• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.915-938
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• 2022

We are interested in the problem of fitting a parabola to a set of data points in ℝ³. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in ℝ³. Our algorithm is mainly based on the steepest descent technique which determines an adequate number λ such that h(λ) = Q(u - λ𝛁Q(u)) < Q(u). Some numerical examples are given to test our algorithm.

• Transactions of Materials Processing
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• v.22 no.6
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• pp.328-333
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• 2013

The current study aims to determine the limit strains more accurately and reasonably when producing a forming limit curve (FLC) from experiments. The international standard ISO 12004-2 in its recent version (2008) states that the limit major strain should be determined by using the best-fit inverse second-order parabola through the experimental strain distribution. However, in cases where fracture does not occur at the center of the specimen, due to insufficient lubrication, the inverse parabola does not give a realistic fit because of its intrinsic symmetry in shape. In this study it is demonstrated that an inverse quartic function can give a much better fit than an inverse parabola in almost all FLC test samples showing asymmetric strain distributions. Using a quartic fit creates more reliable FLCs.

• 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.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.522-525
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• 2005

Light detection and ranging (LIDAR) is one of the effective technologies for monitoring forest inventory, and importance of forestry is increasing because of its function as the sink of green house gases (GHG). This study aims at development of a methodology for better and more accurate estimation of physical parameters of individual trees by removing sudden drops of LIDAR data within a crown. Our study area is located in Aomori prefecture, the northern part of Honshu Island, with the dominant species of Japanese cedar. The results show practicality of our method in the usage of LIDAR data in the field of forest inventory.

• IEMEK Journal of Embedded Systems and Applications
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• v.3 no.3
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• pp.143-150
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• 2008

In this paper, we investigate a real-time environment recognition system based on stereo vision for moving object. This system consists of stereo matching, obstacle detection and distance estimation. In stereo matching part, depth maps can be obtained real road images captured adjustable baseline stereo vision system using belief propagation(BP) algorithm. In detection part, various obstacles are detected using only depth map in case of both v-disparity and column detection method under the real road environment. Finally in estimation part, asymmetric parabola fitting with NCC method improves estimation of obstacle detection. This stereo vision system can be applied to many applications such as unmanned vehicle and robot.

• Journal of Astronomy and Space Sciences
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• v.28 no.1
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• pp.9-12
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• 2011

Results of an analysis of 11 nights of R-filter CCD photometry data of an intermediate polar MU Camelopardalis (MU Cam) obtained at the Korean 1.0 m telescope at Mt. Lemmon are reported. After checking the spin period with our data, $P_{spin}=0.^d01373801(59)$, we compiled the reported data of maxima timing and an O-C diagram analysis has been carried out to understand the spin period variation. A significant spin period variation was detected, and fitting the O-C points to a cubic parabola led to an ephemeris of $BJD_{max}=2453682.4178(94)+0.0137380(13)E-2.07(55){\times}10^{-11}E^2+2.28(52){\times}10^{-15}E^3$. The torque experienced by the magnetic compact star accreting in a disk is estimated as ${\tau}{\approx}1.815{\times}10^{35}gcm^2/s^2$ in a simple approximation in order to show how important monitoring the period variation is. Thus we conclude that monitoring the long-term spin period variation will help to understand the physical condition of magnetic compact stars.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.1
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• pp.55-55
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• 2014

국립 고흥 청소년 우주 체험 센터는 연구와 학생들의 교육을 위해 12GHz 전파 간섭계를 개발했다. 저비용으로 제작하기 위하여 상용 제품들을 주로 사용하였고, 해변 가에 위치한 센터 특성상 강한 바다 바람과 부식에 견디도록 제작하였다. 고흥 간섭계는 직경 1.8m의 off-axis parabola 안테나 3대로 이루어져 있으며, 각 안테나 사이의 기선길이는 4, 19, 20m로, 해상도가 최대 약 4'인 영상을 얻을 수 있다. 수신기는 중심 주파수가 12.177GHz, 대역폭이 10MHz이며 메탄올 천이선과 연속파를 관측할 수 있는 시스템이다. 시스템온도는 100-200K로 추정된다. 각 수신기에서 나오는 신호는 digitizer로 읽어 들이며, 병렬 처리 프로그램으로 software correlation을 수행한다. 태양, 달, Crab Nebula, 그리고 Cassiopeia A 등을 관측하여 프린지를 검출하는데 성공하였다. 가시함수를 구하기 위한 프린지 fitting model의 파라미터들은 기선벡터의 측량과 점전파원 관측을 통하여 정밀하게 측정하였다. 태양에 대한 영상관측결과를 논의하고자 한다.