• Journal of the Korean Data and Information Science Society
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• 제18권3호
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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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• 제21권1호
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• pp.51-59
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• 2010

일반화선형모형에서 회귀함수가 하나의 불연속점을 가질 때, Huh (2009)는 하나의 모수를 가지는 지수족의 가능도함수를 한쪽방향커널을 이용하여 그 불연속점의 위치와 점프크기를 추정하였다. 이 논문에서는 미지의 불연속점 수 q개를 가지는 회귀함수인 경우에, Huh (2009)가 제안한 점프크기 추정량의 점근분포를 이용한 가설검정법을 소개하고, 그 가설검정법을 이용한 불연속점 수를 추정하는 알고리듬을 제안하고, 모의실험을 통하여 추정의 정도를 알아보고자 한다.

• Communications for Statistical Applications and Methods
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• 제15권5호
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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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• 제34권1호
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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.

• 대한수학회논문집
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• 제26권1호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권4호
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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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• 제36권3호
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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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• 제어로봇시스템학회 1986년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 17-18 Oct. 1986
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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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• 제15권6호
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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.

• 터널과지하공간
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• 제13권1호
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• pp.33-43
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• 2003

암반구조물 설계를 위한 지반조사에서 지하 암반에 분포된 불연속면들의 방향성 파악은 시추공 내부에 대한 영상촬영 기법에 전적으로 의존되어 왔다. 그러나, 공내 영상촬영은 고가의 장비가 요구되며 시추작업 완료 후 측정작업이 추가로 소요되어 극히 제한적으로 수행되고 있다. 본 연구에서는 시추조사시 간편하게 불연속면의 방향을 측정하여 신뢰성 있는 지반정보 자료를 제공할 수 있는 Discontinuity Orientation Measurement (DOM) 시추장비 및 불연속면 분포해석 모델 RoSA-DOM을 개발하였다. DOM 시추 장비에서 기 설정된 방향성을 지시하는 기준선이 표시된 시추 코어가 회수되면 코어 상의 절리 단면에서 측정된 3개 지점의 자표를 이용하여 절리면의 경사방향 및 경사각을 산정한다. 또한 코어 축이 절리면을 관통하는 지점의 좌표를 산정하여 절리 위치를 설정한다. 절리군 형성은 clustering algerian을 활용하여 분석한다. 코어 축을 조사선으로 설정하여 전체 절리 간격 및 군 간격을 해석한다. 전체 시추구간 및 특정 구역에서의 RQD를 산정하여 암반의 공학적 활용도 고찰을 위한 기본 자료를 도출한다.