• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.121-142
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• 2002

We are interested in the curve fitting problems in such a way that the sum of the squares of the orthogonal distances to the given data points is minimized. Especially, the fitting an ellipse to the given data points is a problem that arises in many application areas, e.g. computer graphics, coordinate metrology, etc. In [1] the problem of fitting ellipses was considered and numerically solved with general purpose methods. In this paper we present another new ellipse fitting algorithm. Our algorithm if mainly based on the steepest descent procedure with the view of ensuring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.669-684
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• 1999

We are interested in the problem of fitting a curve to a set of points in the plane in such a way that the sum of the squares of the orthogonal distances to given data points ins minimized. In[1] the prob-lem of fitting circles and ellipses was considered and numerically solved with general purpose methods. Especially in [2] H. Spath proposed a special purpose algorithm (Spath's ODF) for parabolas y-b=$c($\chi$-a)^2$ and for rotated ones. In this paper we present another parabola fitting algorithm which is slightly different from Spath's ODF. Our algorithm is mainly based on the steepest descent provedure with the view of en-suring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• Journal of Korea Multimedia Society
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• v.13 no.7
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• pp.1000-1015
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• 2010

In this paper, we propose a novel algorithm for hand gesture recognition. The hand detection method is based on human skin color, and we use the boundary energy information to locate the hand region accurately, then the moment method will be employed to locate the hand palm center. Hand gesture recognition can be separated into 2 step: firstly, the hand posture recognition: we employ the parallel NNs to deal with problem of hand posture recognition, pattern of a hand posture can be extracted by utilize the fitting ellipses method, which separates the detected hand region by 12 ellipses and calculates the white pixels rate in ellipse line. the pattern will be input to the NNs with 12 input nodes, the NNs contains 4 output nodes, each output node out a value within 0~1, the posture is then represented by composed of the 4 output codes. Secondly, the hand gesture tracking and recognition: we employed the Kalman filter to predict the position information of gesture to create the position sequence, distance relationship between positions will be used to confirm the gesture. The simulation have been performed on Windows XP to evaluate the efficiency of the algorithm, for recognizing the hand posture, we used 300 training images to train the recognizing machine and used 200 images to test the machine, the correct number is up to 194. And for testing the hand tracking recognition part, we make 1200 times gesture (each gesture 400 times), the total correct number is 1002 times. These results shows that the proposed gesture recognition algorithm can achieve an endurable job for detecting the hand and its' gesture.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.37 no.3
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• pp.259-266
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• 2013

An automated cell tracking system is used to automatically analyze and track the changes in cell behavior in time-lapse cell images acquired using a microscope with a cell culture. Clustering is the partial overlapping of neighboring cells in the process of cell change. Separating clusters into individual cells is very important for cell tracking. In this study, we proposed an algorithm for separating clusters by using ellipse fitting based on a direct least square method. We extracted the contours of clusters, divided them into line segments, and then produced their fitted ellipses using a direct least square method for each line segment. All of the fitted ellipses could be used to separate their corresponding clusters. In experiments, our algorithm separated clusters with average precisions of 91% for two overlapping cells, 84% for three overlapping cells, and about 73% for four overlapping cells.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2012.05a
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• pp.909-912
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• 2012

An automated cell tracking system is automatically to analyze and track changes of cell behaviors in time-lapse cell images acquired from microscope in the cell culture. In this paper, we proposed and developed an ellipse fitting based algorithm for separating very small size overlapping cells in a cell image consisted of thousands or ten thousands cells. We were extracted contours of clusters and divided them into line segments and then produced their fitted ellipses for each line segment. By experimentations, our algorithm was separated clusters with average 91% precision for two overlapping cells and average 84% precision for three overlapping cells respectively.

• Korean Journal of Optics and Photonics
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• v.15 no.3
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• pp.258-262
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• 2004

The uncertainty of the detector-based candela scale is limited by the area measurement uncertainty of radiometric apertures. The apertures were fabricated with a diamond-turning machine which trimmed the edge of the apertures as sharply as a knife edge. The positions of the apertures were controlled by a digital feedback algorithm to scan the laser spot with the beam waist less than 5 ${\mu}{\textrm}{m}$. The knife edge scan yielded a set of coordinates on the edges of the aperture. The areas of the apertures were obtained by fitting the coordinates to the ellipses. The relative standard uncertainty of the measurement was estimated to be 8${\times}$10$^{-5}$.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.772-777
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• 2003

A vision-based tool position estimation system for the inspection and maintenance manipulator working inside the steam generator bowl of nuclear power plants can help human operators ensure that the inspection probe or plug are inserted to the targeted tube. Some previous research proposed a simplified tube position verification system that counts the tubes passed through during the motion and displays only the position of the tool. In this paper, by using a general camera calibration approach, tool orientation is also estimated. In order to reduce the computation time and avoid the parameter bias problem in an ellipse fitting, a small number of edge points are collected around the large section of the ellipse boundary. Experiment results show that the camera calibration parameters, detected ellipses, and estimated tool position are appropriate.