• Journal of KIISE
• /
• v.44 no.11
• /
• pp.1194-1208
• /
• 2017

A traditional average smoothing method is designed for smoothing out noise, which, however, unintentionally results in smooth corner points on the curvature accompanied with a shrinkage of curves. In this paper, we propose a novel curve smoothing method via polygonal approximation of the input curve. The proposed method determines the smoothing weight for each point of the input curve based on the angle and approximation error between the approximated polygon and the input curve. The weight constrains a displacement of the point after smoothing not to significantly exceed the average noise error of the region. In the experiment, we observed that the resulting smoothed curve is close to the original curve since the point moves toward the average position of the noise after smoothing. As an application to digital cartography, for the same amount of smoothing, the proposed method yields a less area reduction even on small curve segments than the existing smoothing methods.

• Journal of KIISE
• /
• v.42 no.6
• /
• pp.769-780
• /
• 2015

Smoothing a digital curve by averaging its connected points is widely employed to minimize sharp changes of the curve that are generally introduced by noise. An appropriate degree of smoothing is critical since the area or features of the original shape can be distorted at a higher degree while the noise is insufficiently removed at a lower degree. In this paper, we provide a mathematical relationship between the parameters, such as the number of iterations, average distance between neighboring points, weighting factors for averaging and the moving distance of the point on the curve after smoothing. Based on these findings, we propose to control the smoothed curve such that its deviation is bounded particular error level as well as to significantly expedite smoothing for a pixel-based digital curve.

• Journal of applied mathematics & informatics
• /
• v.8 no.3
• /
• pp.731-742
• /
• 2001

A Gaussian smoothing algorithm obtained from a cascade of convolutions with a seven-point kernel is described. We prove that the change of local sums after applying our algorithm to sinusoidal signals is reduced to about two thirds of the change by the binomial coefficients. Hence, our seven point kernel is better than the binomial coefficients when trend curves are needed to be generated. We also prove that if our Gaussian convolution is applied to sinusoidal functions, the amplitude of higher frequencies reduces faster than the lower frequencies and hence that it is a low pass filter.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.43 no.3 s.345
• /
• pp.49-58
• /
• 2006

In this paper, a curve-fitting channel estimation method is proposed for orthogonal frequency division multiplexing (OFDM) system in a time-varying frequency-selective fading channel. The method can greatly improve channel state information (CSI) estimation accuracy by performing smoothing and interpolation through consecutive curve-fitting processes in both time domain and frequency domain. It first evaluates least-squares (LS) estimates using pilot symbols and then the estimates are approximated to a polynomial with proper degree in the LS error sense, starting from one preferred domain in which pilots we densely distributed. Smoothing, interpolation, and prediction are performed subsequently to obtain CSI estimates for data transmission. The channel estimation processes are completed by smoothing and interpolating CSI estimates in the other domain once again using the channel estimates obtained in one domain. The performance of proposed method is influenced heavily on the time variation and frequency selectivity of channel and pilot arrangement. Hence, a proper degree of polynomial and an optimum approximation interval according to various system and channel conditions are required for curve-fitting. From extensive simulation results in various channel environments, we see that the proposed method performs better than the conventional methods including the optimal Wiener filtering method, in terms of the mean square error (MSE) and bit error rate (BER).

• Communications for Statistical Applications and Methods
• /
• v.16 no.3
• /
• pp.519-528
• /
• 2009

This paper deals with nonparametric estimation of discontinuous regression curve. Quite number of researches about this topic have been done. These researches are classified into two categories, the indirect approach and direct approach. The major goal of the indirect approach is to obtain good estimates of jump locations, whereas the major goal of the direct approach is to obtain overall good estimate of the regression curve. Thus it seems that two approaches are quite different in nature, so people say that the comparison of two approaches does not make much sense. Therefore, a thorough comparison of them is lacking. However, even though the main issue of the indirect approach is the estimation of jump locations, it is too obvious that we have an estimate of regression curve as the subsidiary result. The point is whether the subsidiary result of the indirect approach is as good as the main result of the direct approach. The performance of two approaches is compared through a simulation study and it turns out that the indirect approach is a very competitive tool for estimating discontinuous regression curve itself.

• Communications for Statistical Applications and Methods
• /
• v.23 no.3
• /
• pp.189-201
• /
• 2016

In survival analysis, the Nelson-Aalen estimator and Peterson estimator are often used to estimate a cumulative hazard function in randomly right censored data. In this paper, we suggested the smoothing version of the cumulative hazard function estimators using a Bezier curve. We compare them with the existing estimators including a kernel smooth version of the Nelson-Aalen estimator and the Peterson estimator in the sense of mean integrated square error to show through numerical studies that the proposed estimators are better than existing ones. Further, we applied our method to the Cox regression where covariates are used as predictors and suggested a survival function estimation at a given covariate.

• The Korean Journal of Applied Statistics
• /
• v.25 no.6
• /
• pp.1049-1058
• /
• 2012

Nonparametric methods are often used as an alternative to parametric methods to estimate density function and regression function. In this paper we consider improved methods to select the Bezier points in Bezier curve smoothing that is shown to have the same asymptotic properties as the kernel methods. We show that the proposed methods are better than the existing methods through numerical studies.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.10 no.9
• /
• pp.2326-2333
• /
• 2009

In the adaptable bandwidth allocation technique, a transmission plan for variable rate video data is made by smoothing algorithms such as CBA algorithm and the data is sent by the transmission plan considering network traffic. But the CBA algorithm, the MCBA algorithm, MVBA algorithm and the other smoothing algorithms produce a transmission plan where the size of the increasing interval of transmission rate is generally larger than the size of the decreasing interval. And the transmission rate in CBA algorithm, the MCBA algorithm, the MVBA algorithm is changed in overflow curve during the increasing interval of transmission rate. This may cause many frames to be discarded when available transmission rate is larger than transmission rate by the transmission plan. In this paper, the smoothing algorithm, where transmission rate is changed in the middle of underflow curve and overflow curve to decrease the number of discarded frames, but the transmission rate increases at the minimum, and the CBA algorithm, the MCBA algorithm, the MVBA algorithm are applied to a transmission plan in the adaptable bandwidth allocation technique, and the minimum frame rates, the average frame rates, the variation of frame rates, and the numbers of discarded frames are compared in among algorithms.

• Journal of Korean Society for Quality Management
• /
• v.25 no.4
• /
• pp.106-114
• /
• 1997

The smoothing parameter or bandwidth is crucial to performance of the kernel based regression estimator. So the choice of a "optimal" smoothing parameter produce a single curve estimate. If a single estimate is replaced by a family of estimates, it become easy that we understand what varies with choice of the smoothing parameter. This paper suggests the threshold of the maximum bandwidth and the number of the family members in the regression context.n context.

• Journal of Korean Society for Quality Management
• /
• v.32 no.4
• /
• pp.265-273
• /
• 2004

We got the growth distance curve by spline smoothing method with observed marketing data and the growth velocity curve by the derivation of the growth distance curve. Using this growth velocity curve, we defined the several characteristic points which describe the variation of marketing data. In this paper, to specify several patterns of marketing data, we suggested characteristic function by using these characteristic points. In addition, we applied characteristic function to the seventeen brands of electric home products data.