• Journal of Korea Multimedia Society
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• v.7 no.3
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• pp.427-437
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• 2004

Shape comparison between 3D models is essential for shape recognition, retrieval, classification, etc. In this paper, we propose a method for comparing 3D shapes, which is invariant under translation, rotation and scaling of models and is robust to non-uniformly distributed and incomplete data sets. first, a modal model is constructed from input data using vibration modes and then shape similarity is evaluated with modal strain energy. The proposed method provides global-to-local ordering of shape deformation using vibration modes ordered by frequency Thus, we evaluated similarity in terms of global properties of shape without being affected localised shape features using ordered shape representation and modal strain one energy.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.795-834
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• 2016

The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group $Homeo^{\Omega}$ ($D^2$, ${\partial}D^2$) of area preserving homeomorphisms of the 2-disc $D^2$. We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : $Diff^{\Omega}$ ($D^1$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to a homomorphism ${\bar{Cal}}$ : Hameo($D^2$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to that of the vanishing of the basic phase function $f_{\underline{F}}$, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian ${\underline{F}}$ on $S^2$ that is obtained via the natural embedding $D^2{\hookrightarrow}S^2$. Here Hameo($D^2$, ${\partial}D^2$) is the group of Hamiltonian homeomorphisms introduced by $M{\ddot{u}}ller$ and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on $D^2$ via a study of the associated Hamiton-Jacobi equation.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.

• Ocean and Polar Research
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• v.37 no.1
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• pp.11-22
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• 2015

In-situ measurements are labor-intensive, time-consuming, and limited in their ability to observe currents with spatial variations in the surf zone. This paper proposes an optical image-based method of measurement of currents in the surf zone. This method measures nearshore currents by tracking in time wave breaking-induced foam patches from sequential images. Foam patches in images tend to be arrayed with irregular pixel intensity values, which are likely to remain consistent for a short period of time. This irregular intensity feature of a foam patch is characterized and represented as a keypoint using an image-based object recognition method, i.e., Scale Invariant Feature Transform (SIFT). The keypoints identified by the SIFT method are traced from time sequential images to produce instantaneous velocity fields. In order to remove erroneous velocities, the instantaneous velocity fields are filtered by binding them within upper and lower limits, and averaging the velocity data in time and space with a certain interval. The measurements that are obtained by this method are comparable to the results estimated by an existing image-based method of observing currents, named the Optical Current Meter (OCM).

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1037-1049
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• 2015

It is well-known that the spectrum of a $spin^{\mathbb{C}}$ Dirac operator on a closed Riemannian $spin^{\mathbb{C}}$ manifold $M^{2k}$ of dimension 2k for $k{\in}{\mathbb{N}}$ is symmetric. In this article, we prove that over an odd-dimensional Riemannian product $M^{2p}_1{\times}M^{2q+1}_2$ with a product $spin^{\mathbb{C}}$ structure for $p{\geq}1$, $q{\geq}0$, the spectrum of a $spin^{\mathbb{C}}$ Dirac operator given by a product connection is symmetric if and only if either the $spin^{\mathbb{C}}$ Dirac spectrum of $M^{2q+1}_2$ is symmetric or $(e^{{\frac{1}{2}}c_1(L_1)}{\hat{A}}(M_1))[M_1]=0$, where $L_1$ is the associated line bundle for the given $spin^{\mathbb{C}}$ structure of $M_1$.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.781-794
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• 2008

Let $\mathbb{H}_g$ and $\mathbb{D}_g$ be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let $\mathbb{C}^{(h,g)}$ be the Euclidean space of all $h{\times}g$ complex matrices. We present a partial Cayley transform of the Siegel-Jacobi disk $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$ onto the Siegel-Jacobi space $\mathbb{H}_g{\times}\mathbb{C}^{(h,g)}$ which gives a partial bounded realization of $\mathbb{H}_g{\times}\mathbb{C}^{(h,g)}$ by $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$. We prove that the natural actions of the Jacobi group on $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$. and $\mathbb{H}_g{\times}\mathbb{C}^{(h,g)}$. are compatible via a partial Cayley transform. A partial Cayley transform plays an important role in computing differential operators on the Siegel Jacobi disk $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$. invariant under the natural action of the Jacobi group $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$ explicitly.

