• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1471-1484
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• 2020

It may very well be difficult to prove an eigenvalue inequality of Payne-Pólya-Weinberger type for the bi-drifting Laplacian on the bounded domain of the general complete metric measure spaces. Even though we suppose that the differential operator is bi-harmonic on the standard Euclidean sphere, this problem still remains open. However, under certain condition, a general inequality for the eigenvalues of bi-drifting Laplacian is established in this paper, which enables us to prove an eigenvalue inequality of Ashbaugh-Cheng-Ichikawa-Mametsuka type (which is also called an eigenvalue inequality of Payne-Pólya-Weinberger type) for the eigenvalues with lower order of bi-drifting Laplacian on the Gaussian shrinking soliton.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.3
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• pp.735-741
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• 2014

Edge in images appears when a great difference shows up in light and shade between pixels and includes data of the subject's size, location direction and etc. The edge is generally detected by the methods such as Sobel, Roberts, Laplacian, LoG(Laplacian of Gaussian) and etc. However, in AWGN(additive white Gaussian noise) added images, quality of the edge becomes slightly uncertain. Therefore, this paper proposed edge detection algorithm using modified mask of weighting to improve the quality of the existing methods. And in order to verify the performance efficiency of the proposed method, processed image and PFOM(Pratt's figure of merit) has been used as valuation standard for a comparison with the existing methods.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.05a
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• pp.787-789
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• 2017

Edge detection is used in many applications such as image analysis, pattern recognition and computer vision. Existing edge detection methods, there is such Sobel, Prewitt, Roberts, and LoG(Laplacian of Gaussian). In the conventional edge detection method, edge detection is insufficient because the change of the pixel brightness is small when the original image is in low illumination. Therefore, in this paper, we proposed a function to convert the pixel brightness of low illumination image to solve this problem. And it was compared by applying the conventional methods Sobel, Prewitt, Roberts, LoG(Laplacian of Gaussian) to determine the performance of the pixel brightness transform function.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.6C
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• pp.384-390
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• 2011

The paper derives formulas for the mean-squared error distortion and resulting signal-to-noise (SNR) ratio of a fixed-rate scalar quantizer designed optimally in the minimum mean-squared error sense for a Gaussian density with the standard deviation ${\sigma}_q$ when it is mismatched to a Laplacian density with the standard deviation ${\sigma}_q$. The SNR formulas, based on the key parameter and Bennett's integral, are found accurate for a wide range of $p\({\equiv}\frac{\sigma_p}{\sigma_q}\){\geqq}0.25$. Also an upper bound to the SNR is derived, which becomes tighter with increasing rate R and indicates that the SNR behaves asymptotically as $\frac{20\sqrt{3{\ln}2}}{{\rho}{\ln}10}\;{\sqrt{R}}$ dB.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.7
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• pp.1680-1686
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• 2015

Edge detection is an essential preprocessing for most image processing application, and there are several existing detection methods such as Sobel, Roberts, Laplacian, LoG(Laplacian of Gaussian) operators, etc. Those existing edge detection methods have not given satisfactory results since they do not offer enough pixel brightness change in low light level environment. Therefore, in this study new algorithms using brightness transfer function in the preprocessing and for edge detection applying standard deviation and average-weighted local masks are proposed. In addition, the performance of proposed algorithms was evaluated in comparison with the existing edge detection methods such as Sobel, Roberts, Prewitt, Laplacian, LoG operators.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.259-269
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• 1993

A moving average model, LMA(q) and an autoregressive-moving average model, NLARMA(p, q), with Laplacian marginal distribution are constructed and their properties are discussed; Their autocorrelation structures are completely analogus to those of Gaussian process and they are partially time reversible in the third order moments. Finally, we study the mixing property of NLARMA process.

• The Journal of the Acoustical Society of Korea
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• v.30 no.6
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• pp.308-314
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• 2011

This paper presents techniques for estimating directions of multiple sound sources ranging from $0^{\circ}$ to $360^{\circ}$ using circular probability distributions having a periodic property. Phase differences containing direction information of sources can be modeled as mixtures of multiple probability distributions and source directions can be estimated by maximizing log-likelihood functions. Although the von Mises distribution is widely used for analyzing this kind of periodic data, we define a new class of circular probability distributions from Gaussian and Laplacian distributions by adopting a modulo operation to have $2{\pi}$-periodicity. Direction estimation with these circular probability distributions is done by implementing corresponding EM (Expectation-Maximization) algorithms. Simulation results in various reverberant environments confirm that Laplacian distribution provides better performance than von Mises and Gaussian distributions.

• Journal of Korea Multimedia Society
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• v.15 no.6
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• pp.711-721
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• 2012

The objective of this study is to propose an efficient 3D reconstruction method for developing a stereo-vision-based haptics system which can replace "robotic eyes" and "robotic touch." The haptic rendering for 3D images requires to capture depth information and edge information of stereo images. This paper proposes the 3D reconstruction methods using LoG(Laplacian of Gaussian) algorithm and DoG(Difference of Gaussian) algorithm for edge detection in addition to the basic 3D depth extraction method for better haptic rendering. Also, some experiments are performed for evaluating the CPU time and the error rates of those methods. The experimental results lead us to conclude that the DoG method is more efficient for haptic rendering. This paper may contribute to investigate the effective methods for 3D image reconstruction such as in improving the performance of mobile patrol robots.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.37 no.2
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• pp.25-32
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• 2000

Digital watermarking has been recently proposed as the means of intellectual property right protection of multimedia data. We present a novel watermarking scheme to hide a copyright information in a digital image. The method Is based on the 2D DWT(Discrete Wavelet Transform) and image statistics. Gaussian and Laplacian noises as the watermarks are added to the large wavelet coefficients at the high and middle frequency bands in the wavelet domain. Experimental results show that the proposed Laplacian watermark is stronger to several common image distortions, such as noises, JPEG coding as different qualities, Gaussian blurring, and edge enhancement.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.8
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• pp.1973-1980
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• 2014

Edge detection for such as image, lane and object recognition is important image processing method. And some traditional method for this, there are Sobel, Prewitt, Roberts, Laplacian, LoG(Laplacian of Gaussian) and so on. Characteristics of these methods are insufficient in the salt & pepper noise added image. In order to improve such a problem of conventional methods, in this paper, we proposed an algorithm applying the weighted mask for detecting an edge by setting the local mask centered on the adjacent of the central pixel if central pixel of the mask is non-noise, it is intactly set by element of estimated mask, after calculating estimated mask if it is noise.