• Journal for History of Mathematics
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• v.25 no.1
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• pp.71-88
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• 2012

The purpose of this study is to find the way to build the concept image about natural logarithm and the method is using definite integral in calculus under GeoGebra environment. When the students approach to natural logarithm, need to use dynamic program about the definite integral in calculus. Visible reasoning process through using dynamic program(GeoGebra) is the most important part that make the concept image to students. Also, for understand mathematical concept to students, using GeoGebra environment in dynamic program is not only useful but helpful method of teaching and studying. In this article, about graph of natural logarithm using the definite integral, to explore process of understand and to find special feature under GeoGebra environment. And it was obtained from a survey of undergraduate students of mathmatics. Also, relate to this process, examine an aspect of students, how understand about connection between natural logarithm and the definite integral, definition of natural logarithm and mathematical link of e. As a result, we found that undergraduate students of mathmatics can understand clearly more about the graph of natural logarithm using the definite integral when using GeoGebra environment. Futhermore, in process of handling the dynamic program that provide opportunity that to observe and analysis about process for problem solving and real concept of mathematics.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.49 no.4
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• pp.10-16
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• 2012

For high speed visual inspection in semiconductor industries, it is essential to acquire two-dimensional images on regions of interests with a large field of view (FOV) and a high resolution simultaneously. In this paper, an imaging system is newly proposed to achieve high quality image in terms of precision and FOV, which is composed of single lens, a beam splitter, two camera sensors, and stereo image grabbing board. For simultaneously acquired object images from two camera sensors, Zhang's camera calibration method is applied to calibrate each camera first of all. Secondly, to find a mathematical mapping function between two images acquired from different view cameras, the matching matrix from multiview camera geometry is calculated based on their image homography. Through the image homography, two images are finally registered to secure a large inspection FOV. Here the inspection system of using multiple images from multiple cameras need very fast processing unit for real-time image matching. For this purpose, parallel processing hardware and software are utilized, such as Compute Unified Device Architecture (CUDA). As a result, we can obtain a matched image from two separated images in real-time. Finally, the acquired homography is evaluated in term of accuracy through a series of experiments, and the obtained results shows the effectiveness of the proposed system and method.

• Journal of the Korean Society of Costume
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• v.51 no.2
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• pp.181-192
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• 2001

Men study the nature in two ways. Scientists and mathematicians inquire a branch of those two ways. Mathematical formulations are the tools and the expressions of their nature. Meanwhile, the other branch, the art, alms for different inquiry. Instead of formulating the nature, the artists create their masterpieces from their ultimate source, the Mother Nature. For thousands of years these two branches have grown together, influencing each others work. Some mathematicians find that formulation, are not enough to fully express the beauty of nature. It is believed that such a simple expression, formula, easily omits the careful details of nature. The nature is simply too chaotic to be shaped with a formula. Of those mathematicians, Mandelbrot, one of the first to realize this matter, introduced the world of fractal geometry. Fractals give new possibilities. It allows us not to limit ourselves to linear prospect, rather a whole new view of this chaotic beauty of the nature. A popular practice to understand fractals is in costume design. The artistic characteristic and organization mechanism is appalled to costumes. Meanwhile, another practice, rather aggressive, is using computer to create an image of fractals. This image is then used for motives to generate artistic expressions. Computer and paper ironing technique is used for fashion illustration in this research. The works were synthesized arid transformed from computer programs. To add more traditional painting touch to this work, Paper ironing technique was used. Since the of effect of this technique is so random, irregular, and unordered, it corresponds to fractal consideration. This thesis asserts an another prospect to fractal as a structural way of describing nature ailed fashion illustration, rather than restricting it to only mathematical theory.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.557-578
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• 2013

For an ideal $\mathcal{I}$ of a preadditive category $\mathcal{A}$, we study when the canonical functor $\mathcal{C}:\mathcal{A}{\rightarrow}\mathcal{A}/\mathcal{I}$ is local. We prove that there exists a largest full subcategory $\mathcal{C}$ of $\mathcal{A}$, for which the canonical functor $\mathcal{C}:\mathcal{C}{\rightarrow}\mathcal{C}/\mathcal{I}$ is local. Under this condition, the functor $\mathcal{C}$, turns out to be a weak equivalence between $\mathcal{C}$, and $\mathcal{C}/\mathcal{I}$. If $\mathcal{A}$ is additive (with splitting idempotents), then $\mathcal{C}$ is additive (with splitting idempotents). The category $\mathcal{C}$ is ample in several cases, such as the case when $\mathcal{A}$=Mod-R and $\mathcal{I}$ is the ideal ${\Delta}$ of all morphisms with essential kernel. In this case, the category $\mathcal{C}$ contains, for instance, the full subcategory $\mathcal{F}$ of Mod-R whose objects are all the continuous modules. The advantage in passing from the category $\mathcal{F}$ to the category $\mathcal{F}/\mathcal{I}$ lies in the fact that, although the two categories $\mathcal{F}$ and $\mathcal{F}/\mathcal{I}$ are weakly equivalent, every endomorphism has a kernel and a cokernel in $\mathcal{F}/{\Delta}$, which is not true in $\mathcal{F}$. In the final section, we extend our theory from the case of one ideal$\mathcal{I}$ to the case of $n$ ideals $\mathcal{I}_$, ${\ldots}$, $\mathca{l}_n$.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.1
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• pp.33-42
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• 2005

