• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.97-101
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• 1987

The edge, a discontinuity or abrupt change in the gray-level or color, is a fundamentally important primitive feature of an image necessary for the image analysis and classification. Two-dimensional 3x3 compass gradient operators (ex. Sobel, Prewitt, and Kirsch operators)are commonly used in the edge detection and usually detect 8 compass directional components. In this paper, we present a new interpretation of the relationships between the resulting 8 gradient magnitudes and the 8 intensity values of neighboring pixels which are covered by the two-dimensional 3x3 mask. It is expected that a new gradient edge operator may be designed by changing the eigenvalues in the transform domain and the fast optical edge operator may be implemented by using the optical system.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.2
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• pp.82-89
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• 2000

Edge detection is the first step and very important step in image analysis. In this paper, proposed edge detection operators based on informations of edge types and it is different from other classical edge detection operators such as gradient and surface fitting operators. The first, we defined characteristics of edge types such as localization, thinness, length. The second, we defined valid edge types and ideal edge pixel positions in $3\times3$window based on edge characteristics of edge types. And we proposed edge detection algorithm and twelve windows based on valid edge types. In specially, proposed algorithm was shown better performence of edge detection than other operators such as gradient operator and the LoG(Laplacian of Gaussian) operator of zero crossings.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1986.10a
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• pp.53-55
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• 1986

The edge detection system makes use or 3*3 compass gradient masks, which are well suited for digital implementation. Edge angles are quantized to eight equally spaced directions, suitable for chain coding of contours. Use of edge direction msp improves the simple thresholding of gradient modulus image. The concept of local connectivity of the edge direction map is useful improving the performance of this method as well as other edge operators such as Kirsch and Sobel.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1279-1298
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• 2021

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.467-478
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• 2016

In this paper, we propose an Ishikawa-type extra-gradient iterative algorithm for finding a solution of split feasibility, fixed point problems and equilibrium problems of quasi-nonexpansive mappings. It is proven that under suitable conditions, the sequences generated by the proposed iterative algorithms converge weakly to a solution of the split feasibility, fixed point problems and equilibrium problems. An example is given to illustrate the main result of this paper.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.533-546
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• 2018

The object of this work is to study the existence of solutions for a class of p(x)-Kirchhoff type problem under no-flux boundary conditions with dependence on the gradient. We establish our results by using the degree theory for operators of ($S_+$) type in the framework of variable exponent Sobolev spaces.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.5
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• pp.52-65
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• 1997

For the degradation of severe noise and ill-conditioned blur the optimization function has the solution spaces which have many local optima around global solution. General restoration methods such as inverse filtering or gradient methods are mainly dependent on the properties of degradation model and tend to be isolated into a local optima because their convergences are determined in the convex space. Hence we introduce genetic algorithm as a searching method which will search solutions beyond the convex spaces including local solutins. In this paper we introudce improved evaluation square error) and fitness value for gray scaled images. Finally we also proposed the local fine tunign of window size and visit number for delicate searching mechanism in the vicinity of th global solution. Through the experiental results we verified the effectiveness of the proposed genetic operators and evaluation function on noise reduction over the conventional ones, as well as the improved performance of local fine tuning.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.425-443
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• 2010

We investigate the Schr$\ddot{o}$dinger type operator $H_2\;=\;(-\Delta_{\mathbb{H}^n})^2+V^2$ on the Heisenberg group $\mathbb{H}^n$, where $\Delta_{\mathbb{H}^n}$ is the sublaplacian and the nonnegative potential V belongs to the reverse H$\ddot{o}$lder class $B_q$ for $q\geq\frac{Q}{2}$, where Q is the homogeneous dimension of $\mathbb{H}^n$. We shall establish the estimates of the fundamental solution for the operator $H_2$ and obtain the $L^p$ estimates for the operator $\nabla^4_{\mathbb{H}^n}H^{-1}_2$, where $\nabla_{\mathbb{H}^n}$ is the gradient operator on $\mathbb{H}^n$.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.129-150
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• 2022

Let L = -∆ + V be a Schrödinger operator, where the potential V belongs to the reverse Hölder class. In this paper, by the subordinative formula, we investigate the generalized Poisson operator P^L_t,σ, 0 < σ < 1, associated with L. We estimate the gradient and the time-fractional derivatives of the kernel of P^L_t,σ, respectively. As an application, we establish a Carleson measure characterization of the Campanato type space 𝒞^𝛄_L (ℝⁿ) via P^L_t,σ.

• Journal of Korean Society of Water and Wastewater
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• v.18 no.3
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• pp.351-356
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• 2004

Selecting appropriate G values in flocculator operation is important to produce high quality filter effluent in water treatment plants. However, misunderstanding and misleading of G calculation for the case of having power sources more than one or many paddles with one power source in a flocculation basin sometimes have led to low performance in flocculation. Theoretical analysis confirmed that the total G value in one flocculation unit having power sources more than one or with many paddles is the root-square of the sum of square of individual G value. This analysis also can give a simple calculation method of G value for designers and operators in fields.