• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.189-193
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• 1998

In this paper we construct a sequence of spaces which has Gromov-Hausdorff limit such that a geodesic in the limit space is not realized as a limit of geodesics in the spaces of the sequence. This contrasts with the result of Grove and Petersen in [1] where they proved otherwise for Alexandrov spaces with common curvature bounds.

• Journal of Korea Multimedia Society
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• v.19 no.12
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• pp.1927-1935
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• 2016

This paper propose a framework for human body parts in RGB-D image. We conduct tasks of obtaining person area, finding candidate areas and local detection in order to detect hand, foot and head which have features of long accumulative geodesic distance. A person area is obtained with background subtraction and noise removal by using depth image which is robust to illumination change. Finding candidate areas performs construction of graph model which allows us to measure accumulative geodesic distance for the candidates. Instead of raw depth map, our approach constructs graph model with segmented regions by quadtree structure to improve searching time for the candidates. Local detection uses HOG based SVM for each parts, and head is detected for the first time. To minimize false detections for hand and foot parts, the candidates are classified with upper or lower body using the head position and properties of geodesic distance. Then, detect hand and foot with the local detectors. We evaluate our algorithm with datasets collected Kinect v2 sensor, and our approach shows good performance for head, hand and foot detection.

• Journal of KIISE:Software and Applications
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• v.36 no.6
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• pp.479-490
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• 2009

A number of temporal abstraction approaches have been suggested so far to handle the high computational complexity of Markov decision problems (MDPs). Although the structure of temporal abstraction can significantly affect the efficiency of solving the MDP, to our knowledge none of current temporal abstraction approaches explicitly consider the relationship between topology and efficiency. In this paper, we first show that a topological measurement from complex network literature, mean geodesic distance, can reflect the efficiency of solving MDP. Based on this, we build an incremental method to systematically build temporal abstractions using a network model that guarantees a small mean geodesic distance. We test our algorithm on a realistic 3D game environment, and experimental results show that our model has subpolynomial growth of mean geodesic distance according to problem size, which enables efficient solving of resulting MDP.

• Proceeding of KASS Symposium
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• 2008.05a
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• pp.101-106
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• 2008

This paper describes a comparative study of genetic algorithm and mathematical programming technique applied in the design optimization of geodesic dome. In particular, the genetic algorithm adopted in this study uses the so-called re-birthing technique together with the standard GA operations such as fitness, selection, crossover and mutation to accelerate the searching process. The finite difference method is used to calculate the design sensitivity required in mathematical programming techniques and three different techniques such as sequential linear programming (SLP), sequential quadratic programming(SQP) and modified feasible direction method(MFDM) are consistently used in the design optimization of geodesic dome. The optimum member sizes of geodesic dome against several external loads is evaluated by the codes $ISADO-GA{\alpha}$ and ISADO-OPT. From a numerical example, we found that both optimization techniques such as GA and mathematical programming technique are very effective to calculate the optimum member sizes of three dimensional discrete structures and it can provide a very useful information on the existing structural system and it also has a great potential to produce new structural system for large spatial structures.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.965-976
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• 2008

In this article, we constructively prove that on a surface S with genus g$\geq$2, there exit maximal geodesic laminations with 7g-7,...,9g-9 leaves. Thus, S can have ideal cell-decompositions (i.e., S can be (ideally) triangulated by maximal geodesic laminations) with 7g-7,...,9g-9 (ideal) 1-cells. Once there is a triangulation for a compact surface, the Euler characteristic for the surface can be calculated as the alternating sum F-E+V, where F, E, and V denote the number of faces, edges, and vertices, respectively. We also prove that the same formula holds for the ideal cell decompositions.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.325-332
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• 2006

Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation, because the material property has strong axial stiffness, but little bending stiffness. The problem of cutting pattern is highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore the ordinary computer software of structural analysis & design is not suitable for membrane structures. In this study, we develop the program for cutting pattern generation using geodesic line, and investigate the result of example's cutting pattern in detail.

• Proceeding of KASS Symposium
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• 2005.05a
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• pp.125-132
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• 2005

Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The material property of the membrane has strong axial stiffness, but little bending stiffness. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation. In shape finding, membrane structures are unstable structures initially. These soft structures need to be introduced initial stresses because of its initial unstable state, and it happens large deformation phenomenon. And also there are highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore, in this study, to find the structural shape after large deformation caused by Initial stress, we need the shape analysis considering geometric nonlinear ten And the geodesic line on surface of initial equilibrium shape and the cutting pattern generation using the geodesic line is introduced.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07b
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• pp.748-750
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• 2005

Isomap [1] is a manifold learning algorithm, which extends classical multidimensional scaling (MDS) by considering approximate geodesic distance instead of Euclidean distance. The approximate geodesic distance matrix can be interpreted as a kernel matrix, which implies that Isomap can be solved by a kernel eigenvalue problem. However, the geodesic distance kernel matrix is not guaranteed to be positive semidefinite. In this paper we employ a constant-adding method, which leads to the Mercer kernel-based Isomap algorithm. Numerical experimental results with noisy 'Swiss roll' data, confirm the validity and high performance of our kernel Isomap algorithm.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.88-99
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• 2021

The purpose of this paper is to assign a movable frame to an arbitrary point of a rational Bézier curve on the 2-sphere S2 in Euclidean 3-space R3 to provide a better understanding of the geometry of the curve. Especially, we obtain the formula of geodesic curvature for a quadratic rational Bézier curve that allows a curve to be characterized on the surface. Moreover, we give some important results and relations for the Darboux frame and geodesic curvature of a such curve. Then, in specific case, given characterizations for the quadratic rational Bézier curve are illustrated on a unit 2-sphere.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1607-1620
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• 2023

In this paper, we mainly study the problem of the existence of homogeneous geodesics in sub-Finsler manifolds. Firstly, we obtain a characterization of a homogeneous curve to be a geodesic. Then we show that every compact connected homogeneous sub-Finsler manifold and Carnot group admits at least one homogeneous geodesic through each point. Finally, we study a special class of ℓ^p-type bi-invariant metrics on compact semi-simple Lie groups. We show that every homogeneous curve in such a metric space is a geodesic. Moreover, we prove that the Alexandrov curvature of the metric space is neither non-positive nor non-negative.