• The Journal of the Korea Contents Association
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• v.3 no.3
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• pp.11-18
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• 2003

Error diffusion is a procedure for generating high quality bilevel images from continuous-tone images but blurs the edge information. To solve this problem, we propose the improved method appling edge enhanced weights based on local characteristic of the original images. We consider edge information as local characteristic. First, we produce edges by appling 3$\times$3 sobel operator to the original image. The edge is normalized from 0 to 1. Edge information weights are computed by using sinusoidal function and the normalized edge information. The edge enhanced weights are computed by using edge information weights multiplied input pixels. The proposed method is compared with conventional methods by measuring the edge correlation and quality of the recovered images from the halftoned images. The proposed method provides better quality than the conventional method due to the enhanced edge and represents efficiently the detail edge. Also, the proposed method is improved in edge representation than the conventional method.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.38 no.1
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• pp.1-10
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• 2001

In order to generate the gray scale image by the binary state imaging devices such as a digital printer, the gray scale image needs to be converted into the binary image by the halftoning techniques. This paper presents a new error diffusion technique to achieve the homogeneous dot distributions on the binary images. In this paper,'the minimum pixel distance'from the current pixel under binarization to the nearest minor pixel is defined first. Also, the gray levels of the input image are converted into a new variable based on the principal distance for the error diffusion. In the proposed method, the difference in the principal distances is utilized for the error propagation, whereas the gray level difference due to the binarization is diffused to the neighboring pixels in the existing error diffusion techniques. The quantization is accomplished by comparing the updated principal distance with the minimum pixel distance. In order to calculate the minimum pixel distance, MPOA(Minor Pixel Offset Array) is employed to reduce the computational loads and memory resources.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.221-237
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• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Bulletin of the Society of Naval Architects of Korea
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• v.19 no.4
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• pp.19-29
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• 1982

Galerkin's finite element method is applied to a two-dimensional heat convection-diffusion problem arising in the hydrodynamic lubrication of thrust bearings used in naval vessels. A parabolized thermal energy equation for the lubricant, and thermal diffusion equations for both bearing pad and the collar are treated together, with proper juncture conditions on the interface boundaries. it has been known that a numerical instability arises when the classical Galerkin's method, which is equivalent to a centered difference approximation, is applied to a parabolic-type partial differential equation. Probably the simplest remedy for this instability is to use a one-sided finite difference formula for the first derivative term in the finite difference method. However, in the present coupled heat convection-diffusion problem in which the governing equation is parabolized in a subdomain(Lubricant), uniformly stable numerical solutions for a wide range of the Peclet number are obtained in the numerical test based on Galerkin's classical finite element method. In the present numerical convergence errors in several error norms are presented in the first model problem. Additional numerical results for a more realistic bearing lubrication problem are presented for a second numerical model.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.603-618
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• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• Honam Mathematical Journal
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• v.32 no.2
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• pp.193-202
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• 2010

We investigate the estimation of the moisture transfer coefficients in porous media by optimization technique which minimizes the functional defined by the squares error of the numerical solution of an inverse diffusion problem from their experimental values of the moisture content at the some time-steps. In this paper, we solve a diffusion equation numerically by the control volume finite element methods.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.183-200
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• 2019

We have constructed a robust numerical method on Shishkin mesh for a class of convection diffusion type turning point problems with Robin type boundary conditions. Supremum norm is used to derive error estimates which is of order O($N^{-1}$ ln N). Theoretical results are verified by providing numerical examples.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.815-832
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• 1999

High-order weighted difference schemes with uniform meshes are considered for the convection-diffusion problem depending on Reynolds numbers. For small Reynolds numbers, a weighed cen-tral difference scheme is suggested since there is no boundary layer. For large Reynolds numbers, we propose a modified up wind method with an artificial diffusion in order to overcome nonphysical oscilla-tion of central schemes and obtain good accuracy in the boundary later. Existence and corresponding error estimates of the solution for the difference scheme have been shown. Numerical experiments are provided to back up the analysis.

• Proceedings of the KOSOMBE Conference
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• v.1994 no.12
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• pp.9-13
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• 1994

The Heat Anisotropic Diffusion Method has shown very effective for the contour detection of 2-D echocardiogram. To implement this algorithm, we have to choose the parameter C, K, and the threshold level. The choice of C and K are not very sensitive for the good edge detection of the echocardiogram, however the choice of the threshold level is very critical. Until now the threshold level is chosen by the trial and error method. In this paper, we present an automatic threshold decision method from the histogram of the gradient of boundary-like pixels.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.3
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• pp.111-120
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• 2004

This paper proposes a vector error diffusion method for smear artifact reduction in the boundary region. This artifact mainly results from a large accumulation of quantization errors. In particular, color bands with a smear artifact, the width of a few pixels appear along the edges. Accordingly, to reduce this artifact, the proposed halftoning process excludes the large accumulated Quantization error by comparing the vector norms and vector angles between the error-corrected vector and eight primary color patches. When the vector norm of the error corrected vector is larger than those of eight primary color patches, the quantization error vector is excluded from the quantization error distribution process. In addition, the quantization error is also excluded when the angle between eight primary color patches and error corrected vector is large. As a result, the proposed method enables a visually pleasing halftone pattern to be generated by all three color separations into account in a device- independent color space and reduces smear artifact in the boundary regions.