• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.2
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• pp.93-99
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• 2013

Fractal theory has been adopted as an effective tool for modelling complex and irregular natural phenomena facing in the fields of Computer Science, Engineering, Medical, Climatology and so on. In this paper, we presents an algorithm which enhances the performance of the triangular prism method(TPM) which has been widely used for fractal dimension extraction of natural terrains and images. For this, existing sampling methods are analyzed and a new sampling method which takes their merits is proposed. The effectiveness of the proposed algorithm is tested on fractal terrain maps and its performance is compared with that of other methods.

• Journal of Navigation and Port Research
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• v.38 no.1
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• pp.45-52
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• 2014

Fractal theory has been widely used to quantify the complexity of remotely sensed digital elevation models and images. Despite successful applications of fractals to a variety of fields including computer graphics, engineering and geosciences, the performance of fractal estimators depends highly on data sampling. In this paper, we propose an algorithm for computing the fractal dimension based on the triangular prism method and a new sampling method. The proposed sampling method combines existing two methods, that is, the geometric step method and the divisor step method to increase pixel utilization. In addition, while the existing estimation methods are based on $N{\times}M$ window, the proposed method expands to $N{\times}M$ window. The proposed method is applied to generated fractal DEM, Brodatz's image DB and real images taken in the campus to demonstrate its feasibility.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.59-76
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• 2006

This research focuses on the relationship between mathematics and visual art from a perspective of chaos theory which emerged under the influence of post-modernism. Culture and history, which transform dynamically with the passing of time, are models of complexity. Especially, when the three periods of Medieval, Renaissance, and 17-18 Centuries are observed, the Renaissance period is phase transition phenomenon era between Medieval and 17-18 Centuries. The transition stage between the late Medieval times and the Renaissance; and the stage between the Renaissance and the Modern times are also phase transitions. These phenomena closely resemble similarity in Fractal theory, which includes the whole in a partial structure. Phase transition must be preceded by fluctuation. In addition to the pioneers' prominent act of creation in the fields of mathematics and visual an serving as drive behind change, other socio-cultural factors also served as motivations, influencing the transformation of the society through interdependency. In particular, this research focuses on the fact that scientific minds of artists in the Renaissance stimulated the birth of Perspective Geometry.

• Journal of IKEEE
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• v.2 no.2 s.3
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• pp.185-193
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• 1998

Fractal-based monochrome image coding method can be easily applied for color image compression by splitting the color image into different primary spectral channels such as RGB, YIQ or $YC_bC_r$, and encoding each channel independently According to this method, it needs to repeat the fractal coding for each channel, so it have the problem of encoding time. In this paper, a fractal-based coder for color still image is proposed which features the enhancement of compression rate and the reduction of coding time. As the result of the experiment where the proposed algorithm is applied far color images, the compression rate is enhanced by 28 : 1 above with average PSNR value $28{\sim}29[dB]$, do not lossless encoding process using JPEG. And the encoding time is reduced by maximum 11.5 %.

• Korean Journal of Ecology and Environment
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• v.44 no.1
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• pp.58-65
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• 2011

This study aims to investigate the settling velocity of aggregates of cohesive sediment (floc) and its relationship with sediment size, density and fractal dimension. A system of commercial camera and macro-lens is used for the experiment. Through the image-analysis technique, the image taken by the camera system is analyzed. For the experiment, kaolinite and a natural sediment sampled at Lake Apopka in Florida have been tested. From this study, it is known that kaolinite and Lake Apopka sediments show different behaviors mainly depending on the organic matter content. Samples of kaolinite with less organic contents show a more definite trend to follow a fractal theory and relatively strong relationships between the settling velocity, density, fractal dimension and floc size compared to the Lake Apopka sediments rich in organics.

• Korean Institute of Interior Design Journal
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• v.23 no.1
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• pp.88-95
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• 2014

This study intended arousal of other viewpoints that deal with and understand spaces and shapes, by describing the concept of 'dimensions' into visual patterns. Above all, the core concept of spatial dimensions was defined as 'expandability'. Then, first, the 'golden ratio', 'Fibonacci sequence', and 'fractal theory' were defined as elements of each dimension by stage. Second, a 'unit cell' of one dimension as 'minimum unit particles' was set. Next, Fibonacci sequence was set as an extended concept into two dimensions. Expansion into three dimensions was applied to the concept of 'self-similarity repetition' of 'Fractal'. In 'fractal dimension', the concept of 'regularity of irregularity' was set as a core attribute. Plus, Platonic solids were applied as a background concept of the setting of the 'unit cell' from the viewpoint of 'minimum unit particles'. Third, while 'characteristic patterns' which are shown in the courses of 'expansion' of each dimension were embodied for the visual expression forms of dimensions, expansion forms of dimensions are based on the premise of volume, directional nature, and concept of axes. Expressed shapes of each dimension are shown into visually diverse patterns and unexpected formative aspects, along with the expression of relative blank spaces originated from dualism. On the basis of these results, the 'unit cell' that is set as a concept of theoretical factor can be defined as a minimum factor of a basic algorism caused by other purpose. In here, by applying diverse pattern types, the fact that meaning spaces, shapes, and dimensions can be extracted was suggested.

