• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.5
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• pp.77-85
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• 2004

This paper proposes a multi-level vector error diffusion method using 64 primary colors to improve color impulse artifact in bright region. Vector error diffusion method causes color impulse artifact in bright region because we only use the Euclidean distance measure in quantization process. In order to reduce this artifact, the proposed method divides input color into chromatic color and achromatic color according to chroma value. In the case of chromatic color, input color is classified into bright region, middle bright region, and dark region according to lightness value. N candidate primary color is organized using lightness difference between input vector and 60 chromatic primary color vector in the case of bright region. Then, primary color with minimum vector norm between input vector and N candidate primary color in addition to 4 achromatic primary colors is selected as output color. As a result of experiments, the proposed method showed visually pleasing halftone output.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.4
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• pp.87-92
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• 2004

Digital halftoning is to quantize a grayscale image to binary image. The error diffusion halftoning generates high quality bilevel image. But that also has some defects such as warms effect, sharpening and etc. To reduce these defects, Kite proposed the modified threshold modulation that has a parameter to control sharpening. Nevertheless some degradation left near edges with large luminance change. In this paver, we propose a method to control the parameter in proportional to local edge magnitude. The results of computer simulation show more reductions of the sharpening in the halftone image. Especially there are great improvement of quality near edges with large luminance change.

• Journal of Korea Multimedia Society
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• v.8 no.3
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• pp.313-321
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• 2005

Digital halftoning is a process to produce a binary image so that the original image and its binary counterpart appear similar when observed from a distance. Among digital halftoning methods, error diffusion is a procedure for generating high quality bilevel images from continuous-tone images but blurs the edge information in the bilevel images. To solve this problem, we propose the improved error diffusion using local spatial information of the original images. Based on the fact that the human vision perceives not a pixel but local mean of input image, we compute edge enhancement information(EEI) by appling the ratio of a pixel and its adjacent pixels to local mean. The weights applied to local means is computed using the ratio of local activity measure(LAM) to the difference between input pixels of 3$\times$3 blocks and theirs mean. LAM is the measure of luminance changes in local regions and is obtained by adding the square of the difference between input pixels of 3$\times$3 blocks and theirs mean. We add the value to a input pixel of quantizer to enhance edge. The performance of the proposed method is compared with conventional methods by measuring the edge correlation. The halftone images by using the proposed method show better quality due to the enhanced edge. And the detailed edge is preserved in the halftone images by using the proposed method. Also the proposed method improves the quality of halftone images because unpleasant patterns for human visual system are reduced.

• The KIPS Transactions:PartB
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• v.13B no.2 s.105
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• pp.77-82
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• 2006

Digital halftoning is the technique to obtain a bilevel-toned image from continuous-toned image. Among halftoning methods, the error diffusion method gives better subjective quality than other halftoning ones. But it also makes edges of objects blurred. To overcome the defect, we proposes the modified error diffusion to enhance the edges using the property that human vision perceives the local average luminance and doesn't perceive a little variation of the spatial variation. The proposed method computes a spatialactivity, which is the difference between a pixel luminance and the average of its $3{\times}3$ neighborhood pixels' Iuminance weighted according to the spatial positioning. The system also usesof edge enhancement (IEE), which is computed from the normalized spatial activitymultiplied by the average luminance. The IEE is added to the quantizer's input pixel and feeds into the halftoning quantizer. The quantizer produces the halftone image having the enhanced edge. The computer experimental results show that the proposed method produces clearer bilevel-toned images than conventional methodsand the edge of objects is preserved well. Also the performance of the preposed method is improved, compared with that of the conventional method by measuring the edge correlation and the local average accordance at some ranges of viewing distance.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.31-48
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• 2010

In this article, we consider singularly perturbed Boundary Value Problems(BVPs) for second order Ordinary Differential Equations (ODEs) with Neumann boundary condition and discontinuous source term. A parameter-uniform error bound for the solution is established using the Streamline-Diffusion Finite Element Method (SDFEM) on a piecewise uniform meshes. We prove that the method is almost second order of convergence in the maximum norm, independently of the perturbation parameter. Further we derive superconvergence results for scaled derivatives of solution of the same problem. Numerical results are provided to substantiate the theoretical results.

• Journal of Digital Convergence
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• v.12 no.1
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• pp.415-421
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• 2014

In this paper, we proposed problem and improvement of halftoning using random space filling curve. Random space filling curve is developed as a solution for shortcoming which space filling curve has self-similarity. It is used to reduce regular pattern can be occurred in constant brightness area in order that randomness apply to scanning path. But there is a problem that some area along scanning path can show too bright result in halftoning using random space filling curve. In this paper, we analyzed cause of problem and proposed single pixel error diffusion as a solution method. This method can avoid over-accumulated error and show better result in halftoning.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.699-713
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• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.517-529
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• 2009

In this paper, a singularly perturbed reaction-convection-diffusion problem with two parameters is considered. A parameter-uniform error bound for the numerical derivative is derived. The numerical method considered here is a standard finite difference scheme on piecewise-uniform Shishkin mesh, which is fitted to both boundary and initial layers. Numerical results are provided to illustrate the theoretical results.

• Journal of the Korean Recycled Construction Resources Institute
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• v.9 no.3
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• pp.375-382
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• 2021

Self-healing concrete is in the spotlight in that it can effectively extend the lifespan of concrete structures by healing cracks in the structure by themselves without additional repairing or retrofiting actions. Currently, self-healing concrete is a field that is being actively studied around the world, but since most studies focus on the improvement of healing performance, there is a lack of methods to rationally evaluate the self-healing performance of concrete. Although the gas diffusion test method has been developed for the use in the performance evaluation of self-healing concrete, it has revealed that for gas diffusion through the matrix affect the crack diffusion coefficients depending on the environmental conditions such as the saturation of the specimen, the temperature, and humidity during the experiment. Therefore, in this study, the method has been proposed to eliminate the influence of the matrix diffusion when calculating the crack diffusion coefficient. In addition, a pre-conditioning process was introduced to shorten the experimental time. As a result, the crack width could be estimated with an error level of less than 3% in the test time of about 20 minutes.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.2
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• pp.194-200
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• 2002

A method for simulating flow of extremely low Reynolds number in a vortex-in-cell (VIC) was studied. The viscous diffusion was represented by the random walk method. The validity of this method was proven by applying it to the flows passing over a fence placed vertically at an extremely low Reynolds number. The effects of parameters of the VIC method on the random walk method, such as the number of point vortices, the mesh density and the time increment, were investigated by numerical analysis using a one-dimensional diffusion equation. Changes in the relative error of vorticity depending on those parameters were clarified.