• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(II)
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• pp.1364-1366
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• 1987

Laplacian of Gaussian, ${\nabla}^2G$ operator proposed by Marr and Hildreth is known as a rough bandpass filter. This paper shows how to detect the change of intensity corresponding to an arbitrary spatial frequency in an image using ${\nabla}^2G$ operator.

• 대한수학회보
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• 제59권5호
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• pp.1255-1268
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• 2022

We consider the Schrödinger type operator 𝓛 = (-𝚫_ℍⁿ)² + V² on the Heisenberg group ℍⁿ, where 𝚫_ℍⁿ is the sub-Laplacian and the non-negative potential V belongs to the reverse Hölder class RH_s for s ≥ Q/2 and Q ≥ 6. We shall establish the (L^p, L^q) estimates for the Riesz transforms T_𝛼,𝛽,j = V^2𝛼𝛁^j_ℍⁿ𝓛^-𝛽, j = 0, 1, 2, 3, where 𝛁_ℍⁿ is the gradient operator on ℍⁿ, 0 < α ≤ 1-j/4, j/4 < 𝛽 ≤ 1, and 𝛽 - 𝛼 ≥ j/4.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2005년도 추계종합학술대회
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• pp.979-982
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• 2005

This paper is to be pre-processing that decides the text recognizability and quality contained in natural image. Differentiated with the existing studies, In this paper, it suggests the application of partially unified color models, Coiflet Wavelet and text extraction algorithm that uses the closed curve edge features of LoG (laplacian of gaussian)operator. The text image included in natural image such as signboard has the same hue, saturation and value, and there is a certain thickness as for their feature. Each color element is restructured into closed area by LoG operator, the 2nd differential operator. The text area is contracted by Hough Transform, logical AND-OR operator of each color model and Minimum-Distance classifier. This paper targets natural image into which text area is added regardless of the size and resolution of the image, and it is confirmed to have more excellent performance than other algorithms with many restrictions.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.137-152
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• 2014

In this paper, we prove, in the spirit of [3, 12, 20, 22, 23], the existence of infinitely many small solutions to the following quasilinear elliptic equation $-{\Delta}_{p(x)}u+{\mid}u{\mid}^{p(x)-2}u={\mid}u{\mid}^{q(x)-2}u+{\lambda}f(x,u)$ in a smooth bounded domain ${\Omega}$ of ${\mathbb{R}}^N$. We also assume that $\{q(x)=p^*(x)\}{\neq}{\emptyset}$, where $p^*(x)$ = Np(x)/(N - p(x)) is the critical Sobolev exponent for variable exponents. The proof is based on a new version of the symmetric mountainpass lemma due to Kajikiya [22], and property of these solutions are also obtained.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2001년도 추계학술대회 학술발표 논문집
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• pp.283-286
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• 2001

Based on a fuzzy system representation of gray scale images, we derive an edge detection algorithm whose convolution kernel is different from the known kernels such as those of Roberts', Prewitt's or Sobel's gradient. Our fuzzy system representation is an exact representation of the bicubic spline function which represents the gray scale image approximately. Hence the fuzzy system is a continuous function and it provides a natural way to define the gradient and the Laplacian operator. We show that the gradient at grid points can be evaluated by taking the convolution of the image with a 3 3 kernel. We also show that our gradient coupled with the approximate value of the continuous function generates an edge detection method which creates edge images clearer than those by other methods. A few examples of applying our methods are included.

• 대한수학회보
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• 제34권2호
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• pp.155-171
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• 1997

Let $M^n$ be a connected subminifold of a Euclidean space $E^m$, equipped with the induced metric. Denoty by $\Delta$ the Laplacian operator of $M^n$ and by x the position vector. A well-known T. Takahashi's theorem [13] says that $\delta x = \lambda x$ for some constant $\lambda$ if and only if $M^n$ is either minimal subminifold of $E^m$ or minimal submanifold in a hypersphere of $E^m$. In [9], O. Garay studied the hypersurfaces $M^n$ in $E^{n+1}$ satisfying $\delta x = Dx$, where D is a diagonal matrix, and he classified such hypersurfaces. Garay's condition can be seen as a generalization of T.

• 충청수학회지
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• 제22권1호
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• pp.117-121
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• 2009

For $1{\leq}p$, $q{\leq}{\infty}$ and $s{\in}\mathbb{R}$, it is proved that there exists a constant C > 0 such that for any $f{\in}B^{s+2}_{p,q}(\mathbb{R}^n)$ $${\parallel}f{\parallel}_{B^{s+2}_{p,q}(\mathbb{R}^n)}{\leq}C{\parallel}f\;-\;{\Delta}f{\parallel}_{B^{s}_{p,q}(\mathbb{R}^n)}$$, which tells us that the operator $I-\Delta$ is $B^{s+2}_{p,q}$-coercive on the Besov space $B^s_{p,q}$.

• 대한수학회지
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• 제47권1호
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• pp.135-163
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• 2010

Motivated by [Science in China (Ser. A Mathematics) 36 (2006), no. 7, 721?732], this article deals with the following discrete type BVP $\LARGE\left\{{{\;{\Delta}[{\phi}({\Delta}x(n))]\;+\;f(n,\;x(n\;+\;1),{\Delta}x(n),{\Delta}x(n + 1))\;=\;0,\;n\;{\in}\;[0,N],}}\\{\;{x(0)-{\sum}^m_{i=1}{\alpha}_ix(n_i) = A,}}\\{\;{x(N+2)-\;{\sum}^m_{i=1}{\beta}_ix(n_i)\;=\;B.}}\right.$ The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem are established by using a new fixed point theorem obtained in [5]. An example is presented to illustrate the main result. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operator ${\Delta}$x(n).

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2013년도 춘계학술대회
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• pp.892-894
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• 2013

디지털 영상 처리 기술이 발전함에 따라 에지는 여러 응용 분야에서 활용되고 있다. 기존의 에지검출 방법에는 마스크를 이용한 Sobel, Prewitt, Roberts, Laplacian 연산자 등이 있다. 이러한 기존의 방법은 구현이 간단하나, AWGN(additive white Gaussian noise)이 첨가된 영상에서 에지 검출의 오류가 발생한다. 따라서 이와 같은 기존의 방법의 단점을 보완하기 위하여, 본 논문에서는 변형된 마스크를 이용한 에지 검출 알고리즘을 제안하였으며, 제안한 알고리즘은 AWGN 환경에서 우수한 에지검출 특성을 나타내었다.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2013년도 춘계학술대회
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• pp.886-888
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• 2013

에지는 물체의 크기, 방향, 위치 등의 정보를 포함한다. 이러한 에지를 검출하기 위한 기존의 에지검출 방법은 Sobel, Prewitt, Roberts, Laplacian 연산자 등을 이용한 방법이다. 기존의 방법은 에지를 검출하기 위하여 고정된 가중치 마스크를 이용하며 에지 검출 특성이 다소 미흡하다. 따라서 이와 같은 기존의 방법의 단점을 보완하기 위하여, 본 논문에서는 표준편차 및 임계값에 따른 가중치를 이용한 에지 검출 알고리즘을 제안하였다.