• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.309-319
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• 1995

Let (M,g) be an m-dimensional compact orientable Riemannian manifold(connected and $C^\infty$) with metric tensor g.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.87-95
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• 1996

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.451-459
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• 2021

We propose the infinity wave equation which can be derived from the exponential wave equation through the limit p → ∞. The solution of infinity Laplacian equation can be considered as a static solution of the infinity wave equation. We present basic observations and find some special solutions.

• Journal of Computing Science and Engineering
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• v.6 no.3
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• pp.219-226
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• 2012

Recently, shape analysis of human organs has achieved much attention, owing to its potential to localize structural abnormalities. For a group-wise shape analysis, it is important to accurately restore the shape of a target structure in each subject and to build the inter-subject shape correspondences. To accomplish this, we propose a shape modeling method based on the Laplacian deformation framework. We deform a template model of a target structure in the segmented images while restoring subject-specific shape features by using Laplacian surface representation. In order to build the inter-subject shape correspondences, we implemented the progressive weighting scheme for adaptively controlling the rigidity parameter of the deformable model. This weighting scheme helps to preserve the relative distance between each point in the template model as much as possible during model deformation. This area-preserving deformation allows each point of the template model to be located at an anatomically consistent position in the target structure. Another advantage of our method is its application to human organs of non-spherical topology. We present the experiments for evaluating the robustness of shape modeling against large variations in shape and size with the synthetic sets of the second cervical vertebrae (C2), which has a complex shape with holes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.10C
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• pp.991-999
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• 2006

This paper shows that the support growth of an optimum (minimum mean square-error) scalar quantizer for a Laplacian density is logarithmic with the number of quantization points. Specifically, it is shown that, for a unit-variance Laplacian density, the ratio of the support-determining threshold of an optimum quantizer to $\frac 3{\sqrt{2}}1n\frac N 2$ converges to 1, as the number of quantization points grows. Also derived is a limiting upper bound that says that the optimum support cannot exceed the logarithmic growth by more than a constant. These results confirm the logarithmic growth of the optimum support that has previously been derived heuristically.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.44 no.6
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• pp.111-117
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• 2007

This paper presents a novel approach to speech enhancement based on a complex Laplacian probability density function (pdf). With a use of goodness-of-fit (GOF) test we show that the complex Laplacian pdf is more suitable to describe the conventional Gaussian pdf. The likelihood ratio (LR) is applied to derive the speech absence probability in the speech enhancement algorithm. The performance of the proposed algorithm is evaluated by the objective test and yields better results compared with the conventional Gaussian pdf-based scheme.

• 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.

• Journal of Korea Water Resources Association
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• v.32 no.4
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• pp.437-445
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• 1999

The present paper describes the problem of hydrologic response estimation using non-parametric ridge regression method. The method adapted in this work is based on the minimization of the $C_L$ statistics, which is an estimate of the mean square prediction error. For this method, effects of using both the identity matrix and the Laplacian matrix were considered. In addition, we evaluated methods for estimating the error variance of the impulse response. As a result of analyzing synthetic and real data, a good estimation was made when the Laplacian matrix for the weighting matrix and the bias corrected estimate for the error variance were used. The method and procedure presented in present paper will play a robust and effective role on separating hydrologic response.

• 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.

• 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.