• Journal of Korea Multimedia Society
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• v.6 no.1
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• pp.89-96
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• 2003

This paper propose the new method witch is adopted in extracting character features and recognizing numeric characters using fractal dimension and modified Henon Attractor of the Chaos Theory. Firstly, it gets features of mesh feature, projection feature and cross distance feature from numeric character images And their feature hi converted into time series data. Then using the modified Henon system suggested in this paper, it gets last features of numeric character image after calculating Natural Measure and information bit which art meant fractal dimension. Finally, numeric character recognition is performed by statistically finding out the each information bit showing the minimum difference against the normalized pattern database. An Experimental result shows 100% character classification rates for 10 digits and 90% of recognition rates in real situation and the recognition speed was 26 characters per second.

• Proceedings of the KOSOMBE Conference
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• v.1994 no.05
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• pp.43-48
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• 1994

본 논문은 반복 수축 변환의 프랙탈(fractal) 이론에 근거한 심전도 데이터 압축에 관한 연구이다. 심전도 데이터에 반복 함수계(Iterated Function System : IFS) 모델을 적용하여 신호 자체의 자기 유사성(self-similarity)을 반복 수축 변환으로 표현하고, 그 매개변수만을 저장한다. 재구성시는 변환 매개변수를 반복 적용하여 원래의 신호에 근사되어지는 값을 얻게 된다. 심전도 데이타는 부분적으로 자기 유사성을 갖는다고 보고, 부분 자기-유사 프랙탈 모델(piecewise self-affine fractal model)로 표현될 수 있다. 이 모델은 신호를 특정 구간들로 나누어 각 구간들에 대해 최적 프랙탈 보간(fractal interpolation)을 구하고 그 중 오차가 가장 작은 매개변수만을 추출하여 저장한다. 이 방법을 심전도 데이타에 적용한 결과 특정 압축율에 대해 아주 적은 재생오차 (percent root-mean-square difference : PRD)를 얻을 수 있었다.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.39 no.4
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• pp.423-430
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• 2002

When JPEG, a standard of stopped image compression, is high compressed, the image is severely blocked. Since JPEG performs compression after taking DCT(Discrete Cosine Transform). It has a defect that the quality of image becomes low with aliasing in the case of high compression. Though transformation cipher method can have high compression rate, flame nay happen to quality of image by transformation and reverse transformation. In this paper, we use wavelet transform and fractal theory in order to solve these problems. After we apply these two methods to stopped image, we can get some good results, improvement of speed and compression rate, and elimination of blocking appearance. Besides, we show quality of restoration image is better than established one.

• Journal of Sasang Constitutional Medicine
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• v.12 no.1
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• pp.24-36
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• 2000

Purpose : Many believe that the Sasang mentioned in the I Ching and the Sasang of Sasang Medicine (as expounded by Dr. Lee Je-ma in the book Longevity and Life Preservation in Oriental Medicine) refer to different concepts. This is untrue. In order to understand the thought patterns of Dr. Lee Je-ma and his book, it is necessary to first understand the concepts of the I Ching. The I Ching was the most respected text in Dr. Lee Je-ma time, and served as the foundation upon which his medicine stood. The purpose of this research is to understand the concept of Sasang in the I Ching and how it applies to the Sasang medicine. Method : The authors first defined the term Sasang according to the theory of I Ching. It was then discussed in relation to theories of modern science. Inferences were made as to how Sasang corresponds to the terminologies and concepts of modern science. The characteristics of Sasang interpreted through modern science were then applied to the physiology, pathology and pharmacology of Sasang Medicine. Results and Conclusion : 1. The Sasang theory of the I Ching organizes seemingly random and isolated natural phenomena into four distinct groups according to various attributes. The particular characteristics representing each of these four categories are known as Sasang. 2. The Sasang theory of I Ching has a strong correlation to the Theory of Relativity and the Theory of Complementarity, as well as the Digital and Fractal Theories. 3. By applying the Sasang Theory to various fields, the seemingly unrelated principles of physics, chemistry, biology and medicine can be seen as parts of a whole. 4. Sasang Medicine categorizes human morphology, physiology and pharmacology into four categories according to the characteristics defined by the Sasang Theory of the I Ching. 5. Grouping new discoveries of modern physics, chemistry, biology and medicine according to the Sasang Theory will bring to light the intricacies of the Sasang Theory while facilitating the incorporation of modern science into Sasang Medicine.