• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1758-1763
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• 1991

This paper describes a new method to determine the 3D-shape of objects consisting of specular planar surfaces. This method exploits a light source which is made of a diffuse plane with a grid pattern encoded in an M-sequence and uses a single image of the light source reflected by the objects to acquiring orientations and positions of the surfaces of the objects. When grid lines of the light source are reflected by a specular planar surface and perspectively projected on an image plane, a set of lines vanishing at a point are obtained on the image plane. The orientation of the specular planar surface is determined by using the vanishing point, and the position is determined by using the correspondence between lines on the image and lines on the light source, which is obtained by employing a characteristic regularity of the M-sequence. Before the vanishing points are calculated, the lines on the image are classified and correlated with the surfaces of objects by using slopes and positions of the lines and the regularity of the M-sequence. This method requires only a single image.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.6
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• pp.187-193
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• 2004

In this paper, we proposed the GPS position data correction method for autonomous land navigation using vanishing point property and a monocular vision system. Simulations are carried out over driving distances of approximately 60 km on the basis of realistic road data. On a straight road, the proposed method reduces GPS position error by at least 63% within 0.5 m. However, the average accuracy of the method is not presented, because it is difficult to estimate it on other than a straight road in variable conditions.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-46
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• 2023

Geodesic orbit spaces are homogeneous Finsler spaces whose geodesics are all orbits of one-parameter subgroups of isometries. Such Finsler spaces have vanishing S-curvature and hold the Bishop-Gromov volume comparison theorem. In this paper, we obtain a complete description of invariant (α₁, α₂)-metrics on spheres with vanishing S-curvature. Also, we give a description of invariant geodesic orbit (α₁, α₂)-metrics on spheres. We mainly show that a Sp(n + 1)-invariant (α₁, α2)-metric on S⁴ⁿ⁺³ = Sp(n + 1)/Sp(n) is geodesic orbit with respect to Sp(n + 1) if and only if it is Sp(n + 1)Sp(1)-invariant. As an interesting consequence, we find infinitely many Finsler spheres with vanishing S-curvature which are not geodesic orbit spaces.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.1988-1991
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• 2003

본 논문에서는 도로 주변의 나무와 건물, 그리고 옆 차선의 차량 등에 의한 그림자의 영향을 최소화하며 차선을 검출할 수 있는 방법을 제안하였다 우선 Hough transform을 수행하는 데 있어서 계산 시간을 줄이기 위하여 에지 영상에서 수평 투영을 통하여 vanishing line을 검출하였으며, vanishing line 아래 부분에서만 Hough transform을 수행하였다. 그리고 차선 검출을 위하여 Hough 평면에서 θ을 16등분하여 rough한 차선을 검출하였으며, 도로 형태에 대한 사전 지식을 이용하여 차선 검출을 시도하였다. 도로 주변상황이 다른 두 종류의 연속 영상들에 의한 실험 결과, 도로형태에 대하여 가정한 사전 지식과 유사한 영상들에 대하여 차선을 정확하게 검출하였다.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.619-629
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• 1996

In studying smooth 4-manifolds the Donaldson invariant has played a central role. In [D1] Donaldson showed that non-vanishing Donaldson invariant of a smooth closed oriented 4-manifold X gives rise to the indecomposability of X. For instance, the complex algebraic suface X cannot decompose to a connected sum $X_1 #X_2$ with both $b_2^+(X_i) > 0$.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.641-648
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• 2000

The purpose of this paper is to give a necessary and sufficient condition for a smooth manifold to admit a Lorentzian metric. As an application of this result, on Lorentzian manifolds we have shown that the existence of a 1-dimensional distribution is equivalent to the existence of a non-vanishing vector field.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.82-82
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• 2000

The way which estimates a position from Navigation is Dead-reckoning Navigation and Radio Navigation. Generally dead-reckoning navigation uses Gyro and odometer as sensor, but these have problems which are an integrating noise and a noise-sensitivity. Gps which is used by radio-navigation has a Troposthetic error and MultiPath ewer and so on. For minimizing a Troposthetic error and a Multipath error, this paper suggests to an algorithm which use vanishing point on CCD camera.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.343-371
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• 2007

We find the super-replication formulae which would be a generalization of replication formulae. And we apply the formulae to derive periodically vanishing property in the Fourier coefficients of the Hauptmodul $\aleph(j_{1,N})$ as a super-replicable function.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.709-723
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• 2022

In this note, we revise some vanishing and finiteness results on hypersurfaces with finite index in ℝⁿ⁺¹. When the hypersurface is stable minimal, we show that there is no nontrivial L^2p harmonic 1-form for some p. The our range of p is better than those in [7]. With the same range of p, we also give finiteness results on minimal hypersurfaces with finite index.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.699-715
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• 2024

We study the Riemann problem for the pressureless Euler system with the source term depending on the time. By means of the variable substitution, two kinds of Riemann solutions including deltashock and vacuum are constructed. The generalized Rankine-Hugoniot relation and entropy condition of the delta-shock are clarified. Because of the source term, the Riemann solutions are non-self-similar. Moreover, we propose a time-dependent viscous system to show all of the existence, uniqueness and stability of solutions involving the delta-shock by the vanishing viscosity method.