• Korean Journal of Computational Design and Engineering
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• v.6 no.1
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• pp.24-30
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• 2001

An efficient and robust algorithm to compute the exact Voronoi diagram of a circle set is presented. The circles are located in a two dimensional Euclidean space, the radii of the circles are non-negative and not necessarily equal, and the circles are allowed to intersect each other. The idea of the algorithm is to use the topology of the point set Voronoi diagram as a seed so that the correct topology of the circle set Voronoi diagram can be obtained through a number of edge flipping operations. Then, the geometries of the Voronoi edges of the circle set Voronoi diagram are computed. In particular, this paper discusses the topological aspect of the algorithm, and the following paper discusses the geometrical aspect. The main advantages of the proposed algorithm are in its robustness, speed, and the simplicity in its concept as well as implementation. Since the algorithm is based on the result of the point set Voronoi diagram and the flipping operation is the only topological operation, the algorithm is always as stable as the Voronoi diagram construction algorithm of a point set.

• Proceedings of the Society of Korea Industrial and System Engineering Conference
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• 2002.05a
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• pp.467-472
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• 2002

Presented in this paper is an algorithm to compute the Voronoi diagram of a circle set from the Voronoi diagram of a point set. The circles are located in Euclidean plane, the radii of the circles are non-negative and not necessarily equal, and the circles are allowed to intersect each other. The idea of the algorithm is to use the topology of the point set Voronoi diagram as a seed so that the correct topology of the circle set Voronoi diagram can be obtained through a number of edge flipping operations. Then, the geometries of the Voronoi edges of the circle set Voronoi diagram are computed. The main advantages of the proposed algorithm are in its robustness, speed, and the simplicity in its concept as well as implementation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.12
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• pp.6017-6037
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• 2017

In a multi-resolution image encoding system, the image is encoded into a single file as a layer of bit streams, and then it is transmitted layer by layer progressively to reduce the transmission time across a low bandwidth connection. This encoding scheme is also suitable for multiple decoders, each with different capabilities ranging from a handheld device to a PC. In our previous work, we proposed an edge adaptive hierarchical interpolation algorithm for multi-resolution image coding system. In this paper, we enhanced its compression efficiency by adding three major components. First, its prediction accuracy is improved using context adaptive error modeling as a feedback. Second, the conditional probability of prediction errors is sharpened by removing the sign redundancy among local prediction errors by applying sign flipping. Third, the conditional probability is sharpened further by reducing the number of distinct error symbols using error remapping function. Experimental results on benchmark data sets reveal that the enhanced algorithm achieves a better compression bit rate than our previous algorithm and other algorithms. It is shown that compression bit rate is much better for images that are rich in directional edges and textures. The enhanced algorithm also shows better rate-distortion performance and visual quality at the intermediate stages of progressive image transmission.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.123-131
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• 2005

According to ow previous study, we confirmed That the Petrov-Galerkin natural element method(PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin natural element method(BG-NEM). This paper is an extension of PG-NEM to two-dimensional geometrically nonlinear problem. For the analysis, a linearized total Lagrangian formulation is approximated with the PS-NEM. At every load step, the grid points ate updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates The large deformation problem.