• 전자공학회논문지C
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• 제34C권7호
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• pp.51-60
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• 1997

Prototype based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used. In this paper, we propose a fuzzy clustering method that involves adaptively expanding convex polytopes. Thus, the dependency on the use of prototypes can be eliminated. The proposed method makes it possible to effectively represent an arbitrarily distributed data set without a priori knowledge of the number of clusters in the data set. Specifically, nonlinear membership functions are utilized to determine whether a new cluster is created or which vertex of the cluster should be expanded. For this, the membership function of a new vertex is assigned according to not only a distance measure between an incoming pattern vector and a current vertex, but also the amount how much the current vertex has been modified. Therefore, cluster expansion can be only allowed for one cluster per incoming pattern. Several experimental results are given to show the validity of our mehtod.

• 한국멀티미디어학회논문지
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• 제8권12호
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• pp.1572-1580
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• 2005

The common requirements for watermarking are usually invisibility, robustness, and capacity. We proposed the watermarking for 3D mesh model based on projection onto convex sets for invisibility and robustness among requirements. As such, a 3D mesh model is projected alternatively onto two convex sets until it converge a point. The robustness convex set is designed to be able to embed watermark into the distance distribution of vertices. The invisibility convex set is designed for the watermark to be invisible based on the limit range of vertex movement. The watermark can be extracted using the decision values and index that the watermark was embedded with. Experimental results verify that the watermarked mesh model has both robustness against mesh simplification, cropping, affine transformations, and vertex randomization and invisibility.

• 전자공학회논문지CI
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• 제43권2호
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• pp.81-92
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• 2006

본 논문에서는 3D 메쉬 모델에 대한 POCS 기반의 워터마킹 방법을 제안하였다. 제안한 방법에서는 워터마킹 시스템의 조건들 중 견고성 및 비가시성에 대한 볼록 집합을 설계한 후 3D 메쉬 모델의 꼭지점들을 이 두 집합들로 수렴 조건을 만족할 때 까지 반복 교대 투영한다. 견고성 제약 조건 집합은 각 꼭지점의 거리 분포에 워터마크를 삽입하는 방법에 의하여 정의되며, 비가시성 제약 조건 집합은 꼭지점 좌표의 변화량에 의하여 정의된다. 실험 결과로부터 제안한 방법이 좌표 변환, 스케일링, 메쉬 간단화, 절단, 및 꼭지점 잡음 첨가 등의 공격에 대한 우수한 견고성 및 비가시성을 확인하였다.

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.661-669
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• 2021

For a simple, undirected graph G = (V, E), a perfect Roman dominating function (PRDF) f : V → {0, 1, 2} has the property that, every vertex u with f(u) = 0 is adjacent to exactly one vertex v for which f(v) = 2. The weight of a PRDF is the sum f(V) = ∑_v∈V f(v). The minimum weight of a PRDF is called the perfect Roman domination number, denoted by γ_R^P(G). Given a graph G and a positive integer k, the PRDF problem is to check whether G has a perfect Roman dominating function of weight at most k. In this paper, we first investigate the complexity of PRDF problem for some subclasses of bipartite graphs namely, star convex bipartite graphs and comb convex bipartite graphs. Then we show that PRDF problem is linear time solvable for bounded tree-width graphs, chain graphs and threshold graphs, a subclass of split graphs.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2012년도 추계학술발표대회
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• pp.330-332
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• 2012

본 논문에서는 임의의 정렬되지 않은 평면 점집합(Plane Point Set)에서 정렬을 고려한 개선된 Convex Hull 알고리즘을 제안한다. 이 알고리즘은 Convex Hull의 극점(Extreme Point) 특성을 이용하여 처리 데이터를 한정하기 때문에 계산복잡도를 낮춘다. 각 단계마다 볼록 정점(Convex Vertex)만을 판별하는 조건을 이용하여 한 번의 스캔으로 온전한 Convex Set이 구한다. 알고리즘 초기에 점집합의 정렬이 필요한데, 이때 걸리는 시간이 알고리즘 전체 동작시간의 대부분을 차지하는 만큼, 특성에 맞는 방법을 사용하여 빠르게 정렬하였다. 일반적인 상황을 가정하고 점집합을 랜덤하게 구성하여 실험하였으며 기존의 알고리즘에 비해 약 두 배의 속도 향상이 있음을 확인하였다.

• 전기전자학회논문지
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• 제17권1호
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• pp.29-35
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• 2013

본 연구에서는 임의의 정렬되지 않은 점집합에서 정렬을 고려한 개선된 Convex Hull 알고리즘을 제안한다. 이 알고리즘은 Convex Hull의 극점 특성을 이용하여 처리 데이터를 한정하기 때문에 계산복잡도가 낮다. 각 단계마다 볼록 정점을 판별하는 조건을 이용하여 한 번의 스캔으로 완전한 Convex Set을 구한다. 알고리즘 초기에 점집합의 정렬이 필요한데, 이때 걸리는 시간이 알고리즘 전체 동작시간의 대부분을 차지하기 때문에 값과 인덱스를 대치하여 빠르게 정렬하였다. 일반적인 상황을 가정하여 랜덤한 점집합으로 알고리즘의 동작시간을 측정하였으며 기존의 알고리즘에 비해 약 두 배의 속도 향상이 있음을 확인하였다.

• Journal of the Korean Data and Information Science Society
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• 제17권3호
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• pp.753-762
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• 2006

The Snakes and GVF used to find object edges dynamically have assigned their initial contour arbitrarily. If the initial contours are located in the neighboring regions of object edges, Snakes and GVF can be close to the true boundary. If not, these will likely to converge to the wrong result. Therefore, this paper proposes a new initialization of Snakes and GVF using convex hull approximation, which initializes the vertex of Snakes and GVF as a convex polygonal contour near object edges. In simulation result, we show that the proposed algorithm has a faster convergence to object edges than the existing methods. Our algorithm also has the advantage of extracting whole edges in real images.

• 호남수학학술지
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• 제35권1호
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• pp.37-49
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• 2013

Consider a non-degenerate open convex cone C with vertex the origin in the $n$2-dimensional Euclidean space $E^n$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $p$ is independent of the point $p{\in}M$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.185-191
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• 2004

Given a connected graph G, we say that a set EC\;{\subseteq}\;V(G)$ is convex in G if, for every pair of vertices x, $y\;{\in}\;C$, the vertex set of every x - y geodesic in G is contained in C. The convexity number of G is the cardinality of a maximal proper convex set in G. In this paper, we show that every pair k, n of integers with $2\;{\leq}k\;{\leq}\;n\;-\;1$ is realizable as the convexity number and order, respectively, of some connected triangle-free graph, and give a lower bound for the convexity number of k-regular graphs of order n with n > k+1.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.