• ETRI Journal
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• v.10 no.3
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• pp.125-140
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• 1988

Computational geometry has wide applications in pattern recognition, image processing, VLSI design, and computer graphics. Voronoi diagrams in computational geometry possess many important properites which are related to other geometric structures of a set of point. In this pater the design of systolic algorithms for the static and the dynamic Voronoi diagrams is considered. The major motivation for developing the systolic architecture is for VLSI implementation. A new systematic transform technique for designing systolic arrays, in particular, for the problem in computational geometry has been proposed. Following this procedure, a type T systolic array architecture and associated systolic algorithms have been designed for constructing Voronoi diagrams. The functions of the cells in the array are also specified. The resulting systolic array achieves the maximal throughput with O(n) computational complexity.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1601-1606
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• 1991

We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.405-409
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• 1997

Voronoi diagrams are applied in varios field such as NC toolpath generation, VLSI design and robot path planning because of their geometric charcteristics. In this paper, Voronoi diagrams are introduced on polygon constructed by line segments only and with constant offset. Bisector curves for two arbitrary objects, which is the combination of line segment and arc, are defined as parametric fuction where the parameter is used as offset. Offset curves are applied on the generation of laser scanning path for the stereolithography and shows a good result from several examples.

• Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.79-87
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• 2014

Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology and material sciences. In order to solve application problems, the dual structure, called the quasi-triangulation, and its derivative structure, called the beta-complex, are frequently used with the Voronoi diagram itself. However, the Voronoi diagram, the quasi-triangulation, and the beta-complexes are sometimes regarded as somewhat difficult for ordinary users to understand. This paper presents the two-dimensional counterparts of their definitions and introduce the BetaConcept program which implements the theory so that users can easily learn the powerful concept and capabilities of these constructs in a plane. The BetaConcept program was implemented in the standard C++ language with MFC and OpenGL and freely available at Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).

• Korean Journal of Computational Design and Engineering
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• v.11 no.2
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• pp.97-106
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• 2006

Voronoi diagrams have been known for numerous important applications in science and engineering including CAD/CAM. Especially, the Voronoi diagram for 3D spheres has been known as very useful tool to analyze spatial structural properties of molecules or materials modeled by a set of spherical atoms. In this paper, we present two algorithms, the edge-tracing algorithm and the region-expansion algorithm, for constructing the Voronoi diagram of 3D spheres and applications to protein structure analysis. The basic scheme of the edge-tracing algorithm is to follow Voronoi edges until the construction is completed in O(mn) time in the worst-case, where m and n are the numbers of edges and spheres, respectively. On the other hand, the region-expansion algorithm constructs the desired Voronoi diagram by expanding Voronoi regions for one sphere after another via a series of topology operations, starting from the ordinary Voronoi diagram for the centers of spheres. It turns out that the region-expansion algorithm also has the worst-case time complexity of O(mn). The Voronoi diagram for 3D spheres can play key roles in various analyses of protein structures such as the pocket recognition, molecular surface construction, and protein-protein interaction interface construction.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.713-718
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• 1994

Voronoi diagrams for closed shapes have many practical applications, ranging from numerical control machining to mesh generation. Shape offset based on Voronoi diagram avoids the topological problems encountered in traditional offsetting algorithms. In this paper, we propose a procedure for generating a Voronoi diagram and an exact offset for planar curve. A planer curve can be defined by free-form curve segements. The procedure consists of three steps : 1) segmentation by minimum curvature, 2) construction of Voronoi diagram, and 2) generation of the exact offset.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.4
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• pp.235-243
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• 2012

The Voronoi diagram of spheres and power diagram have been known as powerful tools to analyze spatial characteristics of weighted points, and these structures have variety range of applications including molecular spatial structure analysis, location based optimization, architectural design, etc. Due to the fact that both diagrams are based on different distance metrics, one has better usability than another depending on application problems. In this paper, we compare these diagrams in various situations from the user's viewpoint, and show the Voronoi diagram of spheres is more effective in the problems based on the Euclidean distance metric such as nearest neighbor search, path bottleneck locating, and internal void finding.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1999.06a
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• pp.69-76
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• 1999

This paper proposes a new region-oriented coding scheme of still images. The scheme first segments an image into homogeneous regions by making use of Voronoi diagrams. Then luminance components in each Voronoi region are encoded using a transform coding technique which employs the Schmidt's orthogonalization method to produce orthonormal basis-functions for arbitrarily shaped regions. In this technique, coding efficiency depends on the properties of initial vectors to be orthogonalized. Therefore we adaptively select a set of initial vectors as well as the order in which these vectors are orthogonalized. Simulation results indicate that the proposed coding scheme achieves higher coding performance with much less computation than the KLT-based scheme which we reported formerly.

• Journal of Ocean Engineering and Technology
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• v.38 no.3
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• pp.115-123
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• 2024

USBL systems are essential for providing accurate positions of autonomous underwater vehicles (AUVs). On the other hand, the accuracy can be degraded by outliers because of the environmental conditions. A failure to address these outliers can significantly impact the reliability of underwater localization and navigation systems. This paper proposes a novel outlier rejection algorithm for AUV localization using Voronoi diagrams and query point calculation. The Voronoi diagram divides data space into Voronoi cells that center on ultra-short baseline (USBL) data, and the calculated query point determines if the corresponding USBL data is an inlier. This study conducted experiments acquiring GPS and USBL data simultaneously and optimized the algorithm empirically based on the acquired data. In addition, the proposed method was applied to a sensor fusion algorithm to verify its effectiveness, resulting in improved pose estimations. The proposed method can be applied to various sensor fusion algorithms as a preprocess and could be used for outlier rejection for other 2D-based location sensors.

• Journal of Information Processing Systems
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• v.7 no.1
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• pp.17-28
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• 2011

Despite the fact that the deployment of sensor networks and target tracking could both be managed by taking full advantage of Voronoi diagrams, very little few have been made in this regard. In this paper, we designed an optimized barrier coverage and an energy-efficient clustering algorithm for forming Vonoroi-based Wireless Sensor Networks(WSN) in which we proposed a mobile target tracking scheme (CTT&MAV) that takes full advantage of Voronoi-diagram boundary to improve detectability. Simulations verified that CTT&MAV outperforms random walk, random waypoint, random direction and Gauss-Markov in terms of both the average hop distance that the mobile target moved before being detected and lower sensor death rate. Moreover, we demonstrate that our results are robust as realistic sensing models and also validate our observations through extensive simulations.