• Journal of the Korea Institute of Information and Communication Engineering
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• v.23 no.4
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• pp.388-393
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• 2019

As a fiiting method to data with outliers, RANSAC(RANdom SAmple Consensus) based algorithm is widely used in fitting of line, circle, ellipse, etc. CUDA is currently most widely used GPU with massive parallel processing capability. This paper proposes an efficient CUDA implementation of multiple planes fitting using RANSAC with 3d points data, of which one set of 3d points is used for one plane fitting. The performance of the proposed algorithm is demonstrated compared with CPU implementation using both artificially generated data and real 3d heights data of a PCB. The speed-up of the algorithm over CPU seems to be higher in data with lower inlier ratio, more planes to fit, and more points per plane fitting. This method can be easily applied to a wide variety of other fitting applications.

• Current Optics and Photonics
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• v.8 no.2
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• pp.151-155
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• 2024

Optical systems often suffer from optical aberrations caused by imperfect hardware, which places significant constraints on their utility and performance. To reduce these undesirable effects, a comprehensive understanding of the aberrations inherent to optical systems is needed. This article presents an effective method for aberration detection using Zernike polynomials. The process involves scanning the object plane to identify the optimal focus and subsequently fitting the acquired focus data to Zernike polynomials. This fitting procedure facilitates the analysis of various aberrations in the optical system.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.983-994
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• 2000

We consider the problem of determining the circle of best fit to a set of data points in the plane. In [1] and [2] several algorithms already have been given for fitting a circle in least squares sense of minimizing the geometric distances to the given data points. In this paper we present another new descent algorithm which computes a parametric represented circle in order to minimize the sum of the squares of the distances to the given points. For any choice of starting values our algorithm has the advantage of ensuring convergence 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 Korean Society for Geospatial Information Science
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• v.19 no.1
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• pp.97-103
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• 2011

LiDAR system has become a popular tool for generating 3D surface data such as Digital Surface Model. Extraction of valuable information, such as digital building models, from LiDAR data has been an attractive research subject. This research addresses to extract planar patches from LiDAR data. Planar patches are important primitives consisting of man-made objects such as buildings. In order to determine the best fitted planes, this research proposed a method to reduce/eliminate the impact of the outliers and the intersection areas of two planes. After finishing plane fitting, planar patches are segmented by pseudo color values which are calculated by determined three plane parameters for each LiDAR point. In addition, a segmentation procedure is conducted using the pseudo color values to find planar patches. This paper evaluates the feasibility of the proposed method using both airborne and terrestrial LiDAR data.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.4
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• pp.17-22
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• 2003

This paper presents a new circular curve fitting approach of articulated manipulators, based on least square. The approach aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a starting point and an ending point. First a spherical fitting should be performed, using least squares. Then the circular curve fitting can be resulted from the intersection of the fitted sphere and the plane obtained from 3 points, i. e., a starting point, an ending point and the center of a sphere. The proposed algorithms are shown to be efficient by using MATLAB-based simulation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.12C
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• pp.984-994
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• 2010

Pose variation is a critical problem in face recognition. Three-dimensional(3D) face recognition techniques have been proposed, as 3D data contains depth information that may allow problems of pose variation to be handled more effectively than with 2D face recognition methods. This paper proposes a pose-normalized 3D face modeling method that translates and rotates any pose angle to a frontal pose using a plane fitting method by Singular Value Decomposition(SVD). First, we reconstruct 3D face data with stereo vision method. Second, nose peak point is estimated by depth information and then the angle of pose is estimated by a facial plane fitting algorithm using four facial features. Next, using the estimated pose angle, the 3D face is translated and rotated to a frontal pose. To demonstrate the effectiveness of the proposed method, we designed 2D and 3D face recognition experiments. The experimental results show that the performance of the normalized 3D face recognition method is superior to that of an un-normalized 3D face recognition method for overcoming the problems of pose variation.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.7
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• pp.149-154
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• 2001

This study discusses a non-contact optical technique, electronic speckle pattern interferometry(ESPI), that is well suited for a deformation measurement of structure. Phase shifting method and unwrapping method have used to make deformation quantitative widely. In this paper, a previous numerical formula for phase shifting method is reconstructed in addition to least square fitting method to improve sensitivity and phase unwrapping based on vertical-horizontal scanning method is applied to analyze in-plane and out-of-plane deformation quantitatively.

• The Pure and Applied Mathematics
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• v.11 no.2
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• pp.103-115
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• 2004

A computational algorithm is developed for fitting given data in the plane or in 3-space by implicitly defined quadrics. Implicity implies that the type of the quadric is part of the model and need not be known in advance. Starting with some estimate for the coefficients of the quadric the method will alternatively determine the shortest distances from the given points onto the quadric and adapt the coefficients such as to reduce the sum of those squared distances. Numerical examples are given.

• Korean Journal of Optics and Photonics
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• v.8 no.4
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• pp.267-276
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• 1997

We set up a four-wave holographic interferometer using a symmetric dual-beam illumination which is to measure in-plane and out-of-plane displacement simultaneously. In order to acquire the displacement phase map we applied the phase-shifting method and removed the noise of the phase map with least-squares fitting. In this approach the access to information relative to both the difference and sum of phases existing in the two arms of four-wave holographic interferometer was allowed. As a result, in-plane and out-of-plane displacement was measured to the accuracy of λ/40 and λ/100, respectively at λ=632.8nm