• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.79-89
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• 2018

In this paper, we study the maximal property of the volume of the convex hull of d-dimensional independent random vectors. We show that the volume of the random convex hull from a multivariate location-scale family indexed by ${\Sigma}$ is stochastically maximized in simple stochastic order when ${\Sigma}$ is diagonal. The claim can be applied to a broad class of multivariate distributions that include skewed/unskewed multivariate t-distributions. We numerically investigate the proven stochastic relationship between the dependent and independent random convex hulls with the Gaussian random convex hull. The numerical results confirm our theoretical findings and the maximal property of the volume of the independent random convex hull.

• Journal of the Korea Computer Graphics Society
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• v.2 no.2
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• pp.61-68
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• 1996

In this paper we propose a new visualization technique to characterize qualitative information of a large DNA sequence. While a long DNA sequence has huge information, it is not easy to obtain genetic information from the DNA sequence. We transform DNA sequences into a polygon to compute their homology in image domain rather than text domain. Our program visualizes DNA sequences with colored random walk plots and simplify them k-convex hulls. A random walk plot represents DNA sequence as a curve in a plane. A k-convex hull simplifies a random work plot by removing some parts of its insignificant information. This technique gives a biologist an insight to detect and classify DNA sequences with easy. Experiments with real genome data proves our approach gives a good visual forms for long DNA sequences for homology analysis.

• Communications for Statistical Applications and Methods
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• v.22 no.1
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• pp.69-80
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• 2015

In this paper, the probability that a given point is covered by a random convex hull generated by independent and identically-distributed random points in a plane is studied. It is shown that such probability can be expressed in terms of an integral that can be approximated numerically by function-evaluations over the grid-points in a 2-dimensional space. The new integral representation allows such probability be computed efficiently. The computational burdens under the proposed integral representation and those in the existing literature are compared. The proposed method is illustrated through numerical examples where the random points are drawn from (i) uniform distribution over a square and (ii) bivariate normal distribution over the two-dimensional Euclidean space. The applications of the proposed method in statistics are are discussed.

• Journal of IKEEE
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• v.17 no.1
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• pp.29-35
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• 2013

In this paper, we suggest an improved Convex Hull algorithm considering sort in plane point set. This algorithm has low computational complexity since processing data are reduced by characteristic of extreme points. Also it obtains a complete convex set with just one processing using an convex vertex discrimination criterion. Initially it requires sorting of point set. However we can't quickly sort because of its heavy operations. This problem was solved by replacing value and index. We measure the execution time of algorithms by generating a random set of points. The results of the experiment show that it is about 2 times faster than the existing algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.783-788
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• 2003

In this paper, we present a new approach to detect and recognize human face in the image from vision camera equipped on the mobile robot platform. Due to the mobility of camera platform, obtained facial image is small and pose-various. For this condition, new algorithm should cope with these constraints and can detect and recognize face in nearly real time. In detection step, ‘coarse to fine’ detection strategy is used. Firstly, region boundary including face is roughly located by dual ellipse templates of facial color and on this region, the locations of three main facial features- two eyes and mouth-are estimated. For this, simplified facial feature maps using characteristic chrominance are made out and candidate pixels are segmented as eye or mouth pixels group. These candidate facial features are verified whether the length and orientation of feature pairs are suitable for face geometry. In recognition step, pseudo-convex hull area of gray face image is defined which area includes feature triangle connecting two eyes and mouth. And random lattice line set are composed and laid on this convex hull area, and then 2D appearance of this area is represented. From these procedures, facial information of detected face is obtained and face DB images are similarly processed for each person class. Based on facial information of these areas, distance measure of match of lattice lines is calculated and face image is recognized using this measure as a classifier. This proposed detection and recognition algorithms overcome the constraints of previous approach [15], make real-time face detection and recognition possible, and guarantee the correct recognition irregardless of some pose variation of face. The usefulness at mobile robot application is demonstrated.