• Communications of Mathematical Education
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• v.21 no.3
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• pp.515-525
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• 2007

In this study, we study on equations of bisector and trisectors of angle. We analyze various studies related with bisector and trisectors of angle. As a result we have known that trisectors of angle is able to received by paper folding method. Using some concepts of vector we have described equations of bisector and trisectors of angle.

• Communications of Mathematical Education
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• v.22 no.1
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• pp.79-89
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• 2008

In this study, we study on various positions and equations of trisectors of angle. We analyze article related with trisector's equation of angle. We elaborate the article, investigate various case of angles, and find out new equations of trisectors of angle.

• Journal of Korea Multimedia Society
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• v.16 no.11
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• pp.1288-1296
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• 2013

The prominent line at the singe image is the important fact for understanding spatial structure or estimating aesthetic scoring. According to this thesis, the abstraction of the background line helps analyzing vanishing point, reconstitution of 3 dimensions, and determining of image sloppiness. It also makes easy to calculate the rule of thirds. This thesis is composed of section hough transform mapping, prioritizing of the prominent line, and selection of the prominent line. These technologies are departmentalized to be applied abstraction of traffic lane, analyzing of building structure, abstraction of vanishing point, and abstraction of straight line documentation. This gives the choice that users are able to compose technology by considering characteristic of objects and luminous environment. This thesis also can be applied to abstract circle. The interval hough transform is able to select the number of prominent line which users want to abstract. It can analyze important prominent line numbers at the image and then abstract the lines, too. Results of prominent lines by experiments would be show at this thesis.

• Journal of KIISE:Software and Applications
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• v.30 no.5_6
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• pp.444-453
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• 2003

Recently, a great interest of bio-technology(BT) is concentrated and the image analysis technique for electrophoresis gels is highly requested to analyze genetic information or to look for some new bio-activation materials. For this purpose, the location and quantity of each band in a lane should be measured. In most of existing techniques, the approach of peak searching in a profile of a lane is used. But this peak is improper as the representative of a band, because its location does not correspond to that of the brightest pixel or the center of gravity. Also, it is improper to measure band quantity in most of these approaches because various enhancement processes are commonly applied to original images to extract peaks easily. In this paper, we adopt an approach to measure accumulated brightness as a band quantity in each band region, which Is extracted by not using any process of changing relative brightness, and the gravity center of the region is calculated as a band location. Actually, we first extract lanes with an entropy-based threshold calculated on a gel-image histogram. And then, three other methods are proposed and applied to extract bands. In the MER method, peaks and valleys are searched on a vertical search line by which each lane is bisected. And the minimum enclosing rectangle of each band is set between successive two valleys. On the other hand, in the RG-1 method, each band is extracted by using region growing with a peak as a seed, separating overlapped neighbor bands. In the RG-2 method, peaks and valleys are searched on two vertical lines by which each lane is trisected, and the left and right peaks nay be paired up if they seem to belong to the same band, and then each band region is grown up with a peak or both peaks if exist. To compare above three methods, we have measured the location and amount of bands. As a result, the average errors in band location of MER, RG-1, and RG-2 were 6%, 3%, and 1%, respectively, when the lane length is normalized to a unit value. And the average errors in band amount were 8%, 5%, and 2%, respectively, when the sum of band amount is normalized to a unit value. In conclusion, RG-2 was shown to be more reliable in the accuracy of measuring the location and amount of bands.