• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.651-658
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• 2001

The projection matrix plays an important role in the linear model theory. In this paper we derive an algebraic relationship between the projection matrices of submatrices of the design matrix. Using this relationship we can easily obtain the projection matrices of any submatrices of the design matrix. Also we show that every projection matrix can be obtained as a linear combination of Kronecker products of identity matrices and matrices with all elements equal to 1.

• Proceedings of the Korean Society of Medical Physics Conference
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• 2002.09a
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• pp.439-441
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• 2002

The aim of this study is to reconstruct the 3D target volume from multiple projection images. It was assumed that we were already aware of the target position exactly, and all processes were performed in Target Coordinates whose origin was the center of the target. We used six projections: two projections were used to make a Reconstruction Box and four projections were for image acquisition. Reconstruction Box was made up of voxels of 3D matrix. Projection images were transformed into 3D volume in this virtual box using geometrical based back-projection method. Algorithm was applied to an ellipsoid model and horse-shoe shaped model. Projection images were created using C program language by geometrical method and reconstruction was also accomplished using C program language and Matlab(The Mathwork Inc., USA). For ellipsoid model, reconstructed volume was slightly overestimated but target shape and position was proved to be correct. For horse-shoe shaped model, reconstructed volume was somewhat different from original target model but there was a considerable improvement in target volume determination.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• Nuclear Engineering and Technology
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• v.54 no.5
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• pp.1570-1578
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• 2022

During a severe accident, steam generator (SG) tubes undergo rapid changes in the pressure and temperature. Therefore, an appropriate creep model to predict a short term creep damage is essential. In this paper, a novel creep model for Alloy 690 SG tube material was proposed. It is based on the theta (θ) projection method that can represent all three stages of the creep process. The original θ projection method poses a limitation owing to its inability to represent experimental creep curves for SG tube materials for a large strain rate in the tertiary creep region. Therefore, a new modified θ projection method is proposed; subsequently, a master curve for Alloy 690 SG material is also proposed to optimize the creep model parameters, θ_i (i = 1-5). To adapt the implicit creep scheme to the finite element code, a partial derivative of incremental creep with respect to the stress is necessary. Accordingly, creep model parameters with a strictly linear relationship with the stress and temperature were proposed. The effectiveness of the model was validated using a commercial finite element analysis software. The creep model can be applied to evaluate the creep rupture behavior of SG tubes in nuclear power plants.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.24 no.6
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• pp.710-717
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• 2015

Projection stereolithography is an additive manufacturing method that uses beam projection to cure the photo-reactive resin used. The light source of a cross-section layer-form illuminates photo-curable resin for building a three-dimensional (3D) model. This method has high accuracy and a fast molding speed because the processing unit is a face instead of a dot. This study describes a Scalable Projection Stereolithography 3D Printing System for improving the accuracy of the stereolithography. In a conventional projection 3D printer, when printing a small sized model, many pixels are not used in the projection or curing. The proposed system solves this problem through an optical adjustment, and keeps using the original image as possible as filling the whole projection area. The experimental verification shows that the proposed system can maintain the highest level of precision regardless of the output size.

• Advances in robotics research
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• v.2 no.1
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• pp.45-57
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• 2018

Even though the popularity of projection mapping continues to increase and it is being implemented in more and more settings, most current projection mapping systems are limited to special purposes, such as outdoor events, live theater and musical performances. This lack of versatility arises from the large number of projectors needed and their proper calibration. Furthermore, we cannot change the positions and poses of projectors, or their projection targets, after the projectors have been calibrated. To overcome these problems, we propose a projection mapping method using a projector robot that can perform projection mapping in more general or ubiquitous situations, such as shopping malls. We can estimate a projector's position and pose with the robot's self-localization sensors, but the accuracy of this approach remains inadequate for projection mapping. Consequently, the proposed method solves this problem by combining self-localization by robot sensors with position and pose estimation of projection targets based on a 3D model. We first obtain the projection target's 3D model and then use it to accurately estimate the target's position and pose and thus achieve accurate projection mapping with a projector robot. In addition, our proposed method performs accurate projection mapping even after a projection target has been moved, which often occur in shopping malls. In this paper, we employ Ubiquitous Display (UD), which we are researching as a projector robot, to experimentally evaluate the effectiveness of the proposed method.

