• Journal of Korea Multimedia Society
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• v.11 no.6
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• pp.737-745
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• 2008

In this paper, a novel neighborhood metric of histogram equalization (HE) algorithm for contrast enhancement is presented. We present a refinement of HE using neighborhood metrics with a general framework which orders pixels based on a sequence of sorting functions which uses both global and local information to remap the image greylevels. We tested a novel sorting key with the suggestion of using the original image greylevel as the primary key and a novel neighborhood distinction metric as the secondary key, and compared HE using proposed distinction metric and other HE methods such as global histogram equalization (GHE), HE using voting metric and HE using contrast difference metric. We found that our method can preserve advantages of other metrics, while reducing drawbacks of them and avoiding undesirable over-enhancement that can occur with local histogram equalization (LHE) and other methods.

• Journal of Multimedia Information System
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• v.9 no.2
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• pp.87-92
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• 2022

In this study, we aimed to illustrate that the thresholding method gives different results when tested on the original and the refined histograms. We use the global thresholding method, the well-known image segmentation method for separating objects and background from the image, and the refined histogram is created by the neighborhood distinction metric. If the original histogram of an image has some large bins which occupy the most density of whole intensity distribution, it is a problem for global methods such as segmentation and contrast enhancement. We refined the histogram to overcome the big bin problem in which sub-bins are created from big bins based on distinction metric. We suggest the refined histogram for preprocessing of thresholding in order to reduce the big bin problem. In the test, we use Otsu and median-based thresholding techniques and experimental results prove that their results on the refined histograms are more effective compared with the original ones.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.127-134
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• 2000

Let $\Omega$ be a bounded pseudoconvex domain in$C^{n}$ with smooth defining function r and let$z_0\; {\in}\; b{\Omega}$ be a point of finite type. We also assume that $\Omega$ is convex in a neighborhood of $z_0$. Then we prove that all the holomorphic sectional curvatures of the Bergman metric of $\Omega$ are bounded below by a negative constant near $z_0$.

• Journal of Korea Multimedia Society
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• v.18 no.6
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• pp.691-700
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• 2015

Here, we present a new framework for histogram equalization in which both local and global contrasts are enhanced using neighborhood metrics. When checking neighborhood information, filters can simultaneously improve image quality. Filters are chosen depending on image properties, such as noise removal and smoothing. Our experimental results confirmed that this does not increase the computational cost because the filtering process is done by our proposed arrangement of making the histogram while checking neighborhood metrics simultaneously. If the two methods, i.e., histogram equalization and filtering, are performed sequentially, the first method uses the original image data and next method uses the data altered by the first. With combined histogram equalization and filtering, the original data can be used for both methods. The proposed method is fully automated and any spatial neighborhood filter type and size can be used. Our experiments confirmed that the proposed method is more effective than other similar techniques reported previously.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.585-594
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• 2022

In this article we classify four dimensional gradient Ricci solitons (M, g, f) with half harmonic Weyl curvature and at most two distinct Ricci-eigenvalues at each point. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, (V, g) is isometric to one of the following: (i) an Einstein manifold. (ii) a domain in the Riemannian product (ℝ², g₀) × (N, ${\tilde{g}}$), where g₀ is the flat metric on ℝ² and (N, ${\tilde{g}}$) is a two dimensional Riemannian manifold of constant curvature λ ≠ 0. (iii) a domain in ℝ × W with the warped product metric $ds^2+h(s)^2{\tilde{g}}$, where ${\tilde{g}}$ is a constant curved metric on a three dimensional manifold W.

• Journal of Communications and Networks
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• v.16 no.4
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• pp.371-377
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• 2014

Localized topology control is attractive for obtaining reduced network graphs with desirable features such as sparser connectivity and reduced transmit powers. In this paper, we focus on studying how to prolong network lifetime in the context of localized topology control for wireless multi-hop networks. For this purpose, we propose an energy efficient localized topology control algorithm. In our algorithm, each node is required to maintain its one-hop neighborhood topology. In order to achieve long network lifetime, we introduce a new metric for characterizing the energy criticality status of each link in the network. Each node independently builds a local energy-efficient spanning tree for finding a reduced neighbor set while maximally avoiding using energy-critical links in its neighborhood for the local spanning tree construction. We present the detailed design description of our algorithm. The computational complexity of the proposed algorithm is deduced to be O(mlog n), where m and n represent the number of links and nodes in a node's one-hop neighborhood, respectively. Simulation results show that our algorithm significantly outperforms existing work in terms of network lifetime.

• Journal of Intelligence and Information Systems
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• v.18 no.3
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• pp.119-135
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• 2012

Among various recommendation techniques, neighborhood-based Collaborative Filtering (CF) techniques have been one of the most widely used and best performing techniques in literature and industry. This paper proposes new approaches that can enhance the neighborhood-based CF techniques by identifying a few best neighbors (the most similar users to a target user) more accurately with more information about neighbors. The proposed approaches put more weights to the users who have more items co-rated by the target user in similarity computation, which can help to better understand the preferences of neighbors and eventually improve the recommendation quality. Experiments using movie rating data empirically demonstrate simultaneous improvements in both recommendation accuracy and diversity. In addition to the typical single rating setting, the proposed approaches can be applied to the multi-criteria rating setting where users can provide more information about their preferences, resulting in further improvements in recommendation quality. We finally introduce a single metric that measures the balance between accuracy and diversity and discuss potential avenues for future work.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.137-145
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• 2004

In [13], we developed a theory of complex Finsler manifolds to investigate the global geometry of complex Finsler manifolds. There we proved a version of Bonnet-Myers' theorem for complex Finsler manifolds with a certain condition on the Finsler metric which is a generalization of the Kahler condition for the Hermitian metric. In this paper, we show that if the holomorphic sectional curvature of M is ${\geq}\;c^2\;>\;0$, then M is simply connected. This is a generalization of the Synge's theorem in the Riemannian geometry and the Tsukamoto's theorem for Kahler manifolds. The main point of the proof lies in how we can circumvent the convex neighborhood theorem in the Riemannian geometry. A second variation formula of arc length for complex Finsler manifolds is also derived.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1255-1274
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• 2008

The purpose of this paper is to discuss the constant term appearing in the BFK-gluing formula for the zeta-determinants of Laplacians on a complete Riemannian manifold when the warped product metric is given on a collar neighborhood of a cutting compact hypersurface. If the dimension of a hypersurface is odd, generally this constant is known to be zero. In this paper we describe this constant by using the heat kernel asymptotics and compute it explicitly when the dimension of a hypersurface is 2 and 4. As a byproduct we obtain some results for the value of relative zeta functions at s=0.