• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.1
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• pp.130-134
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• 2012

In this paper, we propose a space partitioning technique for swarm robots by using the Centroidal Voronoi Tessellation. The proposed method consists of two parts such as space partition and collision avoidance. The space partition for searching a given space is carried out by a density function which is generated by some accidents. The collision avoidance is implemented by the potential field method. Finally, the numerical experiments show the effectiveness and feasibility of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.3
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• pp.465-472
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• 2015

This paper presents a visual touch recognition for NUI(Natural User Interface) using Voronoi-tessellation algorithm. The proposed algorithms are three parts as follows: hand region extraction, hand feature point extraction, visual-touch recognition. To improve the robustness of hand region extraction, we propose RGB/HSI color model, Canny edge detection algorithm, and use of spatial frequency information. In addition, to improve the accuracy of the recognition of hand feature point extraction, we propose the use of Douglas Peucker algorithm, Also, to recognize the visual touch, we propose the use of the Voronoi-tessellation algorithm. Finally, we demonstrate the feasibility and applicability of the proposed algorithms through some experiments.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.2
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• pp.65.2-65.2
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• 2014

We present a new hydrodynamic simulation code based on the Voronoi tessellation for estimating the density precisely. The code employs both of Lagrangian and Eulerian description by adopting the movable mesh scheme, which is superior to the conventional SPH (smoothed particle hydrodynamics) and AMR (adaptive mesh refinement) schemes. The code first generates unstructured meshes by the Voronoi tessellation at every time step, and then solves the Riemann problem for all surfaces of each Voronoi cell so as to update the hydrodynamic states as well as to move current meshes. Besides, the IEM (incremental expanding method) is devised to compute the Voronoi tessellation to desired degree of speed, thereby the CPU time is turned out to be just proportional to the number of particles, i.e., O(N). We discuss the applications of our code in the context of cosmological simulations as well as numerical experiments for galaxy formation.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1892-1893
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• 2011

본 논문에서는 Centroidal Voronoi Tessellation을 이용하여 군집로봇의 협조탐색을 위한 공간분할기법을 제안한다. 탐색공간은 Centroidal Voronoi Tessellation을 이용하여 분할한다. 전역 경로 계획 및 군집 로봇 간의 충돌 회피는 포텐셜 필드를 이용한다. 탐색공간에 밀도 함수를 사용하여 공간분할의 유동성을 부여한다. 마지막으로, 군집로봇의 협조탐색의 가능성을 시뮬레이션을 통하여 확인한다.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.155-156
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• 2011

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.9A
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• pp.758-766
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• 2011

Cooperative communications are adopted as a promising solution to achieve high data rate over large areas in the future 40 wireless system and the relay station (RS) is the key concept in cooperative communications. However, most existing works in this area focus only on optimal RS selections. In addition, there are only few works consider another crucial issue: how many relay stations we need to place. Only when the number of relay stations is defined, the relay station selection can be performed well. In this paper we derive a formula which describes the impact of varying number of RS on end-to-end link throughput assuming a clustering scheme which is based on Voronoi tessellation. In addition to mathematical analysis on the feasibility of the formula, we also examine its performance through a set of simulations under the Erceg path loss model. Simulation results verify that the link throughput gain of our proposed scheme is promising.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.41 no.9
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• pp.39-45
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• 2004

A design method is proposed for the sequence detection with fixed decision delay with less hardware complexity using the concept of the Voronoi diagram and its dual, the Delaunay tessellation. This detector design is based on the Fixed Delay Tree Search (FDTS) detection. The FDTS is a computationally efficient sequence detection algerian and has been shown to achieve near-optimal performance in the severe Intersymbol Interference (ISI) channels when combined with decision feedback equalization and the appropriate channel coding. In this approach, utilizing the information contained in the Voronoi diagram or equivalently the Delaunay tessellation, the relative location of the detector input sequence in the multi-dimensional Euclidean space is found without any computational redundancy, which leads to a reduced complexity implementation of the detector.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.2
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• pp.101.2-101.2
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• 2013

We present a new computational fluid dynamic (CFD) simulation code. The code employs the moving and polyhedral unstructured mesh scheme, which is known as a superior approach to the conventional SPH (smoothed particle hydrodynamics) and AMR (adaptive mesh refinement) schemes. The code first generates unstructured meshes by the Voronoi tessellation at every time step, and then solves the Riemann problem for surfaces of every Voronoi cell to update the hydrodynamic states as well as to move former generated meshes. For the second-order accuracy, the MUSCL-Hancock scheme is implemented. To increase efficiency for generating Voronoi tessellation we also develop the incremental expanding method, by which the CPU time is turned out to be just proportional to the number of particles, i.e., O(N). We will discuss the applications of our code in the context of cosmological simulations as well as numerical experiments for galaxy formation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.293-305
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• 2009

In this article, we study a reduced-order modelling for distributed feedback control problem of the Burgers equations. Brief review of the centroidal Voronoi tessellation (CVT) are provided. A weighted (nonuniform density) CVT is introduced and low-order approximate solution and compensator-based control design of Burgers equation is discussed. Through weighted CVT (or CVT-nonuniform) method, obtained low-order basis is applied to low-order functional gains to design a low-order controller, and by using the low-order basis order of control modelling was reduced. Numerical experiments show that a solution of reduced-order controlled Burgers equation performs well in comparison with a solution of full order controlled Burgers equation.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.3
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• pp.52-60
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• 2019

This paper presents a numerically robust algorithm to construct a Voronoi diagram of circles in the plane. The circles are allowed to have intersections among them, but one circle cannot fully contain another circle. The Voronoi diagram is a tessellation of the plane into Voronoi regions of given circles. Each circle has its Voronoi region which is defined by a set of points in the plane closer to the circle than any other circles. The distance from a point p to a circle $c_i$ of center $p_i$ and radius $r_i$ is ${\parallel}p-p_i{\parallel}-r_i$, which is the closest Euclidean distance from p to the circle boundary. The proposed algorithm first constructs the point Voronoi diagram of centers of given circles, then it enlarges each point to the circle and expands its Voronoi region accordingly. This region-expansion process is done by local modifications and after completing this process for the whole circles the desired circle Voronoi diagram can be obtained. The proposed algorithm is numerically robust and we provide with a few examples to show its robustness. The algorithm runs in $O(n^2)$ time in the worst case and O(n) time on average where n is the number of the circles. The experiment shows that the region-expansion algorithm is robust and runs fast with strong linear time behavior.