• Progress in Medical Physics
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• v.14 no.3
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• pp.167-174
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• 2003

In the radiation treatment planning (RTP) process, especially for stereotactic radiosurgery (SRS), knowing the exact volume and shape and the precise position of a lesion is very important. Sometimes X-ray projection images, such as angiograms, become the best choice for lesion identification. However, while the exact target position can be acquired by bi-projection images, 3D target reconstruction from bi-projection images is considered to be impossible. The aim of this study was to reconstruct the 3D target volume from multiple projection images. It was assumed that we knew the exact target position in advance, and all processes were performed in Target Coordinates, where the origin was the center of the target. We used six projections: two projections were used to make a Reconstruction Box and four projections were for image acquisition. The Reconstruction Box was made up of voxels of 3D matrices. Projection images were transformed into 3D in this virtual box using a geometric back-projection method. The resolution and the accuracy of the reconstructed target volume were dependent on the target size. An algorithm was applied to an ellipsoid model and a horseshoe-shaped model. Projection images were created geometrically using C program language, and reconstruction was also performed using C program language and Matlab ver. 6(The Mathwork Inc., USA). For the ellipsoid model, the reconstructed volume was slightly overestimated, but the target shape and position proved to be correct. For the horseshoe-shaped model, reconstructed volume was somewhat different from the original target model, but there was a considerable improvement in determining the target volume.

• Proceedings of the KSRS Conference
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• v.2
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• pp.860-863
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• 2006

Epipolar images have to be generated to stereo display aerial images or satellite images. Pushbroom sensor is used to acquire high resolution satellite images. These satellite images have curvilinear epipolar lines unlike the epipolar lines of frame images, which are straight lines. The aforementioned fact makes it difficult to generate epipolar images for pushbroom satellite images. If we assume a linear transition of the sensor having constant speed and attitude during image acquisition, we can generate epipolar images based on parallel projection model (2D Affine model). Recent high resolution images are provided with RPC values so that we can exploit these values to generate epipolar images without using ground control points and tie point. This paper provides a procedure based on the parallel projection model for generating epipolar images directly from a stereo IKONOS images, and experimental results.

• Journal of Applied Reliability
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• v.16 no.4
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• pp.305-312
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• 2016

Purpose: The purpose of this study is to provide a sensitivity analysis of system reliability for recognizing effectiveness of changing of BD mode failures using reliability growth projection model based on NHPP. Methods: Crow extended reliability projection model (CERPM) is used to analyze the changing of two factors 1) the number of BD mode failures, 2) fix effectiveness factor (FEF) values. Results: The system reliability has increased in accordance with the number of BD mode failures and FEF values have increased. Conclusion: It is necessary to design failure modes and FEF values to supervise the reliability.

• Korean Journal of Remote Sensing
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• v.22 no.5
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• pp.451-456
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• 2006

Epipolar images have to be generated to stereo display aerial images or satellite images. Pushbroom sensor is used to acquire high resolution satellite images. These satellite images have curvilinear epipolar lines unlike the epipolar lines of frame images, which are straight lines. The aforementioned fact makes it difficult to generate epipolar images for pushbroom satellite images. If we assume a linear transition of the sensor having constant speed and attitude during image acquisition, we can generate epipolar images based on parallel projection model (20 Affine model). Recent high resolution images are provided with RPC values so that we can exploit these values to generate epipolar images without using ground control points and tie point. This paper provides a procedure based on the parallel projection model for generating epipolar images directly from a stereo IKONOS images, and experimental results.