• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.2
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• pp.121-125
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• 2015

In this paper, we propose a method that extracts features from character patterns using the fractal dimension of chaos theory. The input character pattern image is converted into time-series data. Then, using the modified Henon system suggested in this paper, it determines the last features of the character pattern image after calculating the box-counting dimension, natural measure, information bit, and information (fractal) dimension. Finally, character pattern recognition is performed by statistically finding each information bit that shows the minimum difference compared with a normalized character pattern database.

• Journal of Korea Multimedia Society
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• v.4 no.6
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• pp.518-523
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• 2001

This paper proposes the new method which is adopted in extracting character features and recognizing characters using fractal dimension of the Chaos theory which highly recolonizes a minute difference with strange attractor created from Henon system. This paper implements a high precision character recognition system. firstly, it gets features of mesh, projection and cross distance feature from character images. And their feature is converted into data of time series. Then using modified Henon system suggested in this paper, each characters attractor about standard Korean Character, KSC 5601 is reconstructed. Secondly, in order to analyze the Chaotic degree of each characters attractor, it gets last features of character image after calculating box-counting Dimension, Natural Measure, Information Bit, Information Dimension which are meant fractal dimension. An experimental result shows 97.49% character classification rates for 2350 Korean characters using proposed method in this paper.

• Journal of the Korea Society for Simulation
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• v.18 no.4
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• pp.21-28
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• 2009

In the past, most of battle occurred in flatland and simple military force size gave a big influence in combat result. However, after the World War I, most of battles took place at the various terrain features such as forest, downtown, jungle and many others. Therefore, terrain factor exerts big influence on battle with weapon system in the ground warfare. However, effect of terrain has been explained only by quantitative manner in the battle. Furthermore, combat simulation and modeling applied a method that lower the combat capability of battle factors. In this paper, we present instrumentation that evaluate impact of terrain using fractal dimension. We determine the fractal dimension value by the "box counting dDimension" and density to calculate impact of terrain. Furthermore, we analyzed correlation with fractal dimension and density for battle result that obtained from the EINSTein model which is an agent-based simulation. We compare with 'Stalingrad battle' result out of battle example and analyzed. This study presented a method combat effectiveness that effect of terrain calculate quantitatively using fractal dimension.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.5
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• pp.573-580
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• 2007

This paper presents the numerical estimation of the fatigue life for the frame box's welded parts of the marine vessel engine S60MC-C. The time-variations of the effective stresses at the critical points during a piston cycle are computed through the finite element analysis, by applying the dynamic loadings that were analytically derived in the previous paper. The fatigue lives of the welded parts are estimated by making use of the hot-spot stress extrapolation and the Palmgren-miner cumulative damage rule.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.42
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• pp.143-149
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• 1997

먼저 Cantor dust 의 성질 및 유사성, 축소인자, 불변집합, $\delta$ - covering, Box counting 차원 등에 대한 정의를 하였다, {f_i}{\;}{{\infty}\atop{i=1}}$ 를 $R^n$ 상에서 개집합 조건을 만족시키는 축소인 자 $C_i$에 대한 유사성 이라하자. F를｛{f_i}{\;}{{\infty}\atop {i=1}}$ 에 대한 $R^n$상의 불변집합, 즉, F = $\bigcup_{i=0}^\infty{\;}f_1(F)$를 만족시키는 집합이라 하자. 이때, $\sum\limits_{n=0}^\infty{\;}C^s_i{\;}=1,{\;}0{\;}<{\;}C_1{\;}<{\;}1$ 일 때, $dim{\;}_H{\;}F{\;}={\;}dim{\;}_B{\;}F{\;}={\;}s$ 임을 보임으로서, 자기동형집합의 후랙탈 차원에 대하여 논의 하고자 한다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.372-375
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• 2003

The incidence of blindness resulting from diabetic retinopathy has significantly increased despite the intervention of insulin to control diabetes mellitus. Early signs are microaneurysms, exudates, intraretinal hemorrhages, cotton wool patches, microvascular abnormalities, and venous beading. Advanced stages include neovascularization, fibrous formations, preretinal and vitreous microhemorrhages, and retinal detachment. Microaneurysm count is important because it is an indicator of retinopathy progression. The purpose of this paper is to apply data mining to detect diabetic retinopathy patterns in routine fundus fluorescein angiography. Early symptoms are of principal interest and therefore the emphasis is on detecting microaneurysms rather than vessel tortuosity. The analysis does not involve image-recognition algorithms. Instead, mathematical filtering isolates microaneurysms, microhemorrhages, and exudates as objects of disconnected sets. A neural network is trained on their distribution to return fractal dimension. Hausdorff and box counting dimensions grade progression of the disease. The field is acquired on fluorescein angiography with resolution superior to color ophthalmoscopy, or on patterns produced by physical or mathematical simulations that model viscous fingering of water with additives percolated through porous media. A mathematical filter and neural network perform the screening process thereby eliminating the time consuming operation of determining fractal set dimension in every case.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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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.

• Journal of the Korean Society of Safety
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• v.16 no.1
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• pp.31-36
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• 2001

Surface crack growth characteristics and influence of the stress amplitude in rotary bending fatigue test were evaluated for annealed S35C steel, and than fractal dimensions of fatigue crack paths estimated using the box counting method. The following results that will be helpful to understand the fatigue crack growth mechanism were obtained. (1) Crack growth rate ds/dN and db/dN (s : half crack length at the surface crack, b : crack depth) depended on stress amplitude (${\Delta}{\sigma}/2$), stress intensity factor range (${\Delta}K_A, {\Delta}K_C$) and crack length. (2) At the effect area of 0.3 mm hole notch (s＜0.5 mm) crack growth rate did not depend on these factors. (3) The fractal dimensions (D) increased with stress amplitude (${\Delta}{\sigma}/2$) but decreased with cyclic number.

• KCI Concrete Journal
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• v.14 no.1
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• pp.30-35
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• 2002

The fractal geometry is a non-Euclidean geometry which describes the naturally irregular or fragmented shapes, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cementitious composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is apparent.ent.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.38
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• pp.1-7
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• 1996

프랙탈이란 말은 라틴어 Fractus(부서진 상태를 뜻함)에서 유래되었으며, 1975년 Mandelbrot가 수학 및 자연계의 비정규적 패턴들에 대한 체계적 고찰을 담은 자신의 에세이의 표제를 주기 위해서 만들었다 (〔6〕). 프랙탈을 기술하는데 있어서 가장 중요한 양은 차원(dimension)으로 프랙탈 차원은 정수차원이 아닌 실수 차원을 갖는다. 이 논문에서는 box counting 차원, Hausdorff 차원, s-potential 및 s-energy등에 대한 정의를 하고 정리 2.8, 정리 3.1및 정리 3.2을 증명하고자 한다.