• Communications for Statistical Applications and Methods
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• 제25권1호
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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.

• 한국컴퓨터그래픽스학회논문지
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• 제2권2호
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• pp.61-68
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• 1996

본 논문에서는 대용량의 DNA 염기 배열의 정성 정보를 특징짓기 위한 새로운 가시화 방법을 제안한다. DNA 배열은 배열 자체가 방대한 양의 정보를 포함하고 있기 때문에 분석에 많은 어려움이 있다. 우리는 DNA 염기 배열들사이의 상사성 비교를 위해 DNA 염기 배열을 하나의 이미지 도메인으로 변환한다. 프로그램은 random walk plot으로 DNA 염기 배열을 가시화한 후에 k-convex hull로 단순화 시킨다. Random Walk plot은 염기배열을 평면상에 하나의 커브로 표현한다. k-convex hull은 walk plot으로부터 무의미한 부분을 제거함으로서 walk plot을 단순화한다. 이러한 방법은 유전공학자들에게 쉽게 DNA 배열의 특징을 인식하고 분류할 수 있는 직관을 제공한다. 실제 게놈 데이터로 실험한 결과는 논문에서 제안하는 방법이 긴 DNA 염기배열들 사이의 유사성 분석을 위해 좋은 가시화 도구임을 보여준다.

• Communications for Statistical Applications and Methods
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• 제22권1호
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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.

• 전기전자학회논문지
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• 제17권1호
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• pp.29-35
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• 2013

본 연구에서는 임의의 정렬되지 않은 점집합에서 정렬을 고려한 개선된 Convex Hull 알고리즘을 제안한다. 이 알고리즘은 Convex Hull의 극점 특성을 이용하여 처리 데이터를 한정하기 때문에 계산복잡도가 낮다. 각 단계마다 볼록 정점을 판별하는 조건을 이용하여 한 번의 스캔으로 완전한 Convex Set을 구한다. 알고리즘 초기에 점집합의 정렬이 필요한데, 이때 걸리는 시간이 알고리즘 전체 동작시간의 대부분을 차지하기 때문에 값과 인덱스를 대치하여 빠르게 정렬하였다. 일반적인 상황을 가정하여 랜덤한 점집합으로 알고리즘의 동작시간을 측정하였으며 기존의 알고리즘에 비해 약 두 배의 속도 향상이 있음을 확인하였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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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.