• Imaging Science in Dentistry
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• v.53 no.2
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• pp.153-159
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• 2023

Purpose: The objective of this study was to assess the fractal dimension, lacunarity, trabecular microarchitecture parameters, and cortical linear measurements in the mandibles of male and female individuals to identify differences between them. Materials and Methods: In total, 116 cone-beam computed tomography scans of healthy individuals of different ages (57 men and 59 women, aged between 20 and 60 years) were selected. The following bone parameters were measured: 1) buccal, lingual, and basal cortical bone thickness in 5 standard parasagittal sections (the midline, the left and right sides of the lower lateral incisors, and the left and right sides of the lower canines); 2) the bone volume fraction of 10 sequential axial sections from each patient by creating a volume of interest in the area between the lower canines; and 3) fractal dimension and lacunarity using grayscale images of the same region of the volume of interest in the anterior mandible. Spearman correlation coefficients and the Mann-Whitney test were used. Results: A significant and positive correlation was found between age and cortical thickness, especially in the region of the central incisors. Significant differences between sexes in terms of fractal dimension, lacunarity, and bone volume were found. Women revealed lower fractal dimension values and higher lacunarity and bone volume ratio values than men. Conclusion: Fractal dimension, lacunarity, trabecular bone volume, and cortical thickness were different between men and women of different ages.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.565-576
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• 2007

The article describes a technique for the measurement of the level of complexity of fracture surfaces by the method of vertical sections, and a performed statistical analysis of the effect of profile lines on the fractographic and fractal parameters of fractures, i.e. the profile line development factor, $R_L$, and the fracture surface development factor, $R_S$, (as defined by the cycloid method), as well as the fractal dimension, $D_C$, (as determined by the chord method), and the fractal dimension, $D_{BC}$, (as determined by the box method). The above-mentioned parameters were determined for fracture surfaces of basalt and gravel concretes, respectively, which had previously been subjected to fracture toughness tests. The concretes were made from mixtures of a water/cement ratio ranging from 0.41 to 0.61 and with a variable fraction of coarse aggregate to fine aggregate, $C_{agg.}/F_{agg.}$, in the range from 1.5 to 3.5. Basalt and gravel aggregate of a fraction to maximum 16 mm were used to the tests. Based on the performed analysis it has been established that the necessary number of concrete fracture profile lines, which assures the reliability of obtained testing results, should amount to 12.

• 한국연소학회:학술대회논문집
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• 2002.11a
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• pp.1-9
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• 2002

Simultaneous PIV and OH PLIF measurements are used for shear strain rates and flame locations, respectively. It is believed that the shear strain rates represent flow characteristics such as turbulence intensity and the OH intensity indicates the flame characteristics such as burning velocities. However, these are still lack of geometric information, which may be very important to flame quenching Hence, fractal dimensions 'Df) of the OH images are adopted as an additional information. Finally, the flame structure diagram proposed in this research has three parameters, which consist of strain rates, OH intensities and fractal dimensions. The results show that this diagram classifies turbulent premixed flames more effectively based on flame structures. The regime of weak turbulence is limited to narrow strain ranges and has the fractal dimension of about 2 In the regime of moderate turbulence, OH intensities increase as strain rates increase and the values of fractal dimensions are 1.8 Df 1.95. The regimes of thickened reaction and flame extinction (quenching) show bell-shaped and their values of fractal dimensions are 1.5 Df 1.7 and 0.9 Df 0.6, respectively.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07b
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• pp.927-930
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• 2002

The HFPD measurement method is a technique to analyze aging state of high voltage insulation materials and detect higher frequency signals than conventional PD measurement method therefore it takes less noise effect and could execute active line measurement. It is possible to analyze main discharge phenomena and obtain access to aging progress occurred in insulation materials through accumulation of HFPD signals during determined interval and expression of fractal dimension using statistical process of accumulated signals. In this study, the statistical parameters (skewness & kurtosis) and fractal dimensions are changed by discharge patterns that is shown up different characteristics with applied voltages and times.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.12
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• pp.45-61
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• 1996

This paper presents the ECG data compression using wavelet transform (WT) and adaptive fractal interpolation (AFI). The WT has the subband coding scheme. The fractal compression method represents any range of ECG signal by fractal interpolation parameters. Specially, the AFI used the adaptive range sizes and got good performance for ECG data cmpression. In this algorithm, the AFI is applied into the low frequency part of WT. The MIT/BIH arhythmia data was used for evaluation. The compression rate using WT and AFI algorithm is better than the compression rate using AFI. The WT and AFI algorithm yields compression ratio as high as 21.0 wihtout any entropy coding.

