• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.81-98
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• 1999

In spite of the well developed theory and the practical use of the univariate B-spline, the theory of multivariate B-spline is very new and waits its practical use. We compare in this article the multivariate B-spline approximation with the polynomial approximation for the surface fitting. The graphical and numerical comparisons show that the multivariate B-spline approximation gives much better fitting than the polynomial one, especially for the surfaces which vary very rapidly.

• The Transactions of the Korea Information Processing Society
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• v.3 no.6
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• pp.1553-1567
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• 1996

The numerous applications surface interpolation include the modeling and visualization phenomena. A tetrahedrization is one of pre-processing steps for 4-D space interpolation. The quality of a piecewise linear interpolation 4-D space depends not only on the distribution of the data points in $R^2$, but also on the data values. We show that the quality of approximation can be improved by data dependent tetraheadrization through visualization of 4-D space. This paper discusses Delaunary tetrahedrization method(sphere criterion) and one of the data dependent tetrahedrization methods(least squares fitting criterion). This paper also discusses new data dependent criteria:1) gradient difference, and 2) jump in normal direction derivative.

• Current Optics and Photonics
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• v.2 no.1
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• pp.69-78
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• 2018

This paper presents a precise edge detection algorithm for the critical dimension (CD) measurement of a Thin-Film Transistor Liquid-Crystal Display (TFT-LCD) pattern. The sigmoid surface function is proposed to model the blurred step edge. This model can simultaneously find the position and geometry of the edge precisely. The nonlinear least squares fitting method (Levenberg-Marquardt method) is used to model the image intensity distribution into the proposed sigmoid blurred edge model. The suggested algorithm is verified by comparing the CD measurement repeatability from high-magnified blurry and noisy TFT-LCD images with those from the previous Laplacian of Gaussian (LoG) based sub-pixel edge detection algorithm and error function fitting method. The proposed fitting-based edge detection algorithm produces more precise results than the previous method. The suggested algorithm can be applied to in-line precision CD measurement for high-resolution display devices.

• Journal of the Korean earth science society
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• v.38 no.5
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• pp.333-344
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• 2017

We present the environmental dependence of the luminosity-size relation of galaxies in the local universe (z < 0.01) along with their dependence on galaxy morphology represented by five broad types (E, dEs, S0, Sp, and Irr). The environmental parameters we consider are the local background density and the group/cluster membership together with the clustercenteric distance for the Virgo cluster galaxies. We derive the regression coefficient (${\beta}$), i.e., the slope of the line representing the least-squares fitting to the data and the Pearson correlation coefficient (c.c.) representing the goodness of the least-squares fit along with the confidence interval from bootstrap resampling. We find no significant dependence of the luminosity-size relation on galaxy morphology. However, there is a weak dependence of the luminosity-size relations on the environment of galaxies, in the sense that galaxies in the low density environment have shallower slopes than galaxies in the high density regions except for elliptical galaxies that show an opposite trend.

• Communications for Statistical Applications and Methods
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• v.30 no.3
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• pp.273-289
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• 2023

In this paper, we develop a new time series model for predicting IPO (initial public offering) data with non-negative integer value. The proposed model is based on integer-valued autoregressive (INAR) model with a Poisson thinning operator. Just as the heterogeneous autoregressive (HAR) model with daily, weekly and monthly averages in a form of cascade, the integer-valued heterogeneous autoregressive (INHAR) model is considered to reflect efficiently the long memory. The parameters of the INHAR model are estimated using the conditional least squares estimate and Yule-Walker estimate. Through simulations, bias and standard error are calculated to compare the performance of the estimates. Effects of model fitting to the Korea's IPO are evaluated using performance measures such as mean square error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) etc. The results show that INHAR model provides better performance than traditional INAR model. The empirical analysis of the Korea's IPO indicates that our proposed model is efficient in forecasting monthly IPO volumes.

• 한국데이터정보과학회:학술대회논문집
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• 2003.10a
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• pp.93-100
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• 2003

It is necessary to check the curvature of selected covariates in regression diagnostics. There are various graphical methods using residual plots based on least squares fitting. The sensitivity of LS fitting to outliers can distort their residuals, making the identification of the unknown function difficult to impossible. In this paper, we compare combining conditional expectation and residual plots(CERES Plots) between least square fit and robust fits using Huber M-estimator. Robust CERES will be far less distorted than their LS counterparts in the presence of outliers and hence, will be more useful in identifying the unknown function.

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.905-906
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• 2008

This paper presents a method where the best focues points are calculated using line fitting. Two datasets are selected for each pixel based on the maximum value which is calculated using Laplacian operator. Then linear regression model is used to find lines that approximate these datasets. The best fit lines are found using least squares method. After approximating the two lines, their intersection point is calculated and weights are assigned to calculate the new value for the depth map.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.2
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• pp.40.1-40.1
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• 2015

Off-axis reflective optical systems have attractive advantages relative to their on-axis or refractive counterparts, for example, zero chromatic aberration, no obstruction, and a wide field of view. For the efficient operation of off-axis reflective system, the surface accuracy of freeform mirrors should be higher than the order of wavelengths at which the reflective optical systems operate. Especially for applications in shorter wavelength regions, such as visible and ultraviolet, higher surface accuracy of freeform mirrors is required to minimize the light scattering. In this work, we propose the error compensation algorithm (ECA) for the correction of wavefront errors on freeform mirrors. The ECA converts a form error pattern into polynomial expression by fitting a least square method. The error pattern is measured by using an ultra-high accurate 3-D profilometer (UA3P, Panasonic Corp.). The measured data are fitted by two fitting models: Sag (Delta Z) data model and form (Z) data model. To evaluate fitting accuracy of these models, we compared the fitted error patterns with the measured error pattern.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.467-474
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• 2006

In this paper we present a weighted support vector machine(SVM) and a weighted least squares support vector machine(LS-SVM) for the prediction in the heteroscedastic regression model. By adding weights to standard SVM and LS-SVM the better fitting ability can be achieved when errors are heteroscedastic. In the numerical studies, we illustrate the prediction performance of the proposed procedure by comparing with the procedure which combines standard SVM and LS-SVM and wild bootstrap for the prediction.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.606-608
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• 2003

This paper investigates the accuracy of three-dimensional positioning for EROS A stereo pairs when different numbers of ground control points are employed. The major works of the proposed schemes include: (1) initialization of orientation parameters (2) preliminary orbit fitting, (3) orbit refinement using the least squares filtering technique, and (4) space intersection. The experiment includes validation of positioning accuracy for an EROS A in-track stereo pair when different number of check points are employed.