• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.669-678
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• 2007

An algorithm to detect the number of discontinuity points of the variance function in regression model is proposed. The proposed algorithm is based on the left and right one-sided kernel estimators of the second moment function and test statistics of the existence of a discontinuity point coming from the asymptotic distribution of the estimated jump size. The finite sample performance is illustrated by simulated example.

• Journal of the Korean Data and Information Science Society
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• v.21 no.1
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• pp.51-59
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• 2010

In the case that the regression function has a discontinuity point in generalized linear model, Huh (2009) estimated the location and jump size using the log-likelihood weighted the one-sided kernel function. In this paper, we consider estimation of the unknown number of the discontinuity points in the regression function. The proposed algorithm is based on testing of the existence of a discontinuity point coming from the asymptotic distribution of the estimated jump size described in Huh (2009). The finite sample performance is illustrated by simulated example.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.709-717
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• 2008

The difference of two one-sided kernel estimators is usually used to detect the location of the discontinuity points of regression function. The large absolute value of the statistic imply discontinuity of regression function, so we may use the difference of two one-sided kernel estimators as the test statistic for testing null hypothesis of a smooth regression function. The problem is, however, we only know the asymptotic distribution of the test statistic under $H_0$ and we hardly expect the good performance of test if we rely solely on the asymptotic distribution for determining the critical points. In this paper, we show that if we adjust the bias of test statistic properly, the asymptotic rules hold for even small sample size situation.

• ETRI Journal
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• v.34 no.1
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• pp.87-97
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• 2012

This study presents an automatic matching method for generating a dense, accurate, and discontinuity-preserved digital surface model (DSM) using multiple images acquired by an aerial digital frame camera. The proposed method consists of two main procedures: area-based multi-image matching (AMIM) and stereo-pair epipolar line matching (SELM). AMIM evaluates the sum of the normalized cross correlation of corresponding image points from multiple images to determine the optimal height of an object point. A novel method is introduced for determining the search height range and incremental height, which are necessary for the vertical line locus used in the AMIM. This procedure also includes the means to select the best reference and target images for each strip so that multi-image matching can resolve the common problem over occlusion areas. The SELM extracts densely positioned distinct points along epipolar lines from the multiple images and generates a discontinuity-preserved DSM using geometric and radiometric constraints. The matched points derived by the AMIM are used as anchor points between overlapped images to find conjugate distinct points using epipolar geometry. The performance of the proposed method was evaluated for several different test areas, including urban areas.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.89-98
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• 2011

The Fourier series has a rapid oscillation near end points at jump discontinuity which is called the Gibbs phenomenon. There is an overshoot (or undershoot) of approximately 9% at jump discontinuity. In this paper, we prove that a bunch of series representations (certain nonharmonic Fourier series) give good approximations vanishing Gibbs phenomenon. Also we have an application for approximating some shape of upper part of a vehicle in a different way from the method of cubic splines and wavelets.

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.271-279
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• 2014

Let $T_l$ be a transformation on the interval [-1, 1] defined by Chebyshev polynomial of degree $l(l{\geq}2)$, i.e., $T_l(cos{\theta})=cos(l{\theta})$. In this paper, we consider $T_l$ as a measure preserving transformation on [-1, 1] with an invariant measure $\frac{1}{\sqrt[\pi]{1-x^2}}dx$. We show that If f(x) is a nonconstant step function with finite k-discontinuity points with k < l-1, then it satisfies the Central Limit Theorem. We also give an explicit method how to check whether it satisfies the Central Limit Theorem or not in the cases of general step functions with finite discontinuity points.

• Geomechanics and Engineering
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• v.36 no.3
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• pp.205-215
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• 2024

Manually mapping fractures in construction stone mines is challenging, time-consuming, and hazardous. In this method, there is no physical access to all points. In contrast, digital image processing offers a safe, cost-effective, and fast alternative, with the capability to map all joints. In this study, two methods of detecting the trace of discontinuities using image processing in construction stone mines are presented. To achieve this, we employ two modified Hough transform algorithms and the degree of neighborhood technique. Initially, we introduced a method for selecting the best edge detector and smoothing algorithms. Subsequently, the Canny detector and median smoother were identified as the most efficient tools. To trace discontinuities using the mentioned methods, common preprocessing steps were initially applied to the image. Following this, each of the two algorithms followed a distinct approach. The Hough transform algorithm was first applied to the image, and the traces were represented through line drawings. Subsequently, the Hough transform results were refined using fuzzy clustering and reduced clustering algorithms, along with a novel algorithm known as the farthest points' algorithm. Additionally, we developed another algorithm, the degree of neighborhood, tailored for detecting discontinuity traces in construction stones. After completing the common preprocessing steps, the thinning operation was performed on the target image, and the degree of neighborhood for lineament pixels was determined. Subsequently, short lines were removed, and the discontinuities were determined based on the degree of neighborhood. In the final step, we connected lines that were previously separated using the method to be described. The comparison of results demonstrates that image processing is a suitable tool for identifying rock mass discontinuity traces. Finally, a comparison of two images from different construction stone mines presented at the end of this study reveals that in images with fewer traces of discontinuities and a softer texture, both algorithms effectively detect the discontinuity traces.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.137-141
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• 1986

This paper presents optimal recursive digital filter design to meet simultaneous specifications of magnitude and linear phase characteristics. As is well known, the overshoot in the vicinity of discontinuity is hight. The technique using linear programming (the dual programming) is choosing more specification points in the vicinity of band limit frequency. The resulting filter can shown improved response and numerical accuracy with reduced nonuniform specification points in frequency domain.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.899-908
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• 2008

If the regression function has jump points, nonparametric estimation method based on local smoothing is not statistically consistent. Therefore, when we estimate regression function, it is quite important to know whether it is reasonable to assume that regression function is continuous. If the regression function appears to have jump points, then we should estimate first the location of jump points. In this paper, we propose a procedure which can do both the testing hypothesis of discontinuity of regression function and the estimation of the number and the location of jump points simultaneously. The performance of the proposed method is evaluated through a simulation study. We also apply the procedure to real data sets as examples.

• Tunnel and Underground Space
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• v.13 no.1
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• pp.33-43
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• 2003

Field investigations of the orientations of discontinuity planes inside the borehole for designing the underground rock structures have been depend solely on the borehole image-taking techniques. But, borehole image-taking has to be processed after the completion of drilling operation and also requires the handling of highly expensive apparatus so that practical application is very restricted. In this study Discontinuity Orientation Measurement (DOM) drilling system and discontinuity analysis model RoSA-DOM are developed to acquire the reliable information of rock structure by analyzing the characteristics of joint distribution. DOM drilling system retrieves the rock core on which the reference line of pre-fixed drilling orientation is engraved. Coordinates of three arbitrary points on the joint surface relative to the position of reference line are assessed to determine the orientation of joint plane. The position of joint plane is also allocated by calculating the location of core axis at which joint plane is intersected. Then, the formation of joint set is analyzed by utilizing the clustering algorithm. Total and set spacings are calculated by considering the borehole axis as the scanline. Engineering applicability of in-situ rock mass around the borehole is also estimated by calculating the total and regional RQDs along the borehole axis.