• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.195-210
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• 1995

Let $\Omega_n$ denote the set of all $n \times n$ doubly stochatic matrices. Then it is well known that $\Omega_n$ forms convex polytope of dimension $(n-1)^2$ with n! extreme points in the $n^2$-dimensional Euclidean space.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.49-54
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• 2023

In this paper, we obtain some results concerning the location of zeros of generalized derivatives of polynomials which are analogous to those for the ordinary derivative of polynomials.

• The Korean Journal of Applied Statistics
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• v.33 no.2
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• pp.115-122
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• 2020

K-means clustering uses a spherical or elliptical metric to group data points; however, it does not work well for non-convex data such as the concentric circles. Spectral clustering, based on graph theory, is a generalized and robust technique to deal with non-standard type of data such as non-convex data. Results obtained by spectral clustering often outperform traditional clustering such as K-means. In this paper, we review spectral clustering and show important issues in spectral clustering such as determining the number of clusters K, estimation of scale parameter in the adjacency of two points, and the dimension reduction technique in clustering high-dimensional data.

• East Asian mathematical journal
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• v.24 no.1
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.

• Journal of Korea Multimedia Society
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• v.17 no.12
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• pp.1430-1436
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• 2014

We propose an algorithm which detects the touch of the fingertip on a general wall using the shadow information. Nowadays, there is a demand for presentation systems which can perceive the presenter's action so that the presenter can use natural movements without extra interface hardware. One of the most fundamental techniques in this area is the detection of the fingertip and the recognition of the touch of the fingertip on the screen. The proposed algorithm recognizes the touch of the fingertip without using the depth information, and therefore needs no depth or touch sensing devices. The proposed method computes the convex hull points of both the fingertip and the shadow of the fingertip, and then computes the distance between those points to decide whether a touch event has occured. Using the proposed method, it is possible to develop a new projector device which can perceive a fingertip touch on a general wall.

• Proceedings of the KSRS Conference
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• 2007.10a
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• pp.637-641
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• 2007

Airborne LIDAR (Light Detection and Ranging) technology has reached a degree of the required accuracy in mapping professions, and advanced LIDAR systems are becoming increasingly common in the various fields of application. LiDAR data constitute an excellent source of information for reconstructing the Earth's surface due to capability of rapid and dense 3D spatial data acquisition with high accuracy. However, organizing the LIDAR data and extracting information from the data are difficult tasks because LIDAR data are composed of randomly distributed point clouds and do not provide sufficient semantic information. The main reason for this difficulty in processing LIDAR data is that the data provide only irregularly spaced point coordinates without topological and relational information among the points. This study introduces an efficient and robust method for automatic extraction of building footprints using airborne LIDAR data. The proposed method separates ground and non-ground data based on the histogram analysis and then rearranges the building boundary points using convex hull algorithm to extract building footprints. The method was implemented to LIDAR data of the heavily built-up area. Experimental results showed the feasibility and efficiency of the proposed method for automatic producing building layers of the large scale digital maps and 3D building reconstruction.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.11
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• pp.763-770
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• 2022

In an environment where multiple drones are operated, collisions can occur when path points overlap, and collision avoidance in preparation for this is essential. When multiple drones perform multiple tasks, it is not appropriate to use a method to generate a collision-avoiding path in the path planning phase because the path of the drone is complex and there are too many collision prediction points. In this paper, we generate a path through a commonly used path generation algorithm and propose a collision avoidance method using speed profile optimization from that path segment. The safe distance between drones was considered at the expected point of collision between paths of drones, and it was designed to assign a speed profile to the path segment. The optimization problem was defined by setting the distance between drones as variables in the flight time equation. We constructed the constraints through linearize and convexification, and compared the computation time of SQP and convex optimization method in multiple drone operating environments. Finally, we confirmed whether the results of performing convex optimization in the 20 drone operating environments were suitable for the multiple drone operating system proposed in this study.

• East Asian mathematical journal
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• v.25 no.2
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• pp.179-196
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• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.10a
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• pp.162-165
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• 2017

The proposed paper extracts the region of interest from the x-lay input image and compares it with the reference image. The x-ray image has the same shape, but the size, direction and position of the object are photographed differently. In this way, we measure the erection difference of darkness and darkness using the similarity measurement method for the same object. Distance measurement also calculates the distance between two points with vector coordinates (x, y, z) of x-lay data. Experimental results show that the proposed method improves the accuracy of ROI extraction and the reference image matching time is more efficient than the conventional method.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.48 no.2
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• pp.55-65
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• 2011

In this paper, a novel method of marker detection robust against marker occlusion in augmented reality is proposed. the proposed method consists of four steps. In the first step, in order to effectively detect an occluded marker, we first utilize the Affine-SIFT (ASIFT, Affine-Scale Invariant Features Transform) for detecting matching points between an enrolled marker and an input images with an occluded marker. In the second step, we apply the Principal Component Analysis (PCA) for eliminating outlier of the matching points in the enrolled marker. And then matching points are projected to the first and second axis for longest value and the shortest value of an ellipse are determined by average distance between the projected points and a center of the points. In the third step, Convex-hull vertices including matching points are considered as polygon vertices for estimating a geometric affine transformation. In the final step, by estimating the geometric affine transformation of the points, a marker robust against a marker occlusion is detected. Experimental results have shown that the proposed method effectively detects occlude markers.