• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1065-1081
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• 2011

For any field F, a polynomial f $\in$ F[$x_1,x_2,{\ldots},x_k$] can be associated with a polytope, called its Newton polytope. If the polynomial f has integrally indecomposable Newton polytope, in the sense of Minkowski sum, then it is absolutely irreducible over F, i.e., irreducible over every algebraic extension of F. We present some results giving new integrally indecomposable classes of polygons. Consequently, we have some criteria giving many types of absolutely irreducible bivariate polynomials over arbitrary fields.

• Journal of the Korea Computer Graphics Society
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• v.8 no.1
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• pp.13-20
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• 2002

Recently, there is a great demand for artificial teeth prostheses made of the materials which are sintered at $1500^{\circ}C$ such as zirconia ceramic. Since degree of strength of the materials is very high, however, it is very difficult for technicians to manually fabricate the prostheses for these ceramics. So the prostheses have been fabricated by using CNC(computer numerical control) machines. In doing them by using CNC, it is very important that the prostheses satisfying dentists's requirements are accurately modeled into 3D objects. In this paper, we propose an effective method for modeling single cores such as single caps and Conus cores, which are the main those of artificial teeth prostheses. And we also present the visual examples of 3D models for these single cores modeled by the proposed methods. In special, the method has used Minkowski sum and ZMap for modeling the single cores.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.6
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• pp.72-79
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• 2017

In this paper, we present a new saliency detection algorithm using the mutual information of wavelet subbands. Our method constructs an intermediate saliency map using the power operation and Gaussian blurring for high-frequency wavelet coefficients. After combining three intermediate saliency maps according to the direction of wavelet subband, we find the main directional components using entropy measure. The amount of mutual information of each subband is obtained centering on the subband having the minimum entropy The final saliency map is detected using Minkowski sum based on weights calculated by the mutual information. As a result of the experiment on CAT2000 and ECSSD databases, our method showed good detection results in terms of ROC and AUC with few computation times compared with the conventional methods.

• ETRI Journal
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• v.39 no.4
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• pp.514-524
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• 2017

In this paper, we propose a spatial modulation (SM) scheme referred to as complex quadrature SM (CQSM). In contrast to quadrature SM (QSM), CQSM transmits two complex signal constellation symbols on the real and quadrature spatial dimensions at each channel use, increasing the spectral efficiency. To achieve that, signal symbols transmitted at any given time instant are drawn from two different modulation sets. The first modulation set is any of the conventional QAM/PSK alphabets, while the second is a rotated version of it. The optimal rotation angle is obtained through simulations for several modulation schemes and analytically proven for the case of QPSK, where both results coincide. Simulation results showed that CQSM outperformed QSM and generalized SM by approximately 5 dB and 4.5 dB, respectively, for the same transmission rate. Its performance was similar to that of QSM; however, it achieved higher transmission rates. It was additionally shown numerically and analytically that CQSM outperformed QSM for a relatively large number of transmit antennas.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2402-2406
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• 2005

A collision query determines the intersection between given objects, and is used in computer-aided design and manufacturing, animation and simulation systems, and physically-based modeling. Bounding volume hierarchies are one of the simplest and most widely used data structures for performing collision detection on complex models. In this paper, we present hierarchy of oriented rounded bounding volume for fast proximity queries. Designing hierarchies of new bounding volumes, we use to combine multiple bounding volume types in a single hierarchy. The new bounding volume corresponds to geometric shape composed of a core primitive shape grown outward by some offset such as the Minkowski sum of rectangular box and a sphere shape. In the experiment of parallel close proximity, a number of benchmarks to measure the performance of the new bounding box and compare to that of other bounding volumes.

• Korean Journal of Computational Design and Engineering
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• v.8 no.4
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• pp.243-253
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• 2003

This paper presents a new geometric morphing algorithm for polygons based on a simple geometric structure called direction map, which is mainly composed of a circular list of direction vectors defined by two neighboring vertices of a polygon. To generate a sequence of intermediate morphing shapes, first we merge direction maps of given control shapes based on a certain ordering rule of direction vectors, and scale the length of each direction vectors using Bezier or blossom controls. We show that the proposed algorithm is an improvement of the previous methods based on Minkowski sum (or convolution) in th aspects of computational efficiency and geometric properties.

