• 호남수학학술지
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• 제33권4호
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• pp.557-573
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• 2011

Let G be a compact and connected semisimple Lie group, H a closed subgroup, g (resp. h) the Lie algebra of G (resp. H), B the Killing form of g, g the normal metric on the homogeneous space G/H which is induced by -B. Let D be an invarint connection with Weyl structure (D, g, ${\omega}$) in the tangent bundle over the normal homogeneous Riemannian manifold (G/H, g) which is projectively flat. Then, the affine connection D on (G/H, g) is a Yang-Mills connection if and only if D is the Levi-Civita connection on (G/H, g).

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.393-406
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• 1999

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the second. Radius of con-vergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

• 한국수학사학회지
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• 제29권6호
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• pp.335-351
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• 2016

Spherical convexity may be defined in different ways. It depends on which statement we take as a definition among several statements that can be all used as a definition of convexity of subsets in an affine space. In this article, we consider this question from various perspectives. We compare several different definitions of spherical convexity which are found in mathematical papers. In particular, we focus our discussion on the definitions of J. P. $Benz{\acute{e}}cri$ and N. H. Kuiper who built a solid foundation for theory of convex bodies and convex affine(projective) structures on manifolds.

• 대한수학회보
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• 제52권5호
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• pp.1433-1443
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• 2015

Catenoid and Riemann's minimal surface are foliated by circles, that is, they are union of circles. In $\mathbb{R}^3$, there is no other nonplanar example of circle-foliated minimal surfaces. In $\mathbb{R}^4$, the graph $G_c$ of w = c/z for real constant c and ${\zeta}{\in}\mathbb{C}{\backslash}\{0}$ is also foliated by circles. In this paper, we show that every circle-foliated minimal surface in $\mathbb{R}$ is either a catenoid or Riemann's minimal surface in some 3-dimensional Affine subspace or a graph surface $G_c$ in some 4-dimensional Affine subspace. We use the property that $G_c$ is circle-foliated to construct circle-foliated minimal surfaces in $S^4$ and $H^4$.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 하계종합학술대회논문집
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• pp.773-776
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• 1998

In this paper, we propose an efficient multi-view images coding algorithm which finds the optimal texture from the restricted number of multi-view images. The X-Y plane of the normalized object space is divided into triangular patches. The depth value of the node is determined by applying the block based disparity compensation method and then the texture of the each patch is extracted by applying the affine transformation patch is extracted by applying the affine transformation based disparity compensation method to the multi-view images. We restricted the number of images contributed to determining the texture comapred to traditional methods which use all the multi-view images in the texture extraction. Experimental results show that the SNR of images encoded by the proposed algorithm is better than that of imaes encoded by the traditional method by the amount about 0.2dB for the test sets of multi-view images called dragon, kid, city and santa. The recovered images from the encoded data by the proposed method show the better visual images than the recovered images from the encoded data by the traditional methods.

• 한국컴퓨터그래픽스학회논문지
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• 제9권3호
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• pp.15-21
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• 2003

An algorithm is developed for augmenting a real video with virtual graphics objects without computing Euclidean information. Real motion of the camera is obtained in affine space by a direct linear method using image matches. Then, virtual camera is provided by determining the locations of four basis points in two input images as initialization process. The four pairs of 2D location and its 3D affine coordinates provide Euclidean orthographic projection camera through the whole video sequence. Our method has the capability of generating views of objects shaded by virtual light sources, because we can make use of all the functions of the graphics library written on the basis of Euclidean geometry. Our novel formulation and experimental results with real video sequences are presented.

• 대한수학회지
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• 제43권5호
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• pp.1019-1045
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• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

• 한국산학기술학회논문지
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• 제13권9호
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• pp.3856-3863
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• 2012

스테레오 영상으로부터 3차원 형상을 구현함에 있어 사용자의 개입을 최소로 필요로 하는 기법을 개발하였다. 형상구현은 특정 기하학 그룹을 평가하는 3단계로 이루어진다. 1단계는 영상에 존재하는 epipolar 기하 평가로 각 영상에서의 특정점들을 일치시킨다. 2단계는 소실점 방법을 이용하여 투영공간에서 특정평면을 찾는 affine 기하 평가이다. 3단계에서는 카메라의 자기보정을 포함하며 3차원 모델이 얻어질 수 있는 계량 기하 변수를 구한다. 이 방법의 장점은 형상구현을 위해 스테레오 영상을 보정할 필요가 없는 것으로, 그 구현가능성을 실증하였다.

• 전자공학회논문지CI
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• 제46권1호
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• pp.128-135
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• 2009

동영상에서 시공간상 일정한 위상을 갖는 윤곽선을 정합시켜 물리적 공간에서의 동일한 위치를 추적하는 방법은 명암이 일정한 윤곽선을 정합시키거나 일정한 명암을 전제로 추적하는 방법에 비해 정확성이 높고 조명조건에 대해 안정된 특성이 있다. 본 논문에서는 이러한 성질을 이용하여 조명변화와 노이즈에 강인하게 카메라의 움직임을 추정하는 기법을 소개한다. 우선, 가버 필터뱅크를 사용하여 공간적으로 여과된 연속영상으로부터 계산된 위상의 크기를 기반으로 필터의 방향과 수직인 곳의 광류를 구한 후, 최소제곱법을 적용하여 어파인 모델에 상응하는 카메라의 움직임 파라미터를 구한다. 실험을 통하여 이러한 방법은 조명조건의 변화를 야기하는 디스플레이 기기를 피사체로 하여 카메라의 위치변화를 추정하는 방식의 영상기반 포인팅 디바이스에도 적용될 수 있음을 보인다.

• 대한수학회보
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• 제52권2호
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• pp.649-659
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• 2015

The space $BV^2_{\alpha}(I)$ of all the real functions defined on interval $I=[a,b]{\subset}\mathbb{R}$, which are of bounded second ${\alpha}$-variation (in the sense De la Vall$\acute{e}$ Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function $h:I{\times}\mathbb{R}{\rightarrow}\mathbb{R}$, and prove, in particular, that if H maps $BV^2_{\alpha}(I)$ into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.