• Proceedings of the KOSOMBE Conference
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• v.1996 no.11
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• pp.221-224
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• 1996

This paper presents the ECG data compression using wavelet transform(WT) and adaptive fractal interpolation(AFI). The WT has the subband coding scheme. The fractal compression method represents any range of ECG signal by fractal interpolation parameters. Specially, the AFI used the adaptive range sizes and got good performance for ECG data compression. In this algorithm, the AFI is applied into the low frequency part of WT. The MIT/BIH arrhythmia data was used for evaluation. The compression rate using WT and AFI algorithm is better than the compression rate using AFI. The WT and AFI algorithm yields compression ratio as high as 21.0 without any entroy coding.

• Journal of Korea Water Resources Association
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• v.32 no.5
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• pp.565-577
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• 1999

The geometric patterns of a stream network in a drainage basin can be viewed as a "fractal" with fractal dimensions. Fractals provide a mathematical framework for treatment of irregular, ostensively complex shapes that show similar patterns or geometric characteristics over a range of scale. GIUH (Geomorphological Instantaneous Unit Hydrograph) is based on the hydrologic response of surface runoff in a catchment basin. This model incorporates geomorphologic parameters of a basin using Horton's order ratios. For an ordered drainage system, the fractal dimensions can be derived from Horton's laws of stream numbers, stream lengths and stream areas. In this paper, a fractal approach, which is leading to representation of a 2-parameter Gamma distribution type GIUH, has been carried out to incorporate the self similarity of the channel networks based on the high correlations between the Horton's order ratios. The shape and scale parameter of the GIUH-Nash model of IUH in terms of Horton's order ratios of a catchment proposed by Rosso(l984J are simplified by applying the fractal dimension of main stream length and channel network of a river basin. basin.

• 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.

• Computers and Concrete
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• v.2 no.3
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• pp.239-248
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• 2005

The article presents the results of examination of the fractal dimension D of concrete specimen fracture surfaces obtained in fracture toughness tests. The concretes were made from three different types of coarse aggregate: gravel, dolomite and basalt aggregate. Ordinary concretes (C40) and high-performance concretes (HPC) were subjected to testing after 7, 14, 28 and 90 days of curing, respectively. In fracture toughness and compressive tests, different behaviours of concretes were found, depending on the type of aggregate and class of concrete (C40, HPC). A significant increase in the strength parameters tested occurred also after a period of 28 days (up to the $90^{th}$ day of curing) and was particularly large for concretes C40. Fractal examinations performed on fracture replicas showed that the fractal dimension D was diverse, depending on the coarse aggregate type and concrete class being, however, statistically constant after 7 and 14 days for respective concretes during curing. The fractal dimension D was the greater, the worse strength properties were possessed by the concrete. A cross-grain crack propagation occurred in that case, due to weak cohesion forces at the coarse aggregate/mortar interface. A similar effect was observed for C40 and HPC made from the same aggregate. A greater dimension D was exhibited by concretes C40, in which case the fracture was easier to form compared with high-performance concretes, where, as a result of high aggregate/mortar cohesion forces, the crack propagation was of inter-granular type, and the resulted fracture was flatter.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.6
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• pp.2730-2747
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• 2016

Due to the limitation of the bandwidth resource and capture resolution of depth cameras, low resolution depth maps should be up-sampled to high resolution so that they can correspond to their texture images. In this paper, a novel depth map up-sampling algorithm is proposed by exploiting the fractal internal self-referential feature. Fractal parameters which are extracted from a depth map, describe the internal self-referential feature of the depth map, do not introduce inherent scale and just retain the relational information of the depth map, i.e., fractal transforms provide a resolution-independent description for depth maps and could up-sample depth maps to an arbitrary high resolution. Then, an enhancement method is also proposed to further improve the performance of the up-sampled depth map. The experimental results demonstrate that better quality of synthesized views is achieved both on objective and subjective performance. Most important of all, arbitrary resolution depth maps can be obtained with the aid of the proposed scheme.