• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.8 no.3
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• pp.122-130
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• 2009

The paper presents an algorithm which uses code vectors to represent comer geometry information for searching the similar images from a database. The comers have been extracted by finding the intersections of the detected lines found using Hough transform. Taking the comer as the center coordinate, the angles of the intersecting lines are determined and are represented using code vectors. A code book has been used to code each comer geometry information and indexes to the code book are generated. For similarity measurement, the histogram of the code book indexes is used. This result in a significant small size feature matrix compared to the algorithms using color features. Experimental results show that use of code vectors is computationally efficient in similarity measurement and the comers being noise invariant produce good results in noisy environments.

• International Journal of Control, Automation, and Systems
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• v.5 no.6
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• pp.663-673
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• 2007

This paper presents a new moving obstacle detection method using an optical flow in mobile robot with an omnidirectional camera. Because an omnidirectional camera consists of a nonlinear mirror and CCD camera, the optical flow pattern in omnidirectional image is different from the pattern in perspective camera. The geometry characteristic of an omnidirectional camera has influence on the optical flow in omnidirectional image. When a mobile robot with an omnidirectional camera moves, the optical flow is not only theoretically calculated in omnidirectional image, but also investigated in omnidirectional and panoramic images. In this paper, the panoramic image is generalized from an omnidirectional image using the geometry of an omnidirectional camera. In particular, Focus of expansion (FOE) and focus of contraction (FOC) vectors are defined from the estimated optical flow in omnidirectional and panoramic images. FOE and FOC vectors are used as reference vectors for the relative evaluation of optical flow. The moving obstacle is turned out through the relative evaluation of optical flows. The proposed algorithm is tested in four motions of a mobile robot including straight forward, left turn, right turn and rotation. The effectiveness of the proposed method is shown by the experimental results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.439-444
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• 2001

We provide methods to simulate noise propagation for an outdoor environment. Forward tracing method traces sound vectors from sources to receivers while geometry based computation finds all possible sound propagation between sources and receivers geometrically. We discuss defects in relying on a forward tracing method, and suggest a geometry based method. Geometry based method considers all possible direct and indirect(propagation via limited number of reflections) sound propagation saving computational time compared to forward sound tracing. Our simulation results are visualized using VRML(Virtual Reality Modeling Language).

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.355-362
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in various problems. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem and fillet problem are chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in these problems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.9
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• pp.1320-1327
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in supercavitating flow problem. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in potential flow problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design in potential flow problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem is chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in this flow problem.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1047-1052
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in supercavitating flow problem. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in potential flow problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design in potential flow problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-touse features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem is chosen to illustrate the efficiency of the proposed methodology. Implementation issues for and optimization procedure are addressed in this flow problem.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.959-1008
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• 1999

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand the torsion of a connection. The latter parts of the paper deal with the Levi-Civita connection of a Riemannian manifold. The idea is to get at the connection by first finding its.spary. This is a second order vector field that encodes the second order differential equation for geodesics. The paper also develops some machinery involving lifts of vector fields form a manifold to its tangent bundle and uses a variational approach to produce the Riemannian spray.

• The Mathematical Education
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• v.56 no.1
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• pp.63-80
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• 2017

By analysing the examination papers from third grade high school students, we classified the errors occurred in the problem solving process of high school 'Geometry and Vectors' into several types. There are five main types - (A)Insufficient Content Knowledge, (B)Wrong Method, (C)Logical Invalidity, (D)Unskilled Expression and (E)Interference.. Type A and B lead to an incorrect answer, and type C and D cannot be distinguished by multiple-choice or closed answer questions. Some of these types are classified into subtypes - (B1)Incompletion, (B2)Omitted Condition, (B3)Incorrect Calculation, (C1)Non-reasoning, (C2)Insufficient Reasoning, (C3)Illogical Process, (D1)Arbitrary Symbol, (D2)Using a Character Without Explanation, (D3) Visual Dependence, (D4)Symbol Incorrectly Used, (D5)Ambiguous Expression. Based on the these types of errors, answers of each problem was analysed in detail, and proper ways to correct or prevent these errors were suggested case by case. When problems that were used in the periodical test were given again in descriptive forms, 67% of the students tried to answer, and 14% described flawlessly, despite that the percentage of correct answers were higher than 40% when given in multiple-choice form. 34% of the students who tried to answer have failed to have logical validity. 37% of the students who tried to answer didn't have enough skill to express. In lessons on curves of secondary degree, teachers should be aware of several issues. Students are easily confused between 'focus' and 'vertex', and between 'components of a vector' and 'coordinates of a point'. Students often use an undefined expression when mentioning a parallel translation. When using a character, students have to make sure to define it precisely, to prevent the students from making errors and to make them express in correct ways.

• Proceedings of the Society of Korea Industrial and System Engineering Conference
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• 2002.05a
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• pp.455-460
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• 2002

As the transmission of 3D shape models through Internet becomes more important, the compression issue of shape models gets more critical. The issues for normal vectors have not yet been explored as much as it deserves, even though the size of the data for normal vectors can be significantly larger than its counterparts of topology and geometry. Presented in this paper is an approach to compress the normal vectors of a shape model represented in a mesh using the concept of clustering. It turns out that the proposed approach has a significant compression ratio without a serious sacrifice of the visual quality of the model.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.3
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• pp.255-263
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• 2005

This paper proposes an efficient boundary-based technique for the shape design sensitivity analysis in various disciplines. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in the problems. The formula can be conveniently used for gradient computation in a variety of shape design problems. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite. Perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The potential flow problems and fillet problem are chosen to illustrate the efficiency of the proposed methodology.