• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.831-841
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• 1998

We shall discuss on some vanishing theorems of harmonic sections of a Riemannian vector bundle over a compact Riemannian manifold with boundary. In relating the results of H. Donnelly - P. Li ([4]), for special case of harmonic forms satisfying absolute or relative boundary problem, our results improve the vanishing results of T. Takahashi ([9]).

• ETRI Journal
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• v.28 no.6
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• pp.819-821
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• 2006

Log-polar coordinate image space is proposed as a solution for the problem of unbounded accumulator space in the automatic detection of vanishing points. The proposed method can detect vanishing points at high speed under small memory requirements, as opposed to conventional image space based methods.

• Journal of KIISE
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• v.42 no.5
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• pp.642-651
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• 2015

A vanishing point is a point where parallel lines converge, and they become evident when a camera's lenses are used to project 3D space onto a 2D image plane. Vanishing point detection is the use of the information contained within an image to detect the vanishing point, and can be utilized to infer the relative distance between certain points in the image or for understanding the geometry of a 3D scene. Since parallel lines generally exist for the artificial structures within images, line-detection-based vanishing point-detection techniques aim to find the point where the parallel lines of artificial structures converge. To detect parallel lines in an image, we detect edge pixels through edge detection and then find the lines by using the Hough transform. However, the various textures and noise in an image can hamper the line-detection process so that not all of the lines converging toward the vanishing point are obvious. To overcome this difficulty, it is necessary to assign a different weight to each line according to the degree of possibility that the line passes through the vanishing point. While previous research studies assigned equal weight or adopted a simple weighting calculation, in this paper, we are proposing a new method of assigning weights to lines after noticing that the lines that pass through vanishing points typically belong to artificial structures. Experimental results show that our proposed method reduces the vanishing point-estimation error rate by 65% when compared to existing methods.

• Journal of the Korean Mathematical Society
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• v.40 no.4
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• pp.747-756
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• 2003

We establish a vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds. The hypothesis needed for this result is a growth condition on a primitive of the Kaehler form.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.239-246
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• 1999

We extend the Ding's vanishing theorem of $\delta$-invariant slightly on a Cohen-Macaulay local ring using the concept of Golod paris. we also investigate the relation between the vanishing of $\delta$-invariant and Hochster's Monomial Conjecture.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1341-1353
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• 2019

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.469-479
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• 2022

In this paper, we obtain some vanishing theorems for p-harmonic 1-forms on locally conformally flat Riemannian manifolds which admit an integral pinching condition on the curvature operators.

• Journal of Korea Multimedia Society
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• v.15 no.12
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• pp.1430-1441
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• 2012

In this paper, we present an algorithm that quickly and effectively estimates orthogonal vanishing points in equirectangular images of urban environment. Our algorithm is based on the RANSAC (RANdom SAmple Consensus) algorithm and on the characteristics of the line segment in the spherical panorama image of the $360^{\circ}$ longitude and $180^{\circ}$ latitude field of view. These characteristics can be used to reduce the geometric ambiguity in the line segment classification as well as to improve the robustness of vanishing point estimation. The proposed algorithm is validated experimentally on a wide set of images. The results show that our algorithm provides excellent levels of accuracy for the vanishing point estimation as well as line segment classification.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.1145-1148
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• 2002

This paper presents a new method which is calculated to use only three vanishing points in order to compute the dimensions of object and its pose from a single image of perspective projection taken by a camera and the problem of recovering 3D models from three vanishing points of box scene. Our approach is to compute only three vanishing points without this information such as the focal length, rotation matrix, and translation from images in the case of perspective projection. We assume that the object can be modeled as a linear function of a dimension vector ν. The input of reconstruction is a set of correspondences between features in the model and features in the image. To minimize each the dimensions of the parameterized models, this reconstruction of optimization can be solved by the standard nonlinear optimization techniques with a multi-start method which generates multiple starting points for the optimizer by sampling the parameter space uniformly.

• Clinical and Experimental Pediatrics
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• v.45 no.9
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• pp.1146-1149
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• 2002

Acute vanishing bile syndrome is a cause of progressive cholestasis. It is most often drug or toxin related. It's pathogenesis is unknown. Stevens-Johnson syndorme is a well-recognized immune complex-mediated hypersensitivity reaction. It is induced by drug or infection. It has classic systemic, mucosal, and dermatologic manifestations. We report a case of a 14 years old female suffering from Stevens-Johnson syndrome plus vanishing bile duct syndrome associated with ibuprofen use. We report the case with a brief review of its related literature.