• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.1-14
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• 2008

In this paper, we investigate the existence of solutions of second order impulsive neutral functional differential inclusions which the nonlinearity F admits convex and non-convex values. Some results under weaker conditions are presented. Our results extend previous ones. The methods rely on a fixed point theorem for condensing multivalued maps and Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.393-406
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• 2007

In the framework of generalized convex spaces, we show that generalized KKM maps can be regarded as ordinary KKM maps, and obtain some applications to equilibrium result, maximal element theorems, and almost fixed point theorems on multimaps of the Zima type.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.2
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• pp.69-78
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• 2002

This paper addresses a method to automatically detect out a person's face from a given image that consists of a hair and face view of the person and a complex background scene. Out method involves an effective detection algorithm that exploits the spatial distribution characteristics of human skin color via an adaptive fuzzy color classifier (AFCC), The universal skin-color map is derived on the chrominance component of human skin color in Cb, Cr and their corresponding luminance. The desired fuzzy system is applied to decide the skin color regions and those that are not. We use RGB model for extracting the hair color regions because the hair regions often show low brightness and chromaticity estimation of low brightness color is not stable. After some preprocessing, we apply convex-hull to each region. Consequent face detection is made from the relationship between a face's convex-hull and a head's convex-hull. The algorithm using the convex-hull shows better performance than the algorithm using pattern method. The performance of the proposed algorithm is shown by experiment. Experimental results show that the proposed algorithm successfully and efficiently detects the faces without constrained input conditions in color images.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.719-730
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• 1997

From a minimax inequality related to admissible multimaps, we deduce generalized versions of lopsided saddle point theorems, fixed point theorems, existence of maximizable linear functionals, the Walras excess demand theorem, and the Gale-Nikaido-Debreu theorem.

• Journal of Broadcast Engineering
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• v.21 no.6
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• pp.878-888
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• 2016

This paper proposes an efficient method to remove the boundary artifacts of rendered views caused by damaged depth maps in the 3D video system. First, characteristics of boundary artifacts with the compression noise in depth maps are carefully studied. Then, the artifacts suppression method is proposed by the iterative projection onto convex sets (POCS) algorithm with setting the convex set in pixel and frequency domain. The proposed method is applied to both texture and depth maps separately during view rendering. The simulation results show the boundary artifacts are greatly reduced with improving the quality of synthesized views.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.211-217
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• 2006

In this paper, we have shown that the convergence of one-step, two-step and three-step iterations is equivalent, which are known as Mann, Ishikawa and Noor iteration procedures, for a special class of Lipschitzian operators defined in a closed, convex subset of an arbitrary Banach space.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1194-1200
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• 2006

In this paper, we propose an adaptive MAP (Maximum A Posteriori) high-resolution image reconstruction algorithm using local statistics. In order to preserve the edge information of an original high-resolution image, a visibility function defined by local statistics of the low-resolution image is incorporated into MAP estimation process, so that the local smoothness is adaptively controlled. The weighted non-quadratic convex functional is defined to obtain the optimal solution that is as close as possible to the original high-resolution image. An iterative algorithm is utilized for obtaining the solution, and the smoothing parameter is updated at each iteration step from the partially reconstructed high-resolution image is required. Experimental results demonstrate the capability of the proposed algorithm.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.12
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• pp.5507-5528
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• 2016

In computer vision, salient object is important to extract the useful information of foreground. With active contour analysis acting as the core in this paper, we propose a bottom-up saliency detection algorithm combining with the Bayesian model and the global color distribution. Under the supports of active contour model, a more accurate foreground can be obtained as a foundation for the Bayesian model and the global color distribution. Furthermore, we establish a contour-based selection mechanism to optimize the global-color distribution, which is an effective revising approach for the Bayesian model as well. To obtain an excellent object contour, we firstly intensify the object region in the source gray-scale image by a seed-based method. The final saliency map can be detected after weighting the color distribution to the Bayesian saliency map, after both of the two components are available. The contribution of this paper is that, comparing the Harris-based convex hull algorithm, the active contour can extract a more accurate and non-convex foreground. Moreover, the global color distribution can solve the saliency-scattered drawback of Bayesian model, by the mutual complementation. According to the detected results, the final saliency maps generated with considering the global color distribution and active contour are much-improved.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.139-149
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• 1989

pp.Hartman and G. Stampacchia [6] proved the following theorem in 1966: If f:X.rarw. $R^{n}$ is a continuous map on a compact convex subset X of $R^{n}$ , then there exists $x_{0}$ ..mem.X such that $x_{0}$ , $x_{0}$ -x>.geq.0 for all x.mem.X. This remarkable result has been investigated and generalized by F.E. Browder [1], [2], W. Takahashi [9], S. Park [8] and others. For example, Browder extended this theorem to a map f defined on a compact convex subser X of a topological vector space E into the dual space $E^{*}$; see [2, Theorem 2]. And Takahashi extended Browder's theorem to closed convex sets in topological vector space; see [9, Theorem 3]. In Section 2, we obtain some variational inequalities, especially, generalizations of Browder's and Takahashi's theorems. The generalization of Browder's is an earlier result of the first author [8]. In Section 3, using Theorem 1, we improve and extend some known fixed pint theorems. Theorems 4 and 8 improve Takahashi's results [9, Theorems 5 and 9], respectively. Theorem 4 extends the first author's fixed point theorem [8, Theorem 8] (Theorem 5 in this paper) which is a generalization of Browder [1, Theroem 1]. Theorem 8 extends Theorem 9 which is a generalization of Browder [2, Theorem 3]. Finally, in Section 4, we obtain variational inequalities for multivalued maps by using Theorem 1. We improve Takahashi's results [9, Theorems 21 and 22] which are generalization of Browder [2, Theorem 6] and the Kakutani fixed point theorem [7], respectively.ani fixed point theorem [7], respectively.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.147-159
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• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.