• Journal of the Korea Computer Graphics Society
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• v.11 no.2
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• pp.1-8
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• 2005

하나의 치아가 일부 파손되어 수복되어야 할 보철물을 인레이/온레이(Inlay/Onlay)라 한다. 본 논문에서는 3차원 메쉬 기반 모델에서 보다 정확한 인레이/온레이를 효과적으로 모델링하기 위한 기법을 제안한다. 인레이/온레이는 지대치와 접하는 내면과 밖으로 들어나는 외면으로 구성된다. 인레이/온레이의 내면 모델링은 2차원 다각선상의 Minkowski Sum 알고리즘을 이용하여 지대치와의 접합력을 확보한다. 그리고 미리 데이터베이스에 저장된 표준 치아 모델, 치과의사에 의해 만들어진 FGP(functionally guided plane) 및 메쉬의 변형 기법인 DMFFD(direct manipulation free-form deformation) 기법[16]과 MWD(multiple wires deformation) 기법[24]을 이용하여 외면을 모델링한다. 데이터베이스에 저장된 표준 치아는 인레이/온레이 외면의 형태를 결정하기 위해 사용되며, FGP는 환자의 인접면과 교합면의 특성을 반영하기 위해 사용되었다. 마지막으로 3차원 메쉬의 두 변형 기법인 DMFFD와 MWD 기법은 환자의 인접면과 교합면을 반영한 치아의 형태를 만들어 내기 위해 사용된다. 본 논문에서 제안한 방법은 인레이/온레이의 내면과 외면을 설계할 때 필요한 정보를 미리 설정하여 처리하므로 기존의 방법에 비해 짧은 시간에 보다 정확한 인레이/온레이를 설계할 수 있었다.

• The KIPS Transactions:PartA
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• v.12A no.6 s.96
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• pp.515-522
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• 2005

This paper presents a method for effectively modeling inlay/onlay prostheses restoring a tooth that are partially destroyed. An inlay/onlay is composed of internal surface adhering to an abutment, and external surface revealed to the outside sight. Internal surfaces are modeled using Minkowski sum expanding the grinded surface parts of abutments so that the internal surfaces can adhere to the abutments with closer contact. In modeling external surfaces, we exploit 3D mesh deformation techniques: DMFFD(direct manipulation free-form deformation)[19] and MWD(multiple wires deformation)[17] with three kinds of informations: standard teeth models, mesh data obtained by scanning a plaster cast of a patient's tooth, FGP(functionally guided plane) measuring the occlusion of the patients's teeth. The standard teeth models are used for building up the basic shapes of external surfaces, while the plaster fast and FGP data are used for reflecting the unique properties of adjacent md occlusal surfaces of the patients's teeth, which are slightly different to each other but very important for correct functioning. With these informations as input data, the adjacent and occlusal surfaces are automatically generated as mesh data using the techniques of DMFFD and m, respectively. Our method was implemented so that inlay/onlay prostheses fan be designed more accurately by visualizing the generated mesh models with requirements by dentists.

• Korean Journal of Computational Design and Engineering
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• v.22 no.1
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• pp.37-43
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• 2017

3D printing techniques can be used in various application fields and many researches have been reported. FDM (Fused Deposition modeling) can make multi-material or multi-color models with the simultaneous use of two or more filaments. In a dual-nozzle FDM printers, while the active nozzle is working, the remaining nozzle will be idle. The remaining molten resins inside an idle nozzle can ooze out unwantedly. The spill over from the resting nozzle produces unwanted remaining on the fabricated product. In this research, we suggest a method for optimizing building position of a model to minimize the unwanted spill-over that could possibly contaminate the final product. The method is based on minimizing the two intersection volumes. The first intersection volume is obtained by intersecting the volume defined by the first material and the Minkowski sum between the volume of the first material and the vector obtained by subtracting the center point of the first nozzle from the center point of the second nozzle. The second intersection volume can be obtained by reversing the role of the first and second volumes and nozzles. Some results obtained from the implementation using the Parasolid (Siemens) geometric modeling kernel is presented.

• Journal of KIISE:Databases
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• v.31 no.2
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• pp.122-131
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• 2004

Traditional works on indexing have been suggested for low dimensional data under dynamic environments. But recent database applications require efficient processing of huge sire of high dimensional data under static environments. Thus many indexing strategies suggested especially in partitioning ones do not adapt to these new environments. In our study, we point out these facts and propose a new partitioning strategy, which complies with new applications' requirements and is derived from analysis. As a preliminary step to propose our method, we apply a packing technique on the one hand and exploit observations on the Minkowski-sum cost model on the other, under uniform data distribution. Observations predict that unbalanced partitioning strategy may be more query-efficient than balanced partitioning strategy for high dimensional data. Thus we propose our method, called CSP (Cyclic Spliced Partitioning method). Analysis on this method explicitly suggests metrics on how to partition high dimensional data. By the cost model, simulations, and experiments, we show excellent performance of our method over balanced strategy. By experimental studies on other indices and packing methods, we also show the superiority of our method.