• Korean Management Science Review
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• v.14 no.2
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• pp.69-79
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• 1997

The computational speed of interior point method of linear programming depends on the speed of Cholesky factorization. If the coefficient matrix A has dense columns then the matrix A.THETA. $A^{T}$ becomes a dense matrix. This causes Cholesky factorization to be slow. We study an efficient implementation method of the dense column splitting among dense column resolving technique and analyze the relation between dense column splitting and order methods to improve the sparsity of Cholesky factoror.

• Journal of Broadcast Engineering
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• v.25 no.5
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• pp.798-807
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• 2020

As technologies using digital camera have been developed, 3D images can be constructed from the pictures captured by using multiple cameras. The 3D image data is represented in a form of point cloud which consists of 3D coordinate of the data and the related attributes. Various techniques have been proposed to construct the point cloud data. Among them, Structure-from-Motion (SfM) and Multi-view Stereo (MVS) are examples of the image-based technologies in this field. Based on the conventional research, the point cloud data generated from SfM and MVS may be sparse because the depth information may be incorrect and some data have been removed. In this paper, we propose an efficient algorithm to enhance the point cloud so that the density of the generated point cloud increases. Simulation results show that the proposed algorithm outperforms the conventional algorithms objectively and subjectively.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1341-1356
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• 2018

The author devotes this paper to defining a new class of generalized soft open sets, namely soft somewhere dense sets and to investigating its main features. With the help of examples, we illustrate the relationships between soft somewhere dense sets and some celebrated generalizations of soft open sets, and point out that the soft somewhere dense subsets of a soft hyperconnected space coincide with the non-null soft ${\beta}$-open sets. Also, we give an equivalent condition for the soft csdense sets and verify that every soft set is soft somewhere dense or soft cs-dense. We show that a collection of all soft somewhere dense subsets of a strongly soft hyperconnected space forms a soft filter on the universe set, and this collection with a non-null soft set form a soft topology on the universe set as well. Moreover, we derive some important results such as the property of being a soft somewhere dense set is a soft topological property and the finite product of soft somewhere dense sets is soft somewhere dense. In the end, we point out that the number of soft somewhere dense subsets of infinite soft topological space is infinite, and we present some results which associate soft somewhere dense sets with some soft topological concepts such as soft compact spaces and soft subspaces.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.10a
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• pp.289-292
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• 1996

In Cholesky factorization of the interior point method, dense columns of A matrix make dense Cholesky factor L regardless of sparsity of A matrix. We introduce a method to transform a primal problem to a dual problem in order to preserve the sparsity.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2020.07a
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• pp.266-268
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• 2020

본 논문에서는 dense point cloud 의 평면영역에서 발생하는 bump 을 줄이기 위한 방법을 제시한다. 이상적인 point cloud 의 평면영역에서 점의 위치의 차이가 균일하다는 특성을 이용하여 점의 위치를 재구성하는 방식을 제시한다. 또한 더 작은 개수의 점으로 물체를 나타낼 수 있으며, 더 작은 잡음이 나타나는 sparse point cloud 의 성질을 고려하여 dense point cloud 의 점의 개수 또한 감소시킨다. 따라서 제안하는 알고리즘을 적용하여 dense point cloud 의 잡음을 감소시키면 평면영역의 bump 감소 및 점 개수의 감소를 통한 데이터 전송 시 더 작은 크기로 보낼 수 있다.

• ETRI Journal
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• v.44 no.6
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• pp.1034-1046
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• 2022

The learning-based multiview stereo (MVS) methods for three-dimensional (3D) reconstruction generally use 3D volumes for depth inference. The quality of the reconstructed depth maps and the corresponding point clouds is directly influenced by the spatial resolution of the 3D volume. Consequently, these methods produce point clouds with sparse local regions because of the lack of the memory required to encode a high volume of information. Here, we apply the atrous spatial pyramid pooling (ASPP) module in MVS methods to obtain dense feature maps with multiscale, long-range, contextual information using high receptive fields. For a given 3D volume with the same spatial resolution as that in the MVS methods, the dense feature maps from the ASPP module encoded with superior information can produce dense point clouds without a high memory footprint. Furthermore, we propose a 3D loss for training the MVS networks, which improves the predicted depth values by 24.44%. The ASPP module provides state-of-the-art qualitative results by constructing relatively dense point clouds, which improves the DTU MVS dataset benchmarks by 2.25% compared with those achieved in the previous MVS methods.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.33-41
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• 2020

We introduced the concept of the 𝜖₀-density and the 𝜖₀-dense ace in [1]. This concept is related to the structure of employment. In addition to the double capacity theorem which was introduced in [1], we need the minimal dense subset. In this paper, we investigate a concept of the minimal 𝜖₀-dense subset in the Euclidean m dimensional space.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.39 no.2
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• pp.73-79
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• 2021

Recently there are growing interests on the energy conservation and emission reduction. In the fields of architecture and civil engineering, the energy monitoring of structures is required to response the energy issues. In perspective of thermal monitoring, thermal images gains popularity for their rich visual information. With the rapid development of the drone platform, aerial thermal images acquired using drone can be used to monitor not only a part of structure, but wider coverage. In addition, the stereo photogrammetric process is expected to generate 3D point cloud with thermal information. However thermal images show very poor in resolution with narrow field of view that limit the use of drone-based thermal photogrammety. In the study, we aimed to generate 3D thermal point cloud using visible and thermal images. The visible images show high spatial resolution being able to generate precise and dense point clouds. Then we extract thermal information from thermal images to assign them onto the point clouds by precisely establishing photogrammetric collinearity between the point clouds and thermal images. From the experiment, we successfully generate dense 3D thermal point cloud showing 3D thermal distribution over the building structure.

• Journal of the military operations research society of Korea
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• v.24 no.1
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• pp.146-156
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• 1998

Cholesky factorization is known to be inefficient to problems with dense column and network problems in interior point methods. We use the conjugate gradient method and preconditioners to improve the convergence rate of the conjugate gradient method. Several preconditioners were applied to LPABO 5.1 and the results were compared with those of CPLEX 3.0. The conjugate gradient method shows to be more efficient than Cholesky factorization to problems with dense columns and network problems. The incomplete Cholesky factorization preconditioner shows to be the most efficient among the preconditioners.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.67-70
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• 1998

The computational speed of interior point method of linear programming depends on the speed of Cholesky factorization to solve AΘA$^{T}$ $\Delta$y=b. If the coefficient matrix A has dense columns then the matrix AΘA$^{T}$ becomes a dense matrix. This causes Cholesky factorization to be slow. The Schur complement method is applied to treat dense columns in many implementations but suffers from its numerical unstability. We study efficient implementation of Schur complement method. We achieve improvements in computational speed and numerical stability.rical stability.