• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.65-72
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• 2015

The (affine) development of a smooth curve in a smooth manifold M with respect to an arbitrarily given affine connection in the bundle of affine frames over M is well known (cf. S.Kobayashi and K.Nomizu, Foundations of Differential Geometry, Vol.1). In this paper, we get the generalized affine development of a smooth curve $x_t$ ($t{\in}[0,1]$) in M into the affine tangent space at $x_0$ (${\in}M$) with respect to a given generalized affine connection in the bundle of affine frames over M.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.9B
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• pp.1785-1794
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• 1999

The affine projection algorithm has known t require less computational complexity than RLS but have much faster convergence than NLMS for speech-like input signals. But the affine projection algorithm is still much more computationally demanding than the LMS algorithm because it requires the matrix inversion. In this paper, we show that the affine projection algorithm can be realized with the Gram-Schmidt orthogonalizaion of input vectors. Using the derived relation, we propose an approximate but much more efficient implementation of the affine projection algorithm. Simulation results show that the proposed algorithm has the convergence speed that is comparable to the affine projection algorithm with only a slight extra calculation complexity beyond that of NLMS.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.643-652
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• 2022

In this paper, we will describe affine homogeneous domains in the complex plane. For this study, we deal with the Lie algebra of infinitesimal affine transformations, a structure of the hyperbolic metric involved with affine automorphisms. As a consequence, an affine homogeneous domain is affine equivalent to the complex plane, the punctured plane or the half plane.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.203-207
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• 1999

In this paper, we find a condition of an open subset of the affine space which admits a cocompact affine action. To do it, the asymptotic flag of an open convex subset is introduced and some applications to affine manifolds are presented.

• Journal of Information Processing Systems
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• v.11 no.4
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• pp.643-654
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• 2015

Face recognition under controlled settings, such as limited viewpoint and illumination change, can achieve good performance nowadays. However, real world application for face recognition is still challenging. In this paper, we propose using the combination of Affine Scale Invariant Feature Transform (SIFT) and Probabilistic Similarity for face recognition under a large viewpoint change. Affine SIFT is an extension of SIFT algorithm to detect affine invariant local descriptors. Affine SIFT generates a series of different viewpoints using affine transformation. In this way, it allows for a viewpoint difference between the gallery face and probe face. However, the human face is not planar as it contains significant 3D depth. Affine SIFT does not work well for significant change in pose. To complement this, we combined it with probabilistic similarity, which gets the log likelihood between the probe and gallery face based on sum of squared difference (SSD) distribution in an offline learning process. Our experiment results show that our framework achieves impressive better recognition accuracy than other algorithms compared on the FERET database.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.2
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• pp.93-102
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• 2005

The Nyquist robust stability margin is proposed as a measure of robust stability for systems with Affine TFM(Transfer Function Matrix) parametric uncertainty. The parametric uncertainty is modeled through a Affine TFM MIMO (Multi-Input Multi-Output) description with dead-time, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. Multiloop PI/PID controllers can be tuned by using a modified version of the Ziegler-Nichols (ZN) relations. Consequently, this paper provides sufficient conditions for the robustness of Affine TFM MIMO uncertain systems with dead-time based on Rosenbrock's DNA. Simulation examples show the performance and efficiency of the proposed multiloop design method for Affine uncertain systems with dead-time.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.1
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• pp.17-25
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• 2005

This paper provides sufficient conditions for the robustness of Affine linear TFM(Transfer Function Matrix) MIMO (Multi-Input Multi-Output) uncertain systems based on Rosenbrock's DNA (Direct Nyquist Array). The parametric uncertainty is modeled through a Affine TFM MIMO description, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. For this type of parametric robust performance we show robustness of the Affine TFM systems using Nyquist diagram and GB, DNA(Direct Nyquist Array). Multiloop PI/PB controllers can be tuned by using a modified version of the Ziegler-Nickels (ZN) relations. Simulation examples show the performance and efficiency of the proposed multiloop design method.

• Annual Conference of KIPS
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• 2014.04a
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• pp.781-784
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• 2014

Face recognition under controlled settings, such as limited viewpoint and illumination change, can achieve good performance nowadays. However, real world application for face recognition is still challenging. In this paper, we use Affine SIFT to detect affine invariant local descriptors for face recognition under large viewpoint change. Affine SIFT is an extension of SIFT algorithm. SIFT algorithm is scale and rotation invariant, which is powerful for small viewpoint changes in face recognition, but it fails when large viewpoint change exists. In our scheme, Affine SIFT is used for both gallery face and probe face, which generates a series of different viewpoints using affine transformation. Therefore, Affine SIFT allows viewpoint difference between gallery face and probe face. Experiment results show our framework achieves better recognition accuracy than SIFT algorithm on FERET database.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.53-63
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• 2015

We get a necessary and sufficient condition for a generalized affine connection in the affine orthonormal frame bundle over a smooth manifold (M, g) to be a Yang-Mills connection.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.789-795
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• 1995

For nonintegrable weight $-\rho$, some weight multiplicities of the irreducible module $L(-\rho)$ over $A^{(1)}_{(1)}$ affine Lie algebras are expressed in terms of the colored partition functions. Also we find the multiplicity of $L(-\rho)$ in ther Verma module $M(-\rho)$ for any affine Lie algebras.