• Journal of Korea Multimedia Society
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• v.7 no.12
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• pp.1680-1691
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• 2004

One of the representative methods of optical flow is a gradient method which estimates the movement of an object based on the differential of image brightness. However, the method is ineffective for large displacement of the object and many improved methods have been proposed to copy with such limitations. One of these improved techniques is the multigrid processing, which is used in many optical flow algorithms. As an alternative novel technique we have been proposing an orthogonal functional expansion method, where whole displacements are expanded from low frequency terms. This method is expected to be applicable to flow estimation with large displacement and deformation including expansion and contraction, which are difficult to cope with by conventional optical flow methods. In the orthogonal functional expansion method, the apparent displacement field is calculated iteratively by a projection method which utilizes derivatives of the invariant constraint equations of brightness constancy. One feature of this method is that differentiation of the input image is not necessary, thereby reducing sensitivity to noise. In this paper, we apply our method to several real images in which the objects undergo large displacement and/or deformation including expansion. We demonstrate the effectiveness of the orthogonal functional expansion method by comparing with conventional methods including our optimally scaled multigrid optical flow algorithm.

• The KIPS Transactions:PartB
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• v.9B no.4
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• pp.501-508
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• 2002

In this paper, we propose a content-based image retrieval using the color ratio and moment of object region. We acquire an optimal spatial information by the region splitting that utilizes horizontal-vertical projection and dominant color. It is based on hypothesis that an object locates in the center of image. We use color ratio and moment as feature informations. Those are extracted from the splitted regions and have the invariant property for various transformation, and besides, similarity measure utilizes a modified histogram intersection to acquire correlation information between bins in a color histogram. In experimental results, the proposed method shows more flexible and efficient performance than existing methods based on region splitting.

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.1931-1932
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• 2006

로봇이 어떤 물체를 인지하고 그 물체에 대해 어떤 작업을 하고자 할 때 특정 물체의 인식 문제, 3차원 정보를 획득하는 문제, 자세를 추정하는 문제 등 해결해야 될 문제들이 있다. 물체를 인식하는 과정에서는 주위 배경과 물체의 크기의 변화, 회전, 가려짐 등으로 인해 물체 인식을 어렵게 만드는 요소들이 있다. 2차원 이미지를 통해 3차원 정보를 추출하는 과정은 일반적으로 두 대의 카메라를 이용하여 스테레오 이미지를 통해 얻는다. 이 때 좌우 영상간의 매칭의 과정이 필요하다. 자세 추정의 문제는 카메라 좌표와 물체의 좌표간의 관계를 알아야 한다. Visual Servoing을 어렵게 만드는 많은 요인들이 있으며 본 논문에서는 물체의 크기, 회전, 이동에 불변인 디스크립터(descriptor)를 사용하는 SIFT(Scale Invariant Feature Transform)를 통해 3차원 물체의 인식과 자세를 추정하는 방법을 제시한다. 또한 자세 추정을 위해 2차원 Keypoint들의 매칭을 3차원 정보를 통해 검증하는 방법을 제시한다. (SIFT에 의해 추출된 point를 Keypoint라 명한다.)

• Proceedings of the KSRS Conference
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• v.2
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• pp.1007-1010
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• 2006

This study investigates the spatial structure of the total cloud liquid water content Q fields over the Northwest Pacific Ocean during winter monsoon. The distributions of Q have been estimated from the brightness temperatures of the ocean - atmosphere system $T_B(f)$, where f is frequency, measured by AQUA AMSR-E in January -March 2003. Marine strati (St) and stratocumuli (Sc) are typical for winter monsoon season. They were analysed using mainly high-frequency channel at f = 36.5 GHz, vertical polarisation. $T_B$ data were accompanied by the data on near surface wind speed, air temperature and humidity from the nearest meteorological stations. Tow one-dimensional spectra were computed for downwind and crosswind sections of Q fields. The AMSR-E antenna field of view (14-8 km) and the cloud field sizes (100-1000 km) restricted the spatial scales. The results of case study Jan 31 2003 are presented. Scale-invariant spectrum is typical. In the cases of extended St levels a spectral slope equals about -1.7, conforming to classical -5/3 of turbulence theory. For Sc cases the absolute magnitude of spectral slope is rather higher, as a rule. The value is about -2. In the case when cloud streets are presented, a strait line form of spectrum is less reliable with a slope being rather lower (about -1.4).