• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1021-1031
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• 1999

In this paper we introduce matrix representations of polygroups over hyperrings and show such representations induce representations of the fundamental group over the corresponding fundamental ring. We also introduce the notion of a polygroup hyperring generalizing the notion of a group ring. We establish homo-morphisms among various polygroup hyperrings.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2020.11a
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• pp.322-324
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• 2020

본 논문에서는 스테레오 영상으로부터 얻은 특징점들을 활용하여 기초행렬(Fundamental matrix)을 추정하는 실험을 한다. 획득한 영상들은 보정이 되어 있으며, 특징점 추출 후 매칭은 RANSAC 등의 기존 알고리즘을 활용한다. 기초 행렬을 얻기 위해 스테레오 영상으로부터 정의되는 에피폴라 점, 에피폴라 선, 에피폴라 평면을 정의하고, 이들로부터 얻을 수 있는 기하학적 관계식을 활용하여 기초행렬을 수학적으로 추정해 보고, 실험으로 수학적 이론을 검증해 본다.

• East Asian mathematical journal
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• v.39 no.1
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• pp.23-27
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• 2023

In this paper, we derive the some identities which are related to the multifactorial numbers and the Catalan numbers. We utilize the fundamental theorem of Riordan matrix to obtain those identities.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.1
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• pp.40-48
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• 2002

Three-Dimensional scene reconstruction from images acquired with different viewpoints is possible as estimating Fundamental matrix(F-matrix) that indicates the epipolar geometry of two images. Correspondence points required to calculate F-matrix of two images include noise such as miss matches, so generally it is hard to calculate F-matrix accurately. In this paper, we classify noise into two types; outlier and minute noise. we propose SSOR algorithm that estimate F-matrix effectively. SSOR algorithm is rejecting outlier step by step in a noise environment. To evaluate the performance of proposed algorithm we simulated with synthetic images and real images. As a result of simulation we show that proposed algorithm is better than conventional algorithms.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.469-487
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• 1999

Sign patterns of idempotent matrices, especially symmetric idempotent matrices, are investigated. A number of fundamental results are given and various constructions are presented. The sign patterns of symmetric idempotent matrices through order 5 are determined. Some open questions are also given.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.45 no.1
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• pp.38-46
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• 2008

Key-frame selection algorithm is defined as the process of selecting a necessary images for 3D reconstruction from the uncalibrated images. Also, camera calibration of images is necessary for 3D reconstuction. In this paper, we propose a new method of Key-frame selection with the minimal error for camera calibration. Using the full-auto-calibration, we estimate camera parameters for all selected Key-frames. We remove the false matching using the fundamental matrix computed by algebraic deviation from the estimated camera parameters. Finally we obtain 3D reconstructed data. Our experimental results show that the proposed approach is required rather lower time costs than others, the error of reconstructed data is the smallest. The elapsed time for estimating the fundamental matrix is very fast and the error of estimated fundamental matrix is similar to others.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.11
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• pp.73-82
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• 2014

The LM algorithm is used in solving the least square problem in a non linear system, and is used in various fields. However, in cases the applied field's target functionis complicated and high-dimensional, it takes a lot of time solving the inner matrix and vector operations. In such cases, the LM algorithm is unsuitable in embedded environment and requires a hardware accelerator. In this paper, we implemented the LM algorithm in hardware. In the implementation, we used pipeline stages to divide the target function operation, and reduced the period of data input of the matrix and vector operations in order to accelerate the speed. To measure the performance of the implemented hardware, we applied the refining fundamental matrix(RFM), which is a part of 3D reconstruction application. As a result, the implemented system showed similar performance compared to software, and the execution speed increased in a product of 74.3.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.1
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• pp.75-85
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• 1997

A stable algorithm for computing the fundamental matrix (I-Q)$^{-1}$ of a Markov chain is proposed, where Q is a substochastic matrix. The proposed algorithm utilizes the GTH algorithm (Grassmann, Taskar and Heyman, 1985) which is turned out to be stable for finding the steady state distribution of a finite Markov chain. Our algorithm involves no subtractions and therefore loss of significant digits due to concellation is ruled out completely while Gaussian elimination involves subtractions and thus may lead to loss of accuracy due to cancellation. We present numerical evidence to show that our algorithm achieves higher accuracy than the ordinagy Gaussian elimination.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.555-571
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• 2005

A pair of pants $\Sigma(0,3)$ is a building block of oriented surfaces. The purpose of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a pair of pants. In the level of the matrix group $SL(2,\mathbb{R})$, we shall show that an odd number of traces of matrix presentations of the generators of the fundamental group of $\Sigma(0,3)$ should be negative.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.529-539
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• 2016

In this paper, we obtain solution for the first order matrix dynamical system and also we provide set of necessary and sufficient conditions for complete controllability and complete observability of the Sylvester matrix dynamical system.