• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.337-345
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• 2006

John Harer conjectured that the canonical map from braid group to mapping class group induces zero homology homomorphism. To prove the conjecture it suffices to show that this map preserves the first Araki-Kudo-Dyer-Lashof operation. To get information on this homology operation we need to investigate the image of braiding under the Harer map. The main result of this paper is to give both algebraic and geometric interpretations of the image of braiding under the Harer map. For this we need to calculate long chains of consecutive actions of Dehn twists on the fundamental group of surface.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.273-285
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• 1997

The aim of this paper is to present theorems on the exitence of zeros for mappings defined on convex subsets of topological vector spaces with values in a vector space. In addition to natural assumptions of continuity, convexity, and compactness, the mappings are subject to some geometric conditions. In the first theorem, the mapping satisfies a "Darboux-type" property expressed in terms of an auxiliary numerical function. Typically, this functions is, in this case, related to an order structure on the target space. We derive an existence theorem for "obtuse" quasiconvex mappings with values in an ordered vector space. In the second theorem, we prove the existence of a "common zero" for an arbitrary (not necessarily countable) family of mappings satisfying a general "inwardness" condition againg expressed in terms of numerical functions (these numerical functions could be duality pairings (more generally, bilinear forms)). Our inwardness condition encompasses classical inwardness conditions of Leray-Schauder, Altman, or Bergman-Halpern types.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.158-163
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• 2009

In recent years, there has been increased interest in characterizing and extracting 3D information from 2D images for human tracking and identification. In this paper, we propose a single view-based framework for robust estimation of height and position. In the proposed method, 2D features of target object is back-projected into the 3D scene space where its coordinate system is given by a rectangular marker. Then the position and the height are estimated in the 3D space. In addition, geometric error caused by inaccurate projective mapping is corrected by using geometric constraints provided by the marker. The accuracy and the robustness of our technique are verified on the experimental results of several real video sequences from outdoor environments.

• Korean Journal of Computational Design and Engineering
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• v.2 no.1
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• pp.60-67
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• 1997

CAD systems offer a variety of techniques for designing and rendering models of static 3D objects and even of mechanisms, but relatively few tools exist for interactively specifying arbitrary movements of rigid bodies through space. Such tools are essential, not only for artistic animation, but also, for planning and demonstrating assembly and disassembly procedure of manufactured products. A rigid body motion is a continuous mapping from the time domain to a set of positions. To relieve the designers from the burden of specifying this mapping in abstract mathematical terms, combinations of simple rigid motion primitives, such as linear translations or constant axis rotations, are often used. These simple motions are planar and thus ill-suited for approximating arbitrary motions in 3D-space. Instead, we propose the screw motion primitive, a special combination of linear translations and constant axis rotations, which has a simple geometric representation that can be automatically and unambiguously computed from the starting and ending positions of the moving body. Although, any two positions may be interpolated by an infinity of motions, we chose the screw motion for its relative generality and its computational advantages. The paper covers original algorithms for computing the screw motions from interpolated positions and envelopes of swept regions to predict collisions.

• Structural Engineering and Mechanics
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• v.38 no.3
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• pp.261-281
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• 2011

A new method of formulation of a class of elements that are immune to mesh distortion effects is proposed here. The simple three-noded bar element with an offset of the internal node from the element center is employed here to demonstrate the method and the principles on which it is founded upon. Using the function space approach, the modified formulation is shown here to be superior to the conventional isoparametric version of the element since it satisfies the completeness requirement as the metric formulation, and yet it is in agreement with the best-fit paradigm in both the metric and the parametric domains. Furthermore, the element error is limited to only those that are permissible by the classical projection theorem of strains and stresses. Unlike its conventional counterpart, the modified element is thus not prone to any errors from mesh distortion. The element formulation is symmetric and thus satisfies the requirement of the conservative nature of problems associated with all self-adjoint differential operators. The present paper indicates that a proper mapping set for distortion immune elements constitutes geometric and displacement interpolations through parametric and metric shape functions respectively, with the metric components in the displacement/strain replaced by the equivalent geometric interpolation in parametric co-ordinates.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.11
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• pp.2055-2061
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• 2006

The detection of geometric primitives from a digital image is one of the basic tasks in computer vision area and the Hough transform is a well-known method for detecting analytical shape represented by a number of free parameters. However the basic property of the Hough transform, the one-to-many mapping from an image space to a Hough space, causes the innate problem, the sensitivity to noise. In this paper, we proposed Edge Strength Hough Transform which uses edge strength to reduce the sensitivity to noise and proved the insensitivity using the ratio of peaks in a Mough space. We also experimented the proposed method on lines and got small number of peaks in a Hough space compared to traditional Hough transform, which supports the noise insensitivity of the proposed method.

