• Journal of Positioning, Navigation, and Timing
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• v.9 no.1
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• pp.23-31
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• 2020

It is essential to estimate the vehicle localization for an autonomous safety driving. In particular, since LIDAR provides precise scan data, many studies carried out to estimate the vehicle localization using LIDAR and pre-generated map. The road marking always exists on the road because of provides driving information. Therefore, it is often used for map information. In this paper, we propose to generate the Gaussian mixture map based on road-marking information and localization method using this map. Generally, the probability distributions map stores the single Gaussian distribution for each grid. However, single resolution probability distributions map cannot express complex shapes when grid resolution is large. In addition, when grid resolution is small, map size is bigger and process time is longer. Therefore, it is difficult to apply the road marking. On the other hand, Gaussian mixture distribution can effectively express the road marking by several probability distributions. In this paper, we generate Gaussian mixture map and perform vehicle localization using Gaussian mixture map. Localization performance is analyzed through the experimental result.

• IEIE Transactions on Smart Processing and Computing
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• v.2 no.6
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• pp.332-338
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• 2013

We propose a method for target detection in Infrared images. In order to effectively detect a target region from an image with noises and clutters, spatial information of the target is first considered by analyzing pixel distributions of projections in horizontal and vertical directions. These distributions are represented as Gaussian distributions, and Gaussian Mixture Model is created from these distributions in order to find thresholding points of the target region. Through analyzing the calculated Gaussian Mixture Model, the target region is detected by eliminating various backgrounds such as noises and clutters. This is performed by using a novel thresholding method which can effectively detect the target region. As experimental results, the proposed method has achieved better performance than existing methods.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.633-645
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• 2018

Gaussian error distributions are a common choice in traditional regression models for the maximum likelihood (ML) method. However, this distributional assumption is often suspicious especially when the error distribution is skewed or has heavy tails. In both cases, the ML method under normality could break down or lose efficiency. In this paper, we consider the log-concave and Gaussian scale mixture distributions for error distributions. For the log-concave errors, we propose to use a smoothed maximum likelihood estimator for stable and faster computation. Based on this, we perform comparative simulation studies to see the performance of coefficient estimates under normal, Gaussian scale mixture, and log-concave errors. In addition, we also consider real data analysis using Stack loss plant data and Korean labor and income panel data.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.246-249
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• 2009

Due to the additive white Gaussian noise (AWGN), images are often corrupted. In recent days, Bayesian estimation techniques to recover noisy images in the wavelet domain have been studied. The probability density function (PDF) of an image in wavelet domain can be described using highly-sharp head and long-tailed shapes. If a priori probability density function having the above properties would be applied well adaptively, better results could be obtained. There were some frequently proposed PDFs such as Gaussian, Laplace distributions, and so on. These functions model the wavelet coefficients satisfactorily and have its own of characteristics. In this paper, mixture distributions of Gaussian and Laplace distribution are proposed, which attempt to corporate these distributions' merits. Such mixture model will be used to remove the noise in images by adopting Maximum a Posteriori (MAP) estimation method. With respect to visual quality, numerical performance and computational complexity, the proposed technique gained better results.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.28 no.3
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• pp.171-176
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• 2016

The distribution shapes of air and water temperatures are basic and essential information, which determine the frequency patterns of their occurrence. It is also very useful to understand the changes in long-term air and water temperatures with respect to climate change. The typical distribution shapes of air and water temperatures cannot be well fitted using widely used/accepted normal distributions because their shapes show multimodal distributions. In this study, Gaussian mixture distributions and kernel distributions are suggested as the more suitable models to fit their distribution shapes. Based on the results, the tail shape exhibits different patterns. The tail is long in higher temperature regions of water temperature distribution and in lower temperature regions of air temperature distribution. These types of shape comparisons can be useful to identify the patterns of long-term air and water temperature changes and the relationship between air and water temperatures. It is nearly impossible to identify change patterns using only mean-temperatures and normal distributions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.129-142
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• 2014

We propose a variational segmentation model based on statistical information of intensities in an image. The model consists of both a local region-based energy and a global region-based energy in order to handle misclassification which happens in a typical statistical variational model with an assumption that an image is a mixture of two Gaussian distributions. We find local ambiguous regions where misclassification might happen due to a small difference between two Gaussian distributions. Based on statistical information restricted to the local ambiguous regions, we design a local region-based energy in order to reduce the misclassification. We suggest an algorithm to avoid the difficulty of the Euler-Lagrange equations of the proposed variational model.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.89-97
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• 2021

Due to boundedness and sum constraint, compositional data are often transformed by logratio transformation and their transformed data are put into traditional binary classification or discriminant analysis. However, it may be problematic to directly apply traditional multivariate approaches to the transformed data because class distributions are not Gaussian and Bayes decision boundary are not polynomial on the transformed space. In this study, we propose to use flexible classification approaches to transformed data for compositional data classification. Empirical studies using synthetic and real examples demonstrate that flexible approaches outperform traditional multivariate classification or discriminant analysis.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.6
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• pp.725-730
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• 2007

Gray-level histogram-based threshold selection methods such as Otsu's method, Huang and Wang's method, and etc. have been widely used for the threshold selection in image processing. They are simple and effective, but take too much time to determine the optimal multilevel threshold values as the number of thresholds are increased. In this paper, we measure correlation between gray-levels by using the Gaussian function and define a Gaussian-type finite mixture distribution which is combination of the Gaussian distribution function with the gray-level histogram, and propose a fast and effective threshold selection method using it. We show the effectiveness of the proposed through experimental results applied it to three images and the efficiency though comparison of the computational complexity of the proposed with that of Otsu's method.

• The Korean Journal of Applied Statistics
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• v.22 no.4
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• pp.759-770
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• 2009

A problem of separating signals from noises is considered, when they are randomly mixed in the observation. It is assumed that the noise follows a Gaussian distribution and the signal follows a Gamma distribution, thus the underlying distribution of an observation will be a mixture of Gaussian and Gamma distributions. The parameters of the mixture model will be estimated from the EM algorithm. Then the signals and noises will be classified by a fixed threshold approach based on multiple testing using positive false discovery rate and Bayes error. The proposed method is applied to a real optical emission spectroscopy data for the quantitative analysis of inclusions. A simulation is carried out to compare the performance with the existing method using 3 sigma rule.

• Journal of Communications and Networks
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• v.18 no.2
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• pp.182-189
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• 2016

The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.