형상요소들과의 관계를 규명하고, 프랙탈 차원의 통계적 대표치로서의 기능에 대해 고찰해 보려한다. 본 연구에서는 GIS기법을 적용하여 지형의 프랙탈 특성을 구하였다. 길이를 이용하여 하천이나 해안선의 1차원적 프랙탈 특성을 구하는 것에서 벗어나 면적의 개념 즉, 투영면적과 표면적을 이용하여 지형의 2차원적 프랙탈 특성을 구해보았다. 그리고 프랙탈 차원과 평균경사도와의 상관관계를 검토해 보았다. 연구결과 다음과 같은 결론을 얻게 되었다. 1) 프랙탈 차원을 구하기 위한 척도로서 표면적을 사용한 경우에서도 일반적 프랙탈 차원의 특성과 같이 지형의 복잡성과 비례관계의 성질을 나타내었다. 2) 본 연구에서 제안한 표면적을 이용한 프랙탈 차원은 영천지역에서는 $2.10{\sim}2.24$이고 의성지역은 $2.02{\sim}2.15$으로 나타났다. 이 값들은 통상 알려진 지형의 프랙탈 차원인 $2.10{\sim}2.20$의 범위에 든다. 3) 평균 경사도와 프랙탈 차원의 상관관계는 평균경사도가 $25^{\circ}$ 이상인 지역에서 결정계수 $R^2$값이 $25^{\circ}$ 이하인 지역에 비해 30% 정도 작아진다. 그러므로 모든 지형의 거침도를 표현하기 위해선 프랙탈 차원이 알맞을 것으로 본다. 본 연구결과를 통해 투영면적과 표면적을 이용한 프랙탈 차원 산정공식이 유효함을 확인하였다. 그러나 본 기법이 충분히 타당성을 인정받기 위해선 연구대상지역의 확대를 통하여 경사도와 표면적, 프랙탈 차원과의 상관관계를 더욱 명확히 할 필요가 있다. 향후 연구에선 지형의 복원에 적용 할 수 있을 것이며 fBm모델을 이용하여 교통류 해석에도 적용이 가능할 것이다.

• 한국인터넷방송통신학회논문지
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• 제23권1호
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• pp.145-149
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• 2023

표면의 고해상도 이미지는 나노(nano)사이즈 부터 마이크로미터까지 특정한 크기를 갖는 기공이나 형상에 대한 자세한 정보를 제공한다. 그러나 표면의 고해상도 이미지로 부터 기공이나 형상에 대한 효율적인 연관성을 결정하는 것은 아직 확실하지 않다. 기공이나 형상의 효율적 연관성을 위하여 소자의 표면특성은 SEM 사진을 촬영하고 이미지를 이진화하여 프랙탈 차원으로 고찰하였다. 소자의 표면 분석을 위하여 프랙탈 프로그램은 직접 코딩하였다. 소자 표면 특성과 전기적 특성은 프랙탈 차원과 연관성이 있을 것으로 생각된다. 프랙탈 차원은 내부 기공의 증가와 더불어 감소하였다. 소자 표면의 구조적 특성인 입자의 밀도와 입계는 프랙탈 차원과 연관이 있었다. 입자의 크기는 프랙탈 차원의 증가와 더불어 감소하였으며 균일하게 형성되었다. 입자가 균일하게 형성되면 기공이 적게 존재하여 프랙탈 차원이 증가하였다.