• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.87-93
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• 1998

Mejia and Minda proved that if a hyperbolic simply connected region $\Omega$ is k-convex, then (equation omitted), $z \in \Omega$. We show that this inequality actually characterizes k-convex regions.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.8
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• pp.1931-1940
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• 2014

In this paper, we propose a new hand shape recognition algorithm based on the geometric features using the convex-hull from the depth image acquired by Kinect system. Kinect is a camera providing a depth image and user's skeleton information and used for detecting hand region. In the proposed algorithm, hand region is detected in a depth image acquired by Kinect and convex-hull of the region is found. Boundary points caused by noise and unnecessary points for recognition are eliminated in the convex-hull that changes depending on hand shape. Hand shape is recognized by the sum of internal angle of a polygon that is matched with convex-hull reconstructed with selected boundary points. Through experiments, we confirm that proposed algorithm shows high recognition rate not only for five models but also those cases rotated.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1169-1180
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• 1999

Two-point comparison theorems between hyperbolic and euclidean geometry for convex regions in the complex plane are known([5], [6]). We give new geometric proofs of sharp two-point comparison theorems for convex regions.

• Journal of the Korea Concrete Institute
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• v.20 no.5
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• pp.627-634
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• 2008

This paper presents an optimum mixture design method for proportioning a concrete. In the proposed method, the search space is constrained as the domain defined by the minimal convex region of a database, instead of the available range of each component and the ratio composed of several components. The model for defining the search space which is expressed by the effective region is proposed. The effective region model evaluates whether a mix-proportion is effective on processing for optimization, yielding highly reliable results. Three concepts are adopted to realize the proposed methodology: A genetic algorithm for the optimization; an artificial neural network for predicting material properties; and a convex hull for evaluating the effective region. And then, it was applied to an optimization problem wherein the minimum cost should be obtained under a given strength requirement. Experimental test results show that the mix-proportion obtained from the proposed methodology using convex hulls is found to be more accurate and feasible than that obtained from a general optimum technique that does not consider this aspect.

• Laser Solutions
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• v.18 no.1
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• pp.18-22
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• 2015

In this paper, controlling shape of optical fiber tip for endoscope was investigated for eliminating blind spot. The blind spot of endoscope is generated by divergence angle of optical fiber, so it is easy to generate blind spot when tightly focusing. In order to eliminate this region, fiber tip is necessary to be controlled as convex or concave. Illumination simulation of convex and concave type of fiber tip in the endoscope was in progress, so the distance of non- blind region was investigated in each case. As well as the simulation, the tip was fabricated as concave shape by UV laser machining. Then the beam radiation was measured to observe the blind region. The result showed that controlling the fiber tip as convex or concave shape makes the narrow blind region of illumination in endoscope.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.279-289
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• 1999

Given n points in the plane the planar convex hull prob-lem in that of finding which of these points belong to the perimeter of the smallest convex region (a polygon) containing all n points. Here we suggest two kinds of methods. First we present a new sequential method for constructing the pla-nar convex hull O(1.5n) time in the quadratic decision tree model. Second using the sequential method we suggest a new parallel algo-rithm which solve the planar convex hull O(1.5n/p) time on a maspar Machine (CREW-PRAM) with O(n) processors. Also when we run on a maspar Machine we achieved a 37. 156-fold speedup with 64 pro-cessor.

• Proceedings of the KIEE Conference
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• 2001.11c
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• pp.438-441
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• 2001

This paper describes a system for tracking a face in a input video sequence using facial convex hull based facial segmentation and a robust hausdorff distance. The algorithm adapts YCbCr color model for classifying face region by [l]. Then, we obtain an initial face model with preprocessing and convex hull. For tracking, a Robust Hausdorff distance is computed and the best possible displacement is selected. Finally, the previous face model is updated using the displacement t. It is robust to some noises and outliers. We provide an example to illustrate the proposed tracking algorithm in video sequences obtained from CCD camera.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2008.06a
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• pp.118-118
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• 2008

The oxide CMP has been applied to interlayer dielectric(ILD) and shallow trench isolation (STI) in chip fabrication. Recently the slurry used in oxide CMP being changed from silica slurry to ceria (cerium dioxide) slurry particularly in STI CMP, because the material selectivity of ceria slurry is better than material selectivity of silica slurry. Moreover, the ceria slurry has good a planarization efficiency, compared with silica slurry. However ceria abrasives make a material removal rate too high at the region of wafer center. Then we focuses on why profile of material removal rate is convex. The material removal rate sharply increased to 3216 $\AA$/min by $4^{th}$ run without conditioning. After $4^{th}$ run, material removal rate converged. Furthermore, profile became more convex during 12 run. And average material removal rate decreased when conditioning process is added to end of CMP process. This is due to polishing mechanism of ceria. Then the ceria abrasive remains at the pad, in particular remains more at wafer center contacted region of pad. The field emission scanning electron microscopy (FE-SEM) images showed that the pad sample in the wafer center region has a more ceria abrasive than in wafer outer region. The energy dispersive X-ray spectrometer (EDX) verified the result that ceria abrasive is deposited and more at the region of wafer center. Therefore, this result may be expected as ceria abrasives on pad surface causing the convex profile of material removal rate.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.1
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• pp.70-76
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• 2015

The ship hull is accomplished by assembling various curved surfaces. There are numerous existing methods for ship hull processing, which need certain appropriate processing methods to enable it to be more efficient. The curved hull plates can be divided into convex region and saddle region. It is common to use line heating method to form a saddle region, when it comes to a convex region, it will be triangle heating method to be utilized. A precise analysis for curvature domain is required for the application of proper processing method. There exist various problems on existing calculation methods of curvature domain. Therefore, a more powerful method is demanded to it more accurately. In this study, a method called Dual Contouring is applied to extract curved surfaces, which is able to improve accuracy of extracted area. Based on all above, a best-suited heat processing method should be selected.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.583-595
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• 2016

Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle ${\Delta}ABP$. It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane ${\mathbb{R}}^2$, these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property $S={\frac{4}{3}}T$ for parabolas we study strictly locally convex curves in the plane ${\mathbb{R}}^2$ satisfying $S={\lambda}T+{\nu}U$, where ${\lambda}$ and ${\nu}$ are some functions on the curves. As a result, we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be an open arc of a parabola.