Identifying color codes needs precise color information of their constituents, and is far from trivial because colors usually suffer severe distortions throughout the entire procedures from printing to acquiring image data. To accomplish accurate identification of colors, we need a reliable segmentation method to separate different color regions from each other, which would enable us to process the whole pixels in the region of a color statistically, instead of a subset of pixels in the region. Color image segmentation can be accomplished by performing edge detection on component image(s). In this paper, we separately detected edges on component images from RGB, HSI, and YIQ color models, and performed mathematical analyses and experiments to find out a pair of component images that provided the best edge image when combined. The best result was obtained by combining Y- and R-component edge images.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.10
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• pp.2441-2449
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• 2015

In this digital information era, utilization of images are essential for various media, and the edge is an important characteristical information of an object in images that includes the size, location, direction and etc. Many domestic and international studies are being conducted in order to detect these edge. Existing edge detection methods include Sobel, Prewitt, Roberts, Laplacian, LoG and etc. which apply fixed weight value. As these existing edge detection methods apply fixed weight mask to the image, edge detection characteristic appears slightly insufficient. Accordingly, in order to supplement these problems, this study used bottom-hat transformation from mathematical morphology and opening operation in improving the image and proposed an algorithm that detects for the edge after calculating mask-based gradient. And to evaluate the performance of the proposed algorithm, a comparison was made against the existing Sobel, Roberts, Prewitt, Laplacian, LoG edge detection methods, in illustrating visual images, and similarities were compared by calculating the MSE value based on the standard of each image.

• Journal of Korean Society for Geospatial Information Science
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• v.10 no.3 s.21
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• pp.115-122
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• 2002

The mainly used technique to rectify satellite images with distortion is to develop a mathematical relationship between the pixel coordinates on the image and the corresponding points on the ground. By defining the relationship between two coordinate systems, a polynomial model is designed and various linear transformations are used. These GCP based geometric correction has performed overall plane to plane mapping. In the overall plane mapping, overall structure of a scene is considered, but local variation is discarded. The highly variant height of region is resampled with distortion in the rectified image. To solve this problem, this paper proposed the TIN-based rectification on a satellite image. The TIN based rectification is good to correct local distortion, but insufficient to reflect overall structure of one scene. So, this paper shows the experimental result and the analysis of each rectification model. It also describes the relationship GCP distribution and rectification model. We can choose a geometric correction model as the structural characteristic of a satellite image and the acquired GCP distribution.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.20 no.3
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• pp.1-7
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• 2019

In this paper, we propose an approach to design a practical filter and a mathematical modeling for images. In the areas of signal processing, including high-dimensional image processing, the filtering process has been fundamental and crucial in diverse practical applications such as image processing, computer vision, and pattern recognition. In general, the ideal filter is modeled as circular-shaped in the 2D frequency domain as the rectangular shape is ideal for the 1D frequency domain. This paper proposes an approach to modeling practical and efficient image filter in the 2D frequency domain. Instead of employing a circular-shaped filter, this study proposes a polygon-shaped filter inspired by the concept of a hexagon cellular system for frequency reuse in wireless communication systems. By employing the concept of frequency reuse, bandwidth efficiency is also achieved in the frequency domain. To substantiate the proposed approach, quantitative evaluation is performed using PSNR.

• Journal of Korean Ophthalmic Optics Society
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• v.16 no.4
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• pp.439-444
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• 2011

Purpose: To represent the shape of toric corea in the elliptical function for the determination of curvature distribution and lacrimal thickness between cornea and contact lens when the lens is fitted. Methods: Topography measurements of corneal curvature and curvature equation derived from the assumed elliptical function were evaluated using the Excel program which included the necessary equation derived. Results: Mathematical expressions for the cornea whose ribbon shaped-topography image, in which the center does not coincide with the corneal apex, can be determined. Conclusions: For the application where the higher accuracy on the cornea is not required, such as higher order aberration, the cornea cal be expressed in the simple elliptical function.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.63-78
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• 2011

The purpose of this study is to explore a teaching method of limits of functions with more intuitive and visual of CAS graphing calculators rather than with the rigorous ${\epsilon}-{\delta}$ method. Texas Instruments Voyage200 CAS graphing calculators are used for studying the possibility of the use of technology in calculus course. For this, various related theoretical constructs are reviewed: concept image, concept definition, cognitive conflict, the use of visualization of technology for calculus concepts, the theory of APOS, and local straightness. Based on such theoretical constructs this study suggests a teaching method of limits of functions with embodied visualization of CAS graphing calculators.