• Journal for History of Mathematics
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• v.27 no.6
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• pp.395-402
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• 2014

When the circle inscribed in a square is projected to a picture plane, one sees, in general, an ellipse in a convex quadrilateral. This ellipse is poorly described in the works of Alberti and Durer. There are one parameter family of ellipses inscribed in a convex quadrilateral. Among them only one ellipse is the perspective image of the circle inscribed in the square. We call this ellipse "the projected ellipse." One can easily find the four tangential points of the projected ellipse and the quadrilateral. Then we show how to find the center of the projected ellipse. Finally, we describe a pair of conjugate vectors for the projected ellipse, which finishes the construction of the desired ellipse. Using this algorithm, one can draw the perspective image of the squared-circle tiling.

• Journal of the Institute of Convergence Signal Processing
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• v.14 no.1
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• pp.27-32
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• 2013

It plays an important role to detect the shape of an ellipse in many application areas of image processing. But it is very difficult to detect the ellipse in the real image because the noise was involved in the image, other objects obscured the ellipse or the ellipses were overlap with each other. In this paper, we extract the boundary (edge) to detect ellipse in the image and perform the grouping process in order to reduce amount of information. As a result, the speed of the ellipse detection was improved. Also in order to the ellipse detection, we selected the five ellipse parameters at random And then to select the optimal parameters of the ellipse, the linear least-squares approximation is applied. To verify the ellipse detection, RANSAC algorithm is applied. After the algorithm proposed in this study was implemented, the results applied to the real images showed an aocuracy of 75% and speed was very fast to compared with other researches. It mean that the proposed algorithm was valuable to detect the ellipses in the image.

• School Mathematics
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• v.14 no.3
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• pp.331-355
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• 2012

All the method used in teaching the ellipse was to have students draw the points which have the same sum of distances from the two points so that they can confirm the shapes of the ellipse before showing them the definition of ellipse. In this process, students would not get an opportunity to think or make the definition of ellipse for themselves. This deductive way can hinder students from having clear understanding of why such definition was made. This paper introduces a method of defining the ellipse based on the similarity between a circle and an ellipse, leading into the equation. This method is possible by introducing Analytic Geometry taught in current school mathematics and Transformation Geometry. By doing so, this paper will discuss a fundamental understanding about the ellipse and the feature of the ellipse expandable by intuition. Furthermore this paper will also show various advantages which can be given by defining the ellipse in Transformation Geometry.

• Journal of Power System Engineering
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• v.3 no.2
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• pp.89-97
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• 1999

In this paper the forming simulations of ellipse bulge have been researched by using $PAM-STAMP_{TM}$ to estimate the sheet metal forming and the plastic deformation characteristic of ellipse bulge. Thin elliptical diaphragms of brass, copper, aluminum, and mild steel are bulged in elliptical dies having aspect ratios of 1.33 and 2. In order to compare the simulation results with the experiment and ellipse bulge's theory derived by using Johnson and Duncan's theory, the relations of hydraulic pressure and polar height, polar thickness strain and polar height, were compared. According to this study, the results of simulation and ellipse bulge's theory derived by using Johnson and Duncan's theory, and the bursting pressure and the bursting polar height are good agreement to the experiment. So, the results of simulation by using $PAM-STAMP_{TM}$ and the ellipse bulge's theory will give engineers good information to make assessment the formability and plastic deformation characteristic of hydraulic ellipse bulge test.

• Korean Journal of Applied Biomechanics
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• v.18 no.2
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• pp.19-27
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• 2008

The purpose of this study was to investigate of assessment of the ability of balance control using COP 95% confidence ellipse area while executing single-leg stance with eyes open and eyes closed through GRF system. The subjects participated in this study were 7 female yoga group and 7 female control group. The yoga training affected to improve the ability of balance control because the yoga group's COP AP and ML standard deviation and COP 95% confidence ellipse area were smaller than control group in both a single-leg stance with eyes open and eyes closed. Visual affected to the ability of balance control in a single-leg stance. I consider COP 95% confidence ellipse area as a high variable for determining the ability of balance control, and therefore suggest that additional studies for various groups and subjects will be required in the future.

• Korean Journal of Computational Design and Engineering
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• v.9 no.4
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• pp.277-285
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• 2004

In this paper, a 2 DOF haptic yawing joystick for use as the navigation input device in virtual environments is introduced. The haptic yawing joystick has 360° range for yawing motion and ±100° for pitching motion. The device can support weights of up to 26N for χ axis and 10N for axis with 10kHz of sampling rate. The size of the haptic yawing joystick is so small that it can be assembled on armrest of an arm chair and has relatively larger work space than other conventional 2 DOF joysticks. For the haptic yawing joystick, an ellipse navigation algorithm using the user's velocity in the virtual navigation is proposed. The ellipse represents the velocity of the user. According to the velocity of the navigator, the ellipse size is supposed to be changed. Since the path width of navigation environments is limited, the ellipse size is also limited. The ellipse navigation algorithm is tested in 2 dimensional virtual environments. The test results show that the average velocity of the navigation with the algorithm is faster than the average navigation velocity without the algorithm.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.13 no.1
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• pp.13-20
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• 1995

Error analysis is important in horizontal positioning. In case of error analysis, standard error ellipse is generally used to establish the precision regions, but it will be replaced by 95% confidence ellipse. It is more effective than standard error ellipse in resection for measured procedures and establishment for criterias of relative error. Therefore, In this paper deals with analysis of application to 95% confidence ellipse in horizontal positioning. This study deals with error analysis of plane trilateration network which are various types of control point. also, this paper have studied for theory of error analysis in order to using least square adjustment. Thus, This paper's conclusion are as follows; 95% confidence ellipse could be used to establish of specification in korea, also, it is possible for us to predesign for optimum surveying network by 95% confidence ellipse.

• Proceedings of the Korea Multimedia Society Conference
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• 2003.11a
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• pp.204-207
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• 2003

실시간으로 배경에서 분리된 정확한 얼굴 영역을 찾아내는 것은 인식의 가장 기본적인 선행과제이다 얼굴을 찾기 위한 방법 중에 특징기반의 모서리(edge) 정보의 추출과 ellipse fitting 알고리즘을 이용하여 배경으로부터 얼굴을 효과적으로 분리해낸다. 얼굴인식을 하기 위한 얼굴 데이터베이스를 선처리 되어진 배경과 분리된 영상이 검출 된다.

• Journal of Korea Multimedia Society
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• v.13 no.6
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• pp.833-840
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• 2010

In this paper a method for detecting and extracting the face from the image in YCbCr spaceis proposed. The face region is obtained from the complex original image by using the difference method and the face color information is taken from the reduced face region throughthe Ellipse clustering method. The experimental results showed that the proposed method can efficiently detect and extract the face from the original image under the general light intensity except for low luminance.

• IEIE Transactions on Smart Processing and Computing
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• v.1 no.2
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• pp.73-77
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• 2012

This paper reports a combined depth- and model-based face detection and tracking approach. The proposed algorithm consists of four functional modules; i) color-based candidate region extraction, ii) generation of the depth histogram for handling occlusion, iii) rotation-invariant face region detection using ellipse fitting, and iv) face tracking based on motion prediction. This technique solved the occlusion problem under complicated environment by detecting the face candidate region based on the depth-based histogram and skin colors. The angle of rotation was estimated by the ellipse fitting method in the detected candidate regions. The face region was finally determined by inversely rotating the candidate regions by the estimated angle using Haar-like features that were robustly trained robustly by the frontal face.