• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2393-2396
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• 2005

We present a method to detect on-road vehicle using geometric invariant of feature points on side planes of the vehicle. The vehicles are assumed into a set of planes and the invariant from motion information of features on the plane segments the plane from the theory that a geometric invariant value defined by five points on a plane is preserved under a projective transform. Harris corners as a salient image point are used to give motion information with the normalized correlation centered at these points. We define a probabilistic criterion to test the similarity of invariant values between sequential frames. Experimental results using images of real road scenes are presented.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1725-1741
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• 2017

For a complex smooth projective surface M with an action of a finite cyclic group G we give a uniform proof of the isomorphism between the invariant $H^1(G,\;H^2(M,\;{\mathbb{Z}}))$ and the first cohomology of the divisors fixed by the action, using G-equivariant cohomology. This generalizes the main result of Bogomolov and Prokhorov [4].

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2005.11a
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• pp.229-232
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• 2005

In this paper, an image-based "approach-align -grasp" visual servo control design is proposed for the problem of object grasping, which is based on the binocular stand-alone system. The basic idea consists of considering a vision system as a specific sensor dedicated a task and included in a control servo loop, and we perform automatic grasping follows the classical approach of splitting the task into preparation and execution stages. During the execution stage, once the image-based control modeling is established, the control task can be performed automatically. The proposed visual servoing control scheme ensures the convergence of the image-features to desired trajectories by using the Jacobian matrix, which is proved by the Lyapunov stability theory. And we also stress the importance of projective invariant object/gripper alignment. The alignment between two solids in 3-D projective space can be represented with view-invariant, more precisely; it can be easily mapped into an image set-point without any knowledge about the camera parameters. The main feature of this method is that the accuracy associated with the task to be performed is not affected by discrepancies between the Euclidean setups at preparation and at task execution stages. Then according to the projective alignment, the set point can be computed. The robot gripper will move to the desired position with the image-based control law. In this paper we adopt a constant Jacobian online. Such method describe herein integrate vision system, robotics and automatic control to achieve its goal, it overcomes disadvantages of discrepancies between the different Euclidean setups and proposes control law in binocular-stand vision case. The experimental simulation shows that such image-based approach is effective in performing the precise alignment between the robot end-effector and the object.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.391-401
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• 2019

A module is said to be ${\pi}$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this article, we focus on the class of modules having the ${\pi}$-extending property by looking at the singularity of quotient submodules. By doing so, we provide counterexamples, using hypersurfaces in projective spaces over complex numbers, to show that being generalized ${\pi}$-extending is not inherited by direct summands. Moreover, it is shown that the direct sums of generalized ${\pi}$-extending modules are generalized ${\pi}$-extending.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1090-1093
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• 2004

In this paper, a problem of geometrically distorted images is considered. In particular, the paper discusses the detection of a watermark from a photographed image of the watermarked picture. The image is possibly obtained by using a digital camera. This watermark detection problem is made difficult by various geometric distortions added to the original picture through the printing and photographing processes. In particular, the paper focuses on the geometric distortion due to a projective transformation, as part of a camera 3D-to-2D imaging process. It is well-known that a cross ratio of collinear points is invariant under a perspective projection. By exploiting this fact, a projective-invariant digital watermarking technique is developed. By detecting the picture's corners, and the image center point at the intersection of two main diagonal lines, predefined cross ratios are used to compute the watermark embedded locations. From those identified embedding pixel locations, a watermark can be detected by performing a correlation between a watermark pattern and the image over those pixels. The proposed method does not require an inverse transformation on the distorted image, thus simplifying the detection process. Performance of the proposed method has been analyzed through computer experiments

• 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).

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.569-608
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• 1994

The subject matter of this survey has to do with holomorphic maps from a compact Riemann surface to projective space, which are also called algebrac curves; the theory we survey lies at the crossroads of function theory, projective geometry, and commutative algebra (although we should mention that the present survey de-emphasizes the algebraic aspect). Algebraic curves have been vigorously and continuously investigated since the time of Riemann. The reasons for the preoccupation with algebraic curves amongst mathematicians perhaps have to do with-other than the usual usual reason, namely, the herd mentality prompting us to follow the leads of a few great pioneering methematicians in the field-the fact that algebraic curves possess a certain simple unity together with a rich and complex structure. From a differential-topological standpoint algebraic curves are quite simple as they are neatly parameterized by a single discrete invariant, the genus. Even the possible complex structures of a fixed genus curve afford a fairly complete description. Yet there are a multitude of diverse perspectives (algebraic, function theoretic, and geometric) often coalescing to yield a spectacular result.

• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.547-564
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• 2024

We study totally real and complex subsets of a right quarternionic vector space of dimension n + 1 with a Hermitian form of signature (n, 1) and extend these notions to right quaternionic projective space. Then we give a necessary and sufficient condition for a subset of a right quaternionic projective space to be totally real or complex in terms of the quaternionic Hermitian triple product. As an application, we show that the limit set of a non-elementary quaternionic Kleinian group 𝚪 is totally real (resp. commutative) with respect to the quaternionic Hermitian triple product if and only if 𝚪 leaves a real (resp. complex) hyperbolic subspace invariant.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1998.06b
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• pp.141-146
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• 1998

Currently virtual studio has used the cromakey method in which an image is captured, and the blue portion of that image is replaced by a graphic image or a real image. The replaced image must be changed according to the camera motion. This paper proposes a novel method to extract camera parameters using the recognition of pentagonal patterns which are painted on the blue screen. The corresponding parameters are position, direction and focal length of the camera in the virtual studio. At first, pentagonal patterns are found using invariant features of the pentagon. Then, the projective transformation of two projected images and the camera parameters are calculated using the matched points. Simulation results indicate that camera parameters are more easily calculated compared to the conventional methods.