• Journal of Broadcast Engineering
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• v.23 no.5
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• pp.622-627
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• 2018

In this paper, we introduce an integrated augmented reality system using a small camera and a projector. We extract three-dimensional information of an object with a small portable camera and a projector by using a structured light system. We develop the concept of the virtual camera to generalize the projection method so that the image can be projected at a desired position with only the mesh of the object to be projected without computing the mapping between specific point sets. Therefore, it is possible to project not only simple planes but also complex curved surfaces to desired positions without complicated geometric calculation. Based on a robot with a small camera and a projector, it will largely explain the projector-camera system calibration, the calculation of the position of the recognized object, and the image projection method using the virtual camera concept.

• Journal of Sensor Science and Technology
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• v.23 no.6
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• pp.377-382
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• 2014

Detecting and segmenting diffuse targets in laser ranging data is a critical problem for tactical reconnaissance. In this study, we propose a new method that facilitates the characterization of diffuse irregularly shaped objects using "spin images," i.e., local 2D histograms of laser returns oriented in 3D space, and a clustering process. The proposed "cluster-based spin imaging" method resolves the problem of using standard spin images for diffuse targets and it eliminates much of the computational complexity that characterizes the production of conventional spin images. The direct processing of pre-segmented laser points, including internal points that penetrate through a diffuse object's topmost surfaces, avoids some of the requirements of the approach used at present for spin image generation, while it also greatly reduces the high computational time overheads incurred by searches to find correlated images. We employed 3D airborne range data over forested terrain to demonstrate the effectiveness of this method in discriminating the different geometric structures of individual tree clusters. Our experiments showed that cluster-based spin images have the potential to separate classes in terms of different ages and portions of tree crowns.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2012.05a
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• pp.162-163
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• 2012

In this paper, we propose a synthesis method of elemental images from Kinect images for 3D integral imaging display. Since RGB images and depth image obtained from Kinect are not able to display 3D images in integral imaging system, we need transform the elemental images in integral imaging display. To do so, we synthesize the elemental images based on the geometric optics mapping from the depth plane images obtained from RGB image and depth image. To show the usefulness of the proposed system, we carry out the preliminary experiments using the two person object and present the experimental results.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.1
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• pp.95-104
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• 2007

A new design approach of complex geometries such as wing/body configuration is arranged by using overset mesh techniques under large scale computing environment. For an in-depth study of the flow physics and highly accurate design, several special overlapped structured blocks such as collar grid, tip-cap grid, and etc. which are commonly used in refined drag prediction are adopted to consider the applicability of the present design tools to practical problems. Various pre- and post-processing techniques for overset flow analysis and sensitivity analysis are devised or implemented to resolve overset mesh techniques into the design optimization problem based on Gradient Based Optimization Method (GBOM). In the pre-processing, the convergence characteristics of the flow solver and sensitivity analysis are improved by overlap optimization method. Moreover, a new post-processing method, Spline-Boundary Intersecting Grid (S-BIG) scheme, is proposed by considering the ratio of cell area for more refined prediction of aerodynamic coefficients and efficient evaluation of their sensitivities under parallel computing environment. With respect to the sensitivity analysis, discrete adjoint formulations for overset boundary conditions are derived by a full hand-differentiation. A smooth geometric modification on the overlapped surface boundaries and evaluation of grid sensitivities can be performed by mapping from planform coordinate to the surface meshes with Hicks-Henne function. Careful design works for the drag minimization problems of a transonic wing and a wing/body configuration are performed by using the newly-developed and -applied overset mesh techniques. The results from design applications demonstrate the capability of the present design approach successfully.