• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.221-230
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• 2008

In the study of normal (complex analytic) surface singularities, it is interesting to investigate the invariants. The purpose of this paper is to give a characterization of the vanishing of ${\delta}_2$. In [11], we gave characterizations of minimally elliptic singularities and rational triple points in terms of th.. second plurigenera ${\delta}_2$ and ${\gamma}_2$. In this paper, we also give a characterization of rational triple points in terms of a certain computation sequence. To prove our main theorems, we give two formulae for ${\delta}_2$ and ${\gamma}_2$ of rational surface singularities.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.11
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• pp.3441-3453
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• 1996

A finite element anlaysis is performed for large deformations of a felxible beam. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. The finite elements results are confirmed for several cases of deformations through comparison to a first order elasticity solution obtained by numerical integration, and the agreement between the two is found to be excellent. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformation in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement.

• Journal of Ocean Engineering and Technology
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• v.11 no.4
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• pp.7-22
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• 1997

A finite element analysis is performed for lateral buckling problems on the basis of a geometrically nonlinear formulation for a beam with small elastic strain but with possibly large rotations. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformations in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement. This is illustrated through several numerical examples and followed by appropriate discussion.

• Journal of Cadastre & Land InformatiX
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• v.51 no.2
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• pp.73-82
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• 2021

According to the government's announcement of the safety management enhancement policy for small and medium-sized private construction sites, the subject of mandatory CCTV installation has been expanded from large construction sites to small and medium-sized construction sites. However, since the existing CCTV at construction sites has been used for simple control for safety management, so research is needed for monitoring of construction sites. Therefore, in this study, three vanishing points were calculated based on a single image taken with a monocular camera, and then a camera matrix containing interior orientation parameters information was determined. And the accuracy was verified by calculating the height of the target object from the height of the reference object. Through height determination experiments using vanishing points based on a monocular camera, it was possible to determine the height of target objects only with a single image without separately surveying of ground control points. As a result of the accuracy evaluation, the root mean square error was ±0.161m. Therefore, it is determined that the progress of construction work at the construction sites can be monitored through the single image taken using the single camera.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2010.10a
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• pp.357-359
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• 2010

In monocular images that are used to determine the depth of the vanishing point, the buildings, roads and buildings, such as outdoor video or hallway with room inside for the interior structure, such as the vanishing point in the video is a very strong depth cue. Depth map using the vanishing point in the three-dimensional space, the two-dimensional imaging is used to restore the structure. But if there is a vanishing point vanishing point in the video also depends on the location of the relative depth of different ways to express that need. In this paper we present images of a vanishing point with respect to the improved depth-map was created. Proposed an area where the loss of seven points and areas defined as areas along the proposed direction of different depth.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.69-78
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• 2009

The accuracy of wavelet approximation at resolution h = $2^{-k}$ to a smooth function f is limited by O($h^M$), where M is the number of vanishing moments of the mother wavelet ${\psi}$; that is, the approximation order of wavelet approximation is M - 1. High accuracy points of wavelet approximation are of interest in some applications such as signal processing and numerical approximation. In this paper, we prove the scaling and translating properties of high accuracy points of wavelet approximation. To illustrate the results in this paper, we also present two examples of high accuracy points of wavelet approximation.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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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).

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.989-991
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• 1995

In this paper, we present a new morphological texture spectrum approach to obtain a surface orientation using the variation of texture image caused by projective distortions. Under the assumption that the surface of texture image is smooth continuous, and specially plane or sphere, we apply the mathematical morphology and texture spectrum in order to compute the 3-D surface orientation. If the surface of texture image is plane, the surface orientation can be obtained through a simple procedure. If the surface of texture image is sphere, we find the centroids of texels, and may compute several major axes, their slopes, and vanishing points. Using the texture spectrum between the intersections of the vanishing points and the size of elements in each texels, we can find the surface orientation of texels on the sphere.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.9
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• pp.3196-3210
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• 2014

This paper presents a novel video metrology approach based on robust tracking. From videos acquired by an uncalibrated stationary camera, the foreground likelihood map is obtained by using the Codebook background modeling algorithm, and the multiple moving objects are tracked by a combined tracking algorithm. Then, we compute vanishing line of the ground plane and the vertical vanishing point of the scene, and extract the head feature points and the feet feature points in each frame of video sequences. Finally, we apply a single view mensuration algorithm to each of the frames to obtain height measurements and fuse the multi-frame measurements using RANSAC algorithm. Compared with other popular methods, our proposed algorithm does not require calibrating the camera, and can track the multiple moving objects when occlusion occurs. Therefore, it reduces the complexity of calculation and improves the accuracy of measurement simultaneously. The experimental results demonstrate that our method is effective and robust to occlusion.