• 호남수학학술지
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• 제31권2호
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• pp.185-201
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• 2009

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ of a nonflat complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In this paper, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.920-923
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• 1996

This paper presents a new algorithm for the self-localization of a mobile robot using perspective invariant(Cross Ratio). Most of conventional model-based self-localization methods have some problems that data structure building, map updating and matching processes are very complex. Use of the simple cross ratio can be effective to the above problems. The algorithm is based on two basic assumptions that the ground plane is flat and two parallel walls are available. Also it is assumed that an environmental map is available for matching between the scene and the model. To extract an accurate steering angle for a mobile robot, we take advantage of geometric features such as vanishing points(V.P). Point features for computing cross ratios are extracted robustly using a vanishing point and the intersection points between floor and the vertical lines of door frames. The robustness and feasibility of our algorithms have been demonstrated through experiments in indoor environments using an indoor mobile robot, KASIRI-II(KAist SImple Roving Intelligence).

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.2393-2396
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• 2005

We present a method to detect on-road vehicle using geometric invariant of feature points on side planes of the vehicle. The vehicles are assumed into a set of planes and the invariant from motion information of features on the plane segments the plane from the theory that a geometric invariant value defined by five points on a plane is preserved under a projective transform. Harris corners as a salient image point are used to give motion information with the normalized correlation centered at these points. We define a probabilistic criterion to test the similarity of invariant values between sequential frames. Experimental results using images of real road scenes are presented.

• 한국군사과학기술학회지
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• 제12권4호
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• pp.524-531
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• 2009

In this paper, we propose an automatic image registration method for multi-sensor image fusion such as visible and infrared images. The registration is achieved by finding corresponding feature points in both input images. In general, the global statistical correlation is not guaranteed between multi-sensor images, which bring out difficulties on the image registration for multi-sensor images. To cope with this problem, mutual information is adopted to measure correspondence of features and to select faithful points. An update algorithm for projective transform is also proposed. Experimental results show that the proposed method provides robust and accurate registration results.

• 대한기계학회논문집
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• 제14권2호
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• pp.367-375
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• 1990

A data structure representing 3-D objects was designed for the personal computer. It is very simple to be used in the personal computers which have small memory and low speed. A homogeneous transformation for developing 3-D objects was derived. Each developing procedure consists of five transformations : one translational-three rotational-one translational. Developing a solid is a creative work. So the results of developing vary with the order of surfaces to be developed. One method to reduce the length of seam was considered. The programs used in this study were written in Pascal and Assembly and a modeller that generates 3-D primitives was included. This program is an interactive dual-screen system. While all the menus in Korean are displayed at the monochrome monitor, the development figures with projective views are drawn at the color monitor. The program has wide applications for plate works.

• 한국GIS학회:학술대회논문집
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• 한국GIS학회 2003년도 공동 춘계학술대회 논문집
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• pp.328-333
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• 2003

GIS기술은 실세계의 분석에서부터 3D 가상도시의 구축까지 매우 빠르게 발전하고 있다. 3D가상도시는 GIS 기술, 컴퓨터그래픽스 기술, 가상현실 기술, 데이터베이스 기술에 의해 컴퓨터 속에 구현이 되는 도시를 말한다. 본 연구에서는 1/1,000 수치지도를 이용하여 3D건물모델을 형성하였고, 건물모델을 형성할 때는 삼각형 메쉬를 형성하고 최적의 메쉬를 형성하기 위하여 Divide and Conquer 알고리즘을 사용하였다. 메쉬가 형성된 수치지도의 건물모델에 대하여 기존의 기하파이프라인을 개선함으로서 건물모델을 빠르게 렌더링할 수 있도록 하였다. 건물측면에 대하여는 디지틀 카메라를 이용하여 측면에 대한 이미지를 취득하고 2D Projective Transformation을 적용하여 이미지를 조정하였다.

• 대한수학회지
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• 제49권2호
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• pp.251-263
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• 2012

A CW complex B is said to be I-trivial if there does not exist a $\mathbb{Z}_2$-map from $S^{i-1}$ to S(${\alpha}$) for any vector bundle ${\alpha}$ over B a any integer i with i > dim ${\alpha}$. In this paper, we consider the question of determining whether $\Sigma^k\mathbb{R}P^n$ is I-trivial or not, and to this question we give complete answers when k $\neq$ 1, 3, 8 and partial answers when k = 1, 3, 8. A CW complex B is I-trivial if it is "W-trivial", that is, if for every vector bundle over B, all the Stiefel-Whitney classes vanish. We find, as a result, that $\Sigma^k\mathbb{R}P^n$ is a counterexample to the converse of th statement when k = 2, 4 or 8 and n $\geq$ 2k.

• 대한수학회지
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• 제57권4호
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• pp.873-892
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• 2020

Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere S^n-1 in ℝⁿ. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.

• 한국CDE학회논문집
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• 제20권4호
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• pp.357-366
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• 2015

We review recent research results on coupled line cameras (CLC) as a new geometric tool to reconstruct a scene quadrilateral from image quadrilaterals. Coupled line cameras were first developed as a camera calibration tool based on geometric insight on the perspective projection of a scene rectangle to an image plane. Since CLC comprehensively describes the relevant projective structure in a single image with a set of simple algebraic equations, it is also useful as a geometric reconstruction tool, which is an important topic in 3D computer vision. In this paper we first introduce fundamentals of CLC with reals examples. Then, we cover the related works to optimize the initial solution, to extend for the general quadrilaterals, and to apply for cuboidal reconstruction.

• 대한수학회보
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• 제31권2호
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• pp.163-165
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• 1994

Modules which satisfy the converse of Schur's lemma have been studied by many authors. In [6], R. Ware proved that a projective module P over a semiprime ring R is irreducible if and only if En $d_{R}$(P) is a division ring. Also, Y. Hirano and J.K. Park proved that a torsionless module M over a semiprime ring R is irreducible if and only if En $d_{R}$(M) is a division ring. In case R is a commutative ring, we obtain the following: An R-module M is irreducible if and only if En $d_{R}$(M) is a division ring and M is a multiplication R-module. Throughout this paper, R is commutative ring with identity and all modules are unital left R-modules. Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for each submodule N of M, there exists and ideal I of R such that N=IM. Cyclic R-modules are multiplication modules. In particular, irreducible R-modules are multiplication modules.dules.