• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.379-386
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• 2015

The original geometric mean of two positive definite operators A and B is given by A#B = A^1/2(A^-1/2BA^-1/2)^1/2A^1/2. In this article we provide a new proof to construct from the two-variable geometric mean to the multivariable mean via symmetrization introduced by Lawson and Lim [5]. Finally we provide an algorithm to find three-variable geometric mean via symmetrization, which plays an important role to construct higher-order geometric means.

• The KIPS Transactions:PartA
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• v.12A no.1 s.91
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• pp.13-22
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• 2005

Similarly to the edges defined in a 2D image, we can define the geometric features representing the boundary of the distinctive parts appearing on 3D meshes. The geometric features have been used as basic primitives in several applications such as mesh simplification, mesh deformation, and mesh editing. In this paper, we propose geometric livewire and geometric livelane for extracting geometric features in a 3D mesh, which are the extentions of livewire and livelane methods in images. In these methods, approximate curvatures are adopted to represent the geometric features in a 3D mesh and the 3D mesh itself is represented as a weighted directed graph in which cost functions are defined for the weights of edges. Using a well-known shortest path finding algorithm in the weighted directed graph, we extracted geometric features in the 3D mesh among points selected by a user. In this paper, we also visualize the results obtained from applying the techniques to extracting geometric features in the general meshes modeled after human faces, cows, shoes, and single teeth.

• Bulletin of the Korean Chemical Society
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• v.28 no.10
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• pp.1705-1708
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• 2007

Geometric manipulation of molecules is an essential elementary component in computational modeling programs for molecular structure, stability, dynamics, and design. The computational complexity of transformation of internal coordinates to Cartesian coordinates was discussed before.1 The use of rotation matrices was found to be slightly more efficient than that of quaternion although quaternion operators have been widely advertised for rotational operations, especially in molecular dynamics simulations of liquids where the orientation is a dynamical variable.2 The discussion on computational efficiency is extended here to a more general case in which bond angles and sidechain torsion angles are allowed to vary. The algorithm of Thompson3 is derived again in terms of quaternions as well as rotation matrices, and an algorithm with optimal efficiency is described. The algorithm based on rotation matrices is again found to be slightly more efficient than that based on quaternions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.7 s.262
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• pp.739-746
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• 2007

Recently, models in STL files are widely used in reverse engineering processes, CAD systems and analysis systems. However the models have poor geometric quality and include only triangles, so the models are not suitable for the finite element analysis. This paper presents a general method that generates finite element mesh from STL file models. Given triangular meshes, the method estimates triangles and makes clusters which consist of triangles. The clusters are merged by some geometric indices. After merging clusters, the method applies plane meshing algorithm, based on domain decomposition method, to each cluster and then the result plane mesh is projected into the original triangular set. Because the algorithm uses general methods to generate plane mesh, we can obtain both tri and quad meshes unlike previous researches. Some mechanical part models are used to show the validity of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.5
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• pp.1023-1029
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• 2011

In the industrial vision systems, image correction has great influence on the overall performance of measurement or inspection. The overall area of distorted image is usually splitted into small control areas, and each area is corrected by its control points. The performance of correction methods using control points can be improved by reduction of control areas because the computational time and memory highly depend on the number of control areas. We develop a merging algorithm that reduces control areas and preserves the correction accuracy. The algorithm merges the splitted control areas by use of quad tree method. Experimental results are presented to verify the usefulness of the proposed method.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.54-60
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• 2001

In this paper, a shape-based block layout (SBL) approach is presented to solve the facility layout problem with unequal-area and fixed shapes. The SBL approach employs hybrid genetic algorithm (Hybrid-GA) to find a good solution and the concept of bay structure is used. In the typical facility layout problem with unequal area and fixed shapes, the given geometric constraints of unequal-area and fixed shapes are mostly approximated to original shape by aspect ratio. Thus, the layout results require extensive manual revision to create practical layouts and it produces irregular building shapes and too much unusable spaces. Experimental results show that a SBL model is able to produce better solution and to create more practical layouts than those of existing approaches.

• Korean Journal of Computational Design and Engineering
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• v.19 no.3
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• pp.294-304
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• 2014

This paper presents a real-time rendering algorithm of large-scale geometric data using GLSL (OpenGL shading language). It details the VAO (vertex array object) and VBO(vertex buffer object) to be used for up-loading the large-scale point clouds and polygon meshes to a graphic video memory, and describes the shader program composed by a vertex shader and a fragment shader, which manipulates those large-scale data to be rendered by GPU. In addition, we explain the global rendering procedure that creates and runs the shader program with the VAO and VBO. Finally, a rendering performance will be measured with application examples, from which it will be demonstrated that the proposed algorithm enables a real-time rendering of large amount of geometric data, almost impossible to carry out by previous techniques.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.11-20
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• 2009

The conventional methods of boundary-conformed 2D surfaces generation usually yield some problems. This paper deals with two boundary-conformed 2D surface generation methods, one conventional approach, the linear Coons method, and a new method, boundary-conformed interpolation. In this new method, unidirectional 2D surface has been generated using some of the geometric properties of the given boundary curves. A method of simultaneous displacement of the interpolated curves from the opposite boundaries has been adopted. The geometric properties considered for displacements include weighted combination of angle bisector and linear displacement vectors at all the data-points of the two opposite generating curves. The algorithm has one adjustable parameter that controls the characteristics of transformation of one set of curves from its parents. This unidirectional process has been extended to bi-directional parameterization by superimposing two sets of unidirectional curves generated from both boundary pairs. Case studies show that this algorithm gives reasonably smooth transformation of the boundaries. This algorithm is more robust than the linear Coons method and capable of resolving the 2D boundary-conformed parameterization problems.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.3B
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• pp.557-564
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• 2000

This paper presents a watermarking algorithm for embedding visually recognizable pattern (Mark, Logo, Symbol, stamping or signature) into the image. first, the color image(RGB model)is transformed in YCbCr model and then the Y component is transformed into 3-level wavelet transform. Next, the values are assembled with pattern watermark. PN(pseudo noise) code at spread spectrum communication method and mutilevel watermark weights. This values are inserted into discrete wavelet domain. In our scheme, new calculating method is designed to calculate wavelet transform with integer value in considering the quantization error. and we used the color conversion with fixed-point arithmetic to be easy to make the hardware hereafter. Also, we made the new solution using mutilevel threshold to robust to common signal distortions and malicious attack, and to enhance quality of image in considering the human visual system. the experimental results showed that the proposed watermarking algorithm was superior to other similar water marking algorithm. We showed what it was robust to common signal processing and geometric transform such as brightness. contrast, filtering. scaling. JPEG lossy compression and geometric deformation.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.6
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• pp.58-67
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• 2009

A correspondence matching is one of the important tasks in computer vision, and it is not easy to find corresponding points in variable environment where a scale, rotation, view point and illumination are changed. A SURF(Speeded Up Robust Features) algorithm have been widely used to solve the problem of the correspondence matching because it is faster than SIFT(Scale Invariant Feature Transform) with closely maintaining the matching performance. However, because SURF considers only gray image and local geometric information, it is difficult to match corresponding points on the image where similar local patterns are scattered. In order to solve this problem, this paper proposes an extended SURF algorithm that uses the invariant color and global geometric information. The proposed algorithm can improves the matching performance since the color information and global geometric information is used to discriminate similar patterns. In this paper, the superiority of the proposed algorithm is proved by experiments that it is compared with conventional methods on the image where an illumination and a view point are changed and similar patterns exist.