• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.223-232
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• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.157-166
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• 2014

If there are metals located in the X-ray scanned object, a point outside the metals has its range of projection angle at which projections passing through the point are disturbed by the metals. Roughly speaking, this implies that attenuation information at the point is missing in the blocked projection range. So conventional projection completion MAR algorithms to use the undisturbed projection data on the boundary of the metaltrace is less efficient in reconstructing the attenuation coefficient in detailed parts, in particular, near the metal region. In order to overcome this problem, we propose the algebraic correction technique (ACT) to utilize a pre-reconstructed interim image of the attenuation coefficient outside the metal region which is obtained by solving a linear system designed to reduce computational costs. The reconstructed interim image of the attenuation coefficient is used as prior information for MAR. Numerical simulations support that the proposed correction technique shows better performance than conventional inpainting techniques such as the total variation and the harmonic inpainting.

• ETRI Journal
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• v.46 no.4
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• pp.683-696
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• 2024

The point cloud provides viewers with intuitive geometric understanding but requires a huge amount of data. Moving Picture Experts Group (MPEG) has developed video-based point-cloud compression in the range of 300-700. As the compression rate increases, the complexity increases to the extent that it takes 101.36 s to compress one frame in an experimental environment using a personal computer. To realize real-time point-cloud compression processing, the direct patch projection (DPP) method proposed herein simplifies the complex patch segmentation process by classifying and projecting points according to their geometric positions. The DPP method decreases the complexity of the patch segmentation from 25.75 s to 0.10 s per frame, and the entire process becomes 8.76 times faster than the conventional one. Consequently, this proposed DPP method yields similar peak signal-to-noise ratio (PSNR) outcomes to those of the conventional method at reduced times (4.7-5.5 times) at the cost of bitrate overhead. The objective and subjective results show that the proposed DPP method can be considered when low-complexity requirements are required in lightweight device environments.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2389-2392
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• 2005

We present fast stereo matching algorithm using edge projection. Traditional stereo matching algorithm uses 2D template for the search of corresponding point thus it requires huge the computational cost. In this paper, we reduce the 2D search problem into 1D using edge projection along vertical and horizontal direction inside the region of interest. Also, by accumulation of edge projection along vertical and horizontal direction, the edge projection within the region of interest could simply be obtained by just subtracting two values. Experimental results show that matching algorithm using edge projection also gives comparable discriminating power compared to that of using intensity.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.401-415
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• 2015

In this paper, we propose a modified proximal point algorithm which consists of a resolvent operator technique step followed by a generalized projection onto a moving half-space for approximating a solution of a variational inclusion involving a maximal monotone mapping and a monotone, bounded and continuous operator in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved.

• Proceedings of the Korea Information Processing Society Conference
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• 2019.05a
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• pp.482-484
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• 2019

Learning and analyzing 3D point clouds with deep networks is challenging due to the limited and irregularity of the data. In this paper, we present a data-driven point cloud augmentation technique. The key idea is to learn multilevel features per point and to reconstruct to a similar point set. Our network is applied to a projection loss function that encourages the predicted points to remain on the geometric shapes with a particular target. We conduct various experiments using ShapeNet part data to evaluate our method and demonstrate its possibility. Results show that our generated points have a similar shape and are located closer to the object.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.447-456
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• 2017

The purpose of this paper is to introduce some strong convergence theorems for the problem of finding a common zero of a finite family of monotone operators and the problem of finding a common fixed point of a finite family of nonexpansive in Hilbert spaces by hybrid projection method.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.73-86
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• 2007

The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given spatial $C^1$ Hermite data, we construct a spatial PH curve on a sphere that is a $C^1$ Hermite interpolant of the given data as follows: First, we solve $C^1$ Hermite interpolation problem for the stereographically projected planar data of the given data in $\mathbb{R}^3$ with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in $\mathbb{R}^3$ using the inverse general stereographic projection.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.553-568
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• 2022

In this paper, we introduce and study two different iterative hybrid projection algorithms for solving a fixed point problem of nonexpansive mappings. The first algorithm is generated by the combination of the inertial method and the hybrid projection method. On the other hand, the second algorithm is constructed by the convex combination of three updated vectors and the hybrid projection method. The strong convergence of the two proposed algorithms are proved under very mild assumptions on the scalar control. For illustrating the advantages of these two newly invented algorithms, we created some numerical results to compare various numerical performances of our algorithms with the algorithm proposed by Dong and Lu [11].

• 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.