• 한국CDE학회논문집
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• 제19권2호
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• pp.111-118
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• 2014

In tangible augmented reality (AR) environments, the user interacts with virtual objects by manipulating their physical counterparts, but he or she often encounters awkward situations in which his or her hands are occluded by the augmented virtual objects, which causes great difficulty in figuring out hand positions, and reduces both immersion and ease of interaction. To solve the problem of such hand occlusion, skin color information has been usefully exploited. In this paper, we propose an approach to simple and effective construction of a skin color map which is suitable for hand segmentation and tangible AR interaction. The basic idea used herein is to obtain hand images used in a target AR environment by simple image subtraction and to represent their color information by a convex polygonal map in the YCbCr color space. We experimentally found that the convex polygonal map is more accurate in representing skin color than a conventional rectangular map. After implementing a solution for resolving hand occlusion using the proposed skin color map construction, we showed its usefulness by applying it to virtual design evaluation of digital handheld products in a tangible AR environment.

• 대한수학회보
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• 제49권6호
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• pp.1147-1161
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• 2012

In this paper, a coincidence theorem for a compact ${\Re}\mathfrak{C}$-map is proved in an abstract convex space. Several more general coincidence theorems for noncompact ${\Re}\mathfrak{C}$-maps are derived in abstract convex spaces. Some examples are given to illustrate our coincidence theorems. As applications, an alternative theorem concerning the existence of maximal elements, an alternative theorem concerning equilibrium problems and a minimax inequality for three functions are proved in abstract convex spaces.

• 대한수학회지
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• 제32권2호
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• pp.251-264
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• 1995

Applications of the classical Knaster-Kuratowski-Mazurkiewicz (si-mply, KKM) theorem and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde [L1]. In this direction, the first author [P5] found that certain coincidence theorems on a large class of composites of upper semicontinuous multifunctions imply many fundamental results in the KKM theory.

• 정보처리학회논문지:컴퓨터 및 통신 시스템
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• 제3권1호
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• pp.1-6
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• 2014

현재까지 컨벡스헐 (convex hull) 의 계산 알고리즘들은 주로 점 집합 (point set) 에 대해 연구가 수행되어 왔다. 본 논문에서는 이산 공간에서 다양한 반경을 갖는 구 집합에 대한 컨벡스헐을 근사하는 방법을 제시한다. 구 집합에 대한 컨벡스헐 계산은, 특히 단백질 분자의 구조적인 특성을 연구하는 여러 응용분야에서 계산 효율성을 증대시키기 위한 기반 기술이라 할 수 있다. 분자에 대응하는 구의 집합에 대해 복셀 맵 (voxel map) 자료구조를 적용하고 이를 이용하여 컨벡스헐을 계산하는 알고리즘을 제시한다. 제안된 방법은 GPU를 활용한 병렬처리를 수행하여 평균적으로 6,400개 이하의 구가 포함된 집합에 대해 40ms 이내에 컨벡스헐을 계산하는 성능을 보인다.

• East Asian mathematical journal
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• 제19권2호
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• pp.165-171
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• 2003

We show that any F-harmonic map from a compact manifold M to N is necessarily constant if N possesses a strictly-convex function, and prove 'Liouville type theorems' for F-harmonic maps. Finally, when the target manifold is the real line, we get a result for F-subharmonic functions.

• 대한수학회보
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• 제50권1호
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• pp.305-320
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• 2013

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..

• 호남수학학술지
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• 제31권4호
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• pp.559-578
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• 2009

In this work, we obtain intersection theorem, analytic alternative and von Neumann type minimax theorem in G-convex spaces. We also generalize Ky Fan minimax inequality to acyclic versions in G-convex spaces. The result is applied to formulate acyclic versions of other minimax results, a theorem of systems of inequalities and analytic alternative.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.165-175
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• 2021

In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumbán, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrović-Hussain-Sen-Radenović on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.

• 대한수학회지
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• 제35권4호
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• pp.803-829
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• 1998

We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.1-7
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• 2002

For A bounded subset G of a metric Space (X,d) and $\chi \in X$, let $f_{G}$ be the real-valued function on X defined by $f_{G}$($\chi$)=sup{$d (\chi, g)\in:G$}, and $F(G,\chi)$={$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$}. In this paper we discuss some properties of the map $f_G$ and of the set $ F(G, \chi)$ in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in $ F(G, \chi)$ is also given in this pope.