• Title/Summary/Keyword: Least Squares Fitting

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Visualization of Trivariate Scattered Data Interpolation (트라이 베리에이트 산포된 자료 보간의 가시화)

  • Lee, Kun
    • Journal of the Korea Computer Graphics Society
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    • v.2 no.2
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    • pp.11-20
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    • 1996
  • The numerous application of scattered data include the modeling and visualization of physical phenomena. A tetrahedrization is one of pre-processing steps for 4-D surface interpolation. In this paper, various tetrahedrization methods are discussed including, Delaunay, least squares fitting, gradient difference, and jump in normal direction derivatives. This paper discriminates the characteristics of tetrahedrization through visualizing tetrahedral domain. This paper also, provides the tool that can compare and analyze the quality of 4-D space approximation over tetrahedral domain numerically, as well as graphically.

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A Wafer Pre-Alignment System Using a High-Order Polynomial Transformation Based Camera Calibration (고차 다항식 변환 기반 카메라 캘리브레이션을 이용한 웨이퍼 Pre-Alignment 시스템)

  • Lee, Nam-Hee;Cho, Tai-Hoon
    • Journal of the Semiconductor & Display Technology
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    • v.9 no.1
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    • pp.11-16
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    • 2010
  • Wafer Pre-Alignment is to find the center and the orientation of a wafer and to move the wafer to the desired position and orientation. In this paper, an area camera based pre-aligning method is presented that captures 8 wafer images regularly during 360 degrees rotation. From the images, wafer edge positions are extracted and used to estimate the wafer's center and orientation using least squares circle fitting. These data are utilized for the proper alignment of the wafer. For accurate alignments, camera calibration methods using high order polynomials are used for converting pixel coordinates into real-world coordinates. A complete pre-alignment system was constructed using mechanical and optical components and tested. Experimental results show that alignment of wafer center and orientation can be done with the standard deviation of 0.002 mm and 0.028 degree, respectively.

Building Reconstruction for 3D City Modeling in Korea (국내 실정에 맞는 삼차원 도시모델링을 위한 건물모델 생성방법에 관한 연구)

  • 조영욱;최재완;한동엽;김용일;유기윤
    • Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
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    • 2004.10a
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    • pp.13-18
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    • 2004
  • In this study, a new method is proposed generating 3D wire-frames of building using the lowest level topology, points, which are input by human operators. Through the procedure, it is possible to make prediction occlusion points and generate the topology automatically among points, lines, surfaces from buildings. In order to adjust the error of initial values which are input manually, the least squares adjustment for model-image fitting is carried out using the edge information of aerial imagery. And also, model fitting procedure is done making all surfaces plane of buildings by the least squares adjustment. As a result of those procedure, 3D building models are refined similar to real figures of buildings.

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Efficient Response Surface Modeling using Sensitivity (민감도를 이용한 효율적인 반응표면모델생성)

  • Wang, Se-Myung;Kim, Chwa-Il
    • Proceedings of the KSME Conference
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    • 2003.11a
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    • pp.1882-1887
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    • 2003
  • The response surface method (RSM) became one of famous meta modeling techniques, however its approximation errors give designers several restrictions. Classical RSM uses the least squares method (LSM) to find the best fitting approximation models from the all given data. This paper discusses how to construct RSM efficiently and accurately using moving least squares method (MLSM) with sensitivity information. In this method, several parameters should be determined during the construction of RSM. Parametric study and optimization for these parameters are performed. Several difficulties during approximation processes are described and numerical examples are demonstrated to verify the efficiency of this method.

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S-Domain Equivalent System for Electromagnetic Transient Studies PART I : Frequency Dependent Network Equivalent (전자기 과도현상 해석을 위한 S 영역 등가시스템 PART I : 주파수 의존 시스템 등가)

  • 왕용필
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.52 no.11
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    • pp.632-638
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    • 2003
  • Modern power systems are very complex and to model them completely is impractical for electromagnetic transient studies. Therefore areas outside the immediate area of interest must be represented by some form of frequency dependent equivalent. The s-domain rational function form of frequency dependent equivalent does not need refitting if the simulation time-step is changed in the electromagnetic transient program. This is because the s-domain rational function coefficients are independent of the simulation time-step, unlike the z-domain rational function coefficients. S-domain rational function fitting techniques for representing frequency dependent equivalents have been developed using Least Squares Fitting(LSF). However it does not suffer the implementation error that exited in this work as it ignored the instantaneous term. This paper Presents the formulation for developing 1 Port Frequency Dependent Network Equivalent(FDNE) with the instantaneous term in S-domain and illustrates its use. This 1 port FDNE have been applied to the CIGRE Benchmark Rectifier test AC system. The electromagnetic transient package PSCAD/EMTDC is used to assess the transient response of the 1 port (FDNE) developed with Thevenin and Norton Equivalent network. The study results have indicated the robustness and accuracy of 1 port FDNE for electromagnetic transient studies.

