• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.141-144
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• 2002

In this paper, we propose a new object tracking algorithm using deformed template and Level-Set theory, which is robust against background variation, object flexibility and occlusion. The proposed tracking algorithm consists of two steps. The first step is an estimation of object shape and location, on the assumption that the transformation of object can be approximately modeled by the affine transform. The second step is a refinement of the object shape to fit into the real object accurately, by using the potential energy map and the modified Level Set speed function. Experimental results show that the proposed algorithm can track non-rigid objects with large variation in the backgrounds.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.73-80
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• 1992

We discuss transverse harmonic fields on compact foliated Riemannian manifolds, and give a necessary and sufficient condition for a transverse field to be a transverse harmonic one and the non-existence of transverse harmonic fields. 1. On a foliated Riemannian manifold, geometric transverse fields, that is, transverse Killing, affine, projective, conformal fields were discussed by Kamber and Tondeur([3]), Molino ([5], [6]), Pak and Yorozu ([7]) and others. If the foliation is one by points, then transverse fields are usual fields on Riemannian manifolds. Thus it is natural to extend well known results concerning those fields on Riemannian manifolds to foliated cases. On the other hand, the following theorem is well known ([1], [10]): If the Ricci operator in a compact Riemannian manifold M is non-negative everywhere, then a harmonic vector field in M has a vanishing covariant derivative. If the Ricci operator in M is positive-definite, then a harmonic vector field other than zero does not exist in M.

• Proceedings of the IEEK Conference
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• 2009.05a
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• pp.216-218
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• 2009

This paper proposes an image processing algorithm to stabilize shaken scenes of UAV(Unmanned Aerial Vehicle) caused by vehicle self-vibration and aerodynamic disturbance. The proposed method stabilizes images by compensating estimated shake motion which is evaluated from global motion. The global motion between two continuous images modeled by 6 parameter warping model is estimated by non-linear square method based on Gauss-Newton algorithm with excluding outlier region. The shake motion is evaluated by subtracting the global motion from aerial vehicle motion obtained by averaging global motion. Experimental results show that the proposed method stabilize shaken scenes effectively.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1221-1241
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• 2008

Most of domains people have studied are convex bounded projective (or affine) domains. Edith $Soci{\acute{e}}$-$M{\acute{e}}thou$ [15] characterized ellipsoid in ${\mathbb{R}}^n$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.989-999
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• 2023

The aim of this paper is to study the projective curvature tensor field of the Curvature tensor Rⁱ_jkh on a recurrent non Riemannian space admitting recurrent affine motion, which is also decomposable in the form Rⁱ_jkh=Xⁱ Y_jkh, where Xⁱ and Y_jkh are non-null vector and tensor respectively. In this paper we decompose Special Pseudo Projective Curvature Tensor Field. In the sequal of decomposition we established several properties of such decomposed tensor fields. We have considered the curvature tensor field Rⁱ_jkh in a Finsler space equipped with non symmetric connection and we study the decomposition of such field. In a special Pseudo recurrent Finsler Space, if the arbitrary tensor field 𝜓ⁱ_j is assumed to be a covariant constant then, in view of the decomposition rule, 𝜙_kh behaves as a recurrent tensor field. In the last, we have considered the decomposition of curvature tensor fields in Kaehlerian recurrent spaces and have obtained several related theorems.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.5
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• pp.126-134
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• 2009

This paper describes the vision-based system to track road signs from within a moving vehicle. The proposed system has the standard architecture with particle filter due to its robust tracking performance in complex environment. In the case of tracking road signs in real environment, it has a great difficulty in predicting time series data by reason of an occlusion due to an obstacle and the rapid change of objects on roads. To overcome this problem and improve the tracking performance, this paper proposes the algorithm using an autoregressive model as an state transition model which has affine parameters as states and using robust statistics for determining occlusion due to obstacles. The experiments of this paper show that the proposed method is efficient for real time tracking of road signs and performs well in road signs under occlusion due to obstacles.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.1
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• pp.1-13
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• 2018

Boosting, one of the most successful algorithms for supervised learning, searches the most accurate weighted sum of weak classifiers. The search corresponds to a convex programming with non-negativity and affine constraint. In this article, we propose a novel Conjugate Gradient algorithm with the Modified Polak-Ribiera-Polyak conjugate direction. The convergence of the algorithm is proved and we report its successful applications to boosting.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.621-624
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• 1999

This paper describes a distance estimation method of object's motion in soccer image sequence by tracking field features. And we quantitatively evaluate the estimation accuracy We suppose that the input image sequence is taken with a camera on static axis and includes only zooming and panning transformation between frames. Adaptive template matching is adopted for non-rigid object tracking. For background compensation, feature templates selected from reference frame image are matched in following frames and the matched feature point pairs are used in computing Affine motion parameters. A perspective displacement field model is used for estimating the real distance between two position on Input Image. To quantitatively evaluate the accuracy of the estimation, we synthesized a 3 dimensional virtual stadium with graphic tools and experimented on the synthesized 2 dimensional image sequences. The experiment shows that the average of the error between the actual moving distance and the estimated distance is 1.84%.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.149-157
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• 2003

Let M be an exponentially bounded o-minimal expansion of the standard structure R = (R ,＋,.,<) of the field of real numbers. We prove that if r is a non-negative integer, then every definable $C^{r}$ manifold is affine. Let f : X ${\longrightarrow}$ Y be a definable $C^1$ map between definable $C^1$ manifolds. We show that the set S of critical points of f and f(S) are definable and dim f(S) < dim Y. Moreover we prove that if 1 < s < ${\gamma}$ < $\infty$, then every definable $C^{s}$ manifold admits a unique definable $C^{r}$ manifold structure up to definable $C^{r}$ diffeomorphism.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.475-486
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• 2018

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology ${\mathbb{Z}}^2{\bigoplus}{\mathbb{Z}}_2$ which yield an orbit manifold reversing fiber orientation, up to topological conjugacy. We show that those nonabelian groups are $D_4$(the dihedral group), $Q_8$(the quaternion group), and $C_8.C_4$(the $1^{st}$ non-split extension by $C_8$ of $C_4$ acting via $C_4/C_2=C_2$).