• Imaging Science in Dentistry
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• v.31 no.1
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• pp.35-42
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• 2001

Purpose: To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Materials and Methods : Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10×20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We compared fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Results: Fractal dimension at interdental crest area of normal group was 1.979±0.018 and that of patient group 1.971±0.012 (p>0.05). Fractal dimension at furcation area of normal group was 1.986±0.024 and that of patient group 1.974±0.015 (p<0.05). The ratio of fractal dimension at interdental crest area to interdental middle 1/3 of normal group was 1.003±0.015 and that of patient group 0.993±0.018 (p<0.05). The ratio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006±0.018 and that of patient group 0.994±0.018 (p<0.05). Conclusion : The ratio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis.

• Imaging Science in Dentistry
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• v.36 no.2
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• pp.69-72
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• 2006

Purpose : We evaluated the fractal dimension changes on bovine rib radiographs according to the decalcification degree and the exposure time in the bovine rib. Materials and Methods : Twenty 5 mm thick cross-sectional blocks from bovine rib bone were progressively decalcified in 30 mL 0.1 N hydrochloric acid for 5, 30, and 90 minutes. They were radiographed at three exposure time settings (0.22, 0.36, 0.43 mAs) before and after each decalcification stage. We selected $100{\times}100$ pixel-sized regions of interests (ROIs) on trabecular bone and calculated fractal dimensions by box-counting method. Results : Repeated measures ANOVA showed that fractal dimensions gradually decreased after acid-induced demineralization and with more exposure (P<0.001). Conclusion : The fact that fractal dimensions decrease after decalcification might support the hypothesis that patients with osteoporosis have decreased radiographic fractal dimension in trabecular bone in comparison to normal subjects.

• Imaging Science in Dentistry
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• v.35 no.3
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• pp.121-125
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• 2005

Purpose : The purpose of this study was to investigate whether the fractal dimension of successive panoramic radiographs of bone after implant placement is useful in the characterization of structural change in alveolar bone. Materials and Methods. Twelve subjects with thirty-five implants were retrospectively followed-up from one week to six months after implantation. Thirty-six panoramic radiographs from twelve patients were classified into 1 week, 1-2 months and 3-6 months after implantation and digitized. The windows of bone apical and mesial or distal to the implant were defined as periapical region of interest (ROI) and interdental ROI; the fractal dimension of the image was calculated. Results There was not a statistically significant difference in fractal dimensions during the period up to 6 months after implantation. The fractal dimensions were higher in 13 and 15mm than 10 and 11.5mm implant length at interdental ROIs in 3-6 months after implantation (P<0.01). Conclusion : Longer fixtures showed the higher fractal dimension of bone around implant. This investigation needs further exploration with large numbers of implants for longer follow-up periods.

• Journal of the Korean Society of Safety
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• v.13 no.4
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• pp.71-78
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• 1998

Real crack and fracture surfaces have irregularities producing zigzag contours. These irregularities are analysed by a fractal geometry which has been by a Mandelbrot. We obtained a fractal dimension which is one of the fractal characteristics. It is also estimated by an vertical section method that fractal characteristics in the fractured surfaces can be obtained as the crack grows. Moreover fractal fracture energy that corresponds to an energy release rate is shown to find relationships between fractal dimensions and crack behaviors. From these results, we concluded that a fractal characteristics analysis for a crack can be applied to a fracture mechanics.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.11
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• pp.1737-1742
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• 2001

The fractal-based method for describing rubbed surface texture has aroused great interest. The determination of rubbed surface topography is believed to be extremely important in the areas of contact mechanics, adhesion and friction. In order to describe topography of the rubbed surface, the wear test was carried out with annular surfaces of wear testing specimens in dry friction. furthermore, the relation between the fractal dimensions and the frictional conditions are also investigated and fractal descriptors was applied to rubbed surface with image processing. Fractal dimension can be determined by sum of intensity difference of image surface pixel. Fractal dimension increased according as the applied load and sliding distance increase. Topography of the rubbed surface can be effectively obtained by fractal dimensions.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.609-615
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• 2001

This study proposes analysis and evaluation method of time series ultrasonic signal using attractor analysis for fusion joint part of polyethylene piping. Quantitatively characteristics of fusion joint part is analysed features extracted from time series. Trajectory changes in the attractor indicated a substantial difference in fractal characteristics. These differences in characteristics of fusion joint part enables the evaluation of unique characteristics of fusion joint part. In quantitative fractal feature extraction, feature values of 4.291 in the case of debonding and 3.694 in the case of bonding were proposed on the basis of fractal dimensions. In quantitative quadrant feature extraction, 1,306 point in the case of bonding(one quadrant) and 1,209 point(one quadrant) in the case of debonding were proposed on the basis of fractal dimensions. Proposed attractor feature extraction can be used for integrity evaluation of polyethylene piping material which is in case of bonding or debonding.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.305-314
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• 2016

In this study, an analysis is performed for comparing the fractal dimension of Jackson Pollock's art works with that of Korean Infomel art works. In order to test the hypothesis that Jackson Pollock's fractal dimension is different from Korean Informel's, data is collected for the fractal dimensions of 30 Jackson Pollock's and 45 Korean Informel art works. The results show that Korean Informel's fractal dimension is larger than Jackson Pollock's. This might be interpreted that the pattern (in finer scale) of Korean Informel art works is closer to planes, rather than lines or points, compared to that of Jackson Pollock's.

• The korean journal of orthodontics
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• v.46 no.5
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• pp.323-330
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• 2016

Objective: The purpose of this study was to determine whether the results of fractal analysis can be used as criteria for midpalatal suture maturation evaluation. Methods: The study included 131 subjects aged over 18 years of age (range 18.1-53.4 years) who underwent cone-beam computed tomography. Skeletonized images of the midpalatal suture were obtained via image processing software and used to calculate fractal dimensions. Correlations between maturation stage and fractal dimensions were calculated using Spearman's correlation coefficient. Optimal fractal dimension cut-off values were determined using a receiver operating characteristic curve. Results: The distribution of maturation stages of the midpalatal suture according to the cervical vertebrae maturation index was highly variable, and there was a strong negative correlation between maturation stage and fractal dimension (-0.623, p < 0.001). Fractal dimension was a statistically significant indicator of dichotomous results with regard to maturation stage (area under curve = 0.794, p < 0.001). A test in which fractal dimension was used to predict the resulting variable that splits maturation stages into ABC and D or E yielded an optimal fractal dimension cut-off value of 1.0235. Conclusions: There was a strong negative correlation between fractal dimension and midpalatal suture maturation. Fractal analysis is an objective quantitative method, and therefore we suggest that it may be useful for the evaluation of midpalatal suture maturation.

• Journal of the Korean Geotechnical Society
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• v.19 no.2
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• pp.199-206
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• 2003

Particle-size distribution in soils is one of the most fundamental physical properties of soils. One of the latest developments in the study of particle-size distributions has focused on the use of fractal theories. In this study, the fragmentation fractals were used for determining the characteristics of the particle-size distribution curve. It was shown that the mass-size distribution method was more practical than the cumulative number-size distribution method. From the co-relation between fractal dimensions($D_{tot}$) and the coefficient of uniformity($C_{u}$), there was a sharp increase in fractal dimensions for $C_{u}$<4, but fractal dimension converged the single value for $D_{u}$$\geq$6. Fractal dimensions were affected by small sized particles for $C_{c}$$\geq$3 and large sized particles for $C_{c}$/<3. As a result of the analysis of the influence of the effective size($D_{10}$), it was observed that the changes of $D_{tot}$/ were nominal beyond the effective size.

• 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.