Plotting positions and approximating first two moments of order statistics for Gumbel distribution: estimating quantiles of wind speed

  • Hong, H.P.;Li, S.H.
    • Wind and Structures
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    • v.19 no.4
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    • pp.371-387
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    • 2014
  • Probability plotting positions are popular and used as the basis for distribution fitting and for inspecting the quality of the fit because of its simplicity. The plotting positions that lead to excellent approximation to the mean of the order statistics should be used if the objective of the fitting is to estimate quantiles. Since the mean depends on the sample size and is not amenable for simple to use closed form solution, many plotting positions have been presented in the literature, including a new plotting position that is derived based on the weighted least-squares method. In this study, the accuracy of using the new plotting position to fit the Gumbel distribution for estimating quantiles is assessed. Also, plotting positions derived by fitting the mean of the order statistics for all ranks is proposed, and an approximation to the covariance of the order statistics for the Gumbel (and Weibull) variate is given. Relative bias and root-mean-square-error of the estimated quantiles by using the proposed plotting position are shown. The use of the proposed plotting position to estimate the quantiles of annual maximum wind speed is illustrated.

A simple approach for circular Arc detection using a least squares fitting and preprocessing (최소자승법과 전 처리를 이용한 원호 검출의 간단한 접근)

  • Nkurunziza, Armel;Kim, Jong-nam
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2016.05a
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    • pp.840-843
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    • 2016
  • The circular arc is a very useful feature for object detection and recognition in industrial environments. In this paper, a new method to detect circular arcs is proposed. The detection of the circular arc includes the estimation of the center, the radius and the two ending points of the arc. This new method is based on determining the best part of the circular arc (part which does not contains outliers points) using 3 points designated along the arc. A least square method is applied to the best part of the arc and the center and the radius of the arc are obtained. The distance between the remaining edge's points (points which are not lying on the best part of the arc) and the radius is used to the two ending points of the arc.

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Geometric Fitting of Parametric Curves and Surfaces

  • Ahn, Sung-Joon
    • Journal of Information Processing Systems
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    • v.4 no.4
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    • pp.153-158
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    • 2008
  • This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.

Quality Inspection of Dented Capsule using Curve Fitting-based Image Segmentation

  • Kwon, Ki-Hyeon;Lee, Hyung-Bong
    • Journal of the Korea Society of Computer and Information
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    • v.21 no.12
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    • pp.125-130
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    • 2016
  • Automatic quality inspection by computer vision can be applied and give a solution to the pharmaceutical industry field. Pharmaceutical capsule can be easily affected by flaws like dents, cracks, holes, etc. In order to solve the quality inspection problem, it is required computationally efficient image processing technique like thresholding, boundary edge detection and segmentation and some automated systems are available but they are very expensive to use. In this paper, we have developed a dented capsule image processing technique using edge-based image segmentation, TLS(Total Least Squares) curve fitting technique and adopted low cost camera module for capsule image capturing. We have tested and evaluated the accuracy, training and testing time of the classification recognition algorithms like PCA(Principal Component Analysis), ICA(Independent Component Analysis) and SVM(Support Vector Machine) to show the performance. With the result, PCA, ICA has low accuracy, but SVM has good accuracy to use for classifying the dented capsule.

The Influence of Assay Error Weight on Gentamicin Pharmacokinetics Using the Bayesian and Nonlinear Least Square Regression Analysis in Appendicitis Patients

  • Jin, Pil-Burm
    • Archives of Pharmacal Research
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    • v.28 no.5
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    • pp.598-603
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    • 2005
  • The purpose of this study was to determine the influence of weight with gentamicin assay error on the Bayesian and nonlinear least squares regression analysis in 12 Korean appen dicitis patients. Gentamicin was administered intravenously over 0.5 h every 8 h. Three specimens were collected at 48 h after the first dose from all patients at the following times, just before regularly scheduled infusion, at 0.5 h and 2 h after the end of 0.5 h infusion. Serum gentamicin levels were analyzed by fluorescence polarization immunoassay technique with TDxFLx. The standard deviation (SD) of the assay over its working range had been determined at the serum gentamicin concentrations of 0, 2, 4, 8, 12, and 16 ${\mu}g$/mL in quadruplicate. The polynominal equation of gentamicin assay error was found to be SD (${\mu}g$/mL) = 0.0246-(0.0495C)+ (0.00203C$^2$). There were differences in the influence of weight with gentamicin assay error on pharmacokinetic parameters of gentamicin using the nonlinear least squares regression analysis but there were no differences on the Bayesian analysis. This polynominal equation can be used to improve the precision of fitting of pharmacokinetic models to optimize the process of model simulation both for population and for individualized pharmacokinetic models. The result would be improved dosage regimens and better, safer care of patients receiving gentamicin.