• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1301-1324
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• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• Journal of Biomedical Engineering Research
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• v.36 no.4
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• pp.79-85
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• 2015

The purpose of this study is to develop an automatic algorithm for vessel segmentation in X-Ray angiogram using Random Forest (RF). The proposed algorithm is composed of the following steps: First, the multiscale hessian-based filtering is performed in order to enhance the vessel structure. Second, eigenvalues and eigenvectors of hessian matrix are used to learn the RF classifier as feature vectors. Finally, we can get the result through the trained RF. We evaluated the similarity between the result of proposed algorithm and the manual segmentation using 349 frames, and compared with the results of the following two methods: Frangi et al. and Krissian et al. According to the experimental results, the proposed algorithm showed high similarity compared to other two methods.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.625-639
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• 1996

A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.701-715
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• 2021

In this paper, we study almost complex Norden Silver manifolds and Kaehler-Norden Silver manifolds. We define adapted connections of first, second and third type to an almost complex Norden Silver manifold and establish the necessary and sufficient conditions for the integrability of almost complex Norden Silver structure. Moreover, we investigate that a complex Norden Silver map is a harmonic map between Kaehler-Norden Silver manifolds.

• Geophysics and Geophysical Exploration
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• v.6 no.2
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• pp.95-100
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• 2003

In this study, we developed reflection tomography inversion algorithm using Straight Ray Technique (SRT) which can calculate travel time easily and fast for complex geological structure. The inversion process begins by setting the initial velocity model as a constant velocity model that hat only impedance boundaries. The inversion process searches a layer-interface structure model that is able to explain the given data satisfactorily by inverting to minimize data misfit. For getting optimal solution, we used Gauss-Newton method that needed constructing the approximate Hessian matrix. We also applied the Marquart-Levenberg regularization method to this inversion process to prevent solution diverging. The ability of the method to resolve typical target structures was tested in a synthetic salt dome inversion. Using the inverted velocity model, we obtained the migration image close to that of the true velocity model.

• Journal of Advanced Information Technology and Convergence
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• v.9 no.1
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• pp.89-102
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• 2019

Collagen can be used in building artificial skin replacements for treatment of burns and towards the reconstruction of bone as well as researching cell behavior and cellular interaction. The strength of collagen in connective tissue rests on the characteristics of collagen fibers. 3D confocal imaging of collagen fibers enables the characterization of their spatial distribution as related to their function. However, the image stacks acquired with confocal laser-scanning microscope does not clearly show the collagen architecture in 3D. Therefore, we developed a new method to reconstruct, visualize and characterize collagen fibers from fluorescence confocal images. First, we exploit the tensor voting framework to extract sparse reliable information about collagen structure in a 3D image and therefore denoise and filter the acquired image stack. We then propose to segment the collagen fibers by defining an energy term based on the Hessian matrix. This energy term is minimized by a min cut-max flow algorithm that allows adaptive regularization. We demonstrate the efficacy of our methods by visualizing reconstructed collagen from specific 3D image stack.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.6
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• pp.48-60
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• 2011

Nowadays, the 3D community is actively researching on 3D imaging and free-viewpoint video (FVV). The free-viewpoint rendering in multi-view video, virtually move through the scenes in order to create different viewpoints, has become a popular topic in 3D research that can lead to various applications. However, there are restrictions of cost-effectiveness and occupying large bandwidth in video transmission. An alternative to solve this problem is to generate virtual views using a single texture image and a corresponding depth image. A critical issue on generating virtual views is that the regions occluded by the foreground (FG) objects in the original views may become visible in the synthesized views. Filling this disocclusions (holes) in a visually plausible manner determines the quality of synthesis results. In this paper, a new approach for handling disocclusions using depth based inpainting algorithm in synthesized views is presented. Patch based non-parametric texture synthesis which shows excellent performance has two critical elements: determining where to fill first and determining what patch to be copied. In this work, a noise-robust filling priority using the structure tensor of Hessian matrix is proposed. Moreover, a patch matching algorithm excluding foreground region using depth map and considering epipolar line is proposed. Superiority of the proposed method over the existing methods is proved by comparing the experimental results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.12
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• pp.3804-3821
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• 1996

The configuration optimization is a structural optimization method which includes the coordinates of a structure as well as the sectional properties in the design variable set. Effective reduction of the weight of discrete structures can be obrained by changing the geometry while satisfying stress, Ei;er bickling, displacement, and frequency constraints, etc. However, the nonlinearity due to the configuration variables may cause the difficulties of the convergence and expensive computational cost. An efficient approximation method for the configuration optimization has been developed to overcome the difficulties. The method approximates the constraint functions based onthe second-order Taylor series expansion with reciprocal design variables. The Hessian matrix is approzimated from the information on previous design points. The developed algotithms are coded and the examples are solved.

• Journal of Internet of Things and Convergence
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• v.10 no.3
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• pp.25-33
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• 2024

In tomographic image reconstruction, the focus is on developing CT image reconstruction methods that can maintain high image quality while reducing patient radiation exposure. Typically, statistical image reconstruction methods have the ability to generate high-quality and accurate images while significantly reducing patient radiation exposure. However, in cases like CT image reconstruction, which involve multi-dimensional parameter estimation, the degree of the Hessian matrix of the penalty function is very large, making it impossible to calculate. To solve this problem, the author proposed the PEMG-1 algorithm. However, the PEMG-1 algorithm has issues with the convergence speed, which is typical of statistical image reconstruction methods, and increasing the penalty log-likelihood. In this study, we propose a reconstruction algorithm that ensures fast convergence speed and monotonic increase in likelihood. The basic structure of this algorithm involves sequentially updating groups of pixels instead of updating all parameters simultaneously with each iteration.