• 한국정보통신학회논문지
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• 제23권4호
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• pp.388-393
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• 2019

외란(Outlier)이 있는 데이터를 피팅(Fitting)하는 방법으로 RANSAC(RANdom SAmple Consensus)알고리즘이 선, 원, 타원 등 의 피팅에 많이 사용되고 있다. 본 논문은 다수의 평면에 대한 3차원 포인트 데이터가 주어질 때 각 평면에 대해 RANSAC기반 평면 피팅을 최근 딥러닝 등에 많이 사용되는 GPU의 하나인 CUDA를 이용하여 효율적으로 수행하는 알고리즘을 제안한다. 모의 데이터와 실제 데이터를 이용하여 제안된 알고리즘의 성능을 CPU와 비교하여 보인다. 외란이 많고 인라이어(inlier) 비율이 낮을수록 CPU대비 속도가 향상되고 평면의 개수가 많을수록 평면당 데이터개수가 많을수록 병렬처리에 의한 속도가 가속됨을 보인다. 제안된 방법은 다중 평면 피팅외의 다른 피팅에도 쉽게 적용할 수 있다.

• Current Optics and Photonics
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• 제8권2호
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• pp.151-155
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• 2024

Optical systems often suffer from optical aberrations caused by imperfect hardware, which places significant constraints on their utility and performance. To reduce these undesirable effects, a comprehensive understanding of the aberrations inherent to optical systems is needed. This article presents an effective method for aberration detection using Zernike polynomials. The process involves scanning the object plane to identify the optimal focus and subsequently fitting the acquired focus data to Zernike polynomials. This fitting procedure facilitates the analysis of various aberrations in the optical system.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.983-994
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• 2000

We consider the problem of determining the circle of best fit to a set of data points in the plane. In [1] and [2] several algorithms already have been given for fitting a circle in least squares sense of minimizing the geometric distances to the given data points. In this paper we present another new descent algorithm which computes a parametric represented circle in order to minimize the sum of the squares of the distances to the given points. For any choice of starting values our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.669-684
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• 1999

We are interested in the problem of fitting a curve to a set of points in the plane in such a way that the sum of the squares of the orthogonal distances to given data points ins minimized. In[1] the prob-lem of fitting circles and ellipses was considered and numerically solved with general purpose methods. Especially in [2] H. Spath proposed a special purpose algorithm (Spath's ODF) for parabolas y-b=$c($\chi$-a)^2$ and for rotated ones. In this paper we present another parabola fitting algorithm which is slightly different from Spath's ODF. Our algorithm is mainly based on the steepest descent provedure with the view of en-suring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• 대한공간정보학회지
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• 제19권1호
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• pp.97-103
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• 2011

라이다 시스템은 신속하고 정확한 3차원 데이터 생성으로 인해 주목받는 시스템이 되었다. 지형공간정보 분야에서 원시 라이다 데이터로부터 3차원 건물모델과 같은 가치가 부가된 정보를 생산하는 기술은 오랫동안 관심 있는 연구주제로 다루어졌다. 본 논문은 라이다 데이터로부터 건물과 같은 인공지물의 주요 구성요소인 3차원 평면을 추출하는 내용을 담고 있다. 이 연구에서는 최적의 평면을 결정하기 위해 라이다 데이터에 포함된 이상치의 영향을 제거 또는 최소화 시키고, 두 평면이 만나는 지역에서 정확한 평면을 추출하는 하는 방법을 소개한다. 각 라이다 포인트에 대해서 plane fitting이 수행된 후, 결정된 세 개의 평면식 매개변수들은 의사색상값으로 변환되고, 이를 이용하여 평면을 추출하게 된다. 제안된 방법은 항공 라이다와 지상라이다 데이터 두 가지를 사용하여 그 유효성을 검증하였다.

• 한국공작기계학회논문집
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• 제12권4호
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• pp.17-22
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• 2003

This paper presents a new circular curve fitting approach of articulated manipulators, based on least square. The approach aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a starting point and an ending point. First a spherical fitting should be performed, using least squares. Then the circular curve fitting can be resulted from the intersection of the fitted sphere and the plane obtained from 3 points, i. e., a starting point, an ending point and the center of a sphere. The proposed algorithms are shown to be efficient by using MATLAB-based simulation.

• 한국통신학회논문지
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• 제35권12C호
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• pp.984-994
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• 2010

Pose variation is a critical problem in face recognition. Three-dimensional(3D) face recognition techniques have been proposed, as 3D data contains depth information that may allow problems of pose variation to be handled more effectively than with 2D face recognition methods. This paper proposes a pose-normalized 3D face modeling method that translates and rotates any pose angle to a frontal pose using a plane fitting method by Singular Value Decomposition(SVD). First, we reconstruct 3D face data with stereo vision method. Second, nose peak point is estimated by depth information and then the angle of pose is estimated by a facial plane fitting algorithm using four facial features. Next, using the estimated pose angle, the 3D face is translated and rotated to a frontal pose. To demonstrate the effectiveness of the proposed method, we designed 2D and 3D face recognition experiments. The experimental results show that the performance of the normalized 3D face recognition method is superior to that of an un-normalized 3D face recognition method for overcoming the problems of pose variation.

• 한국정밀공학회지
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• 제18권7호
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• pp.149-154
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• 2001

This study discusses a non-contact optical technique, electronic speckle pattern interferometry(ESPI), that is well suited for a deformation measurement of structure. Phase shifting method and unwrapping method have used to make deformation quantitative widely. In this paper, a previous numerical formula for phase shifting method is reconstructed in addition to least square fitting method to improve sensitivity and phase unwrapping based on vertical-horizontal scanning method is applied to analyze in-plane and out-of-plane deformation quantitatively.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권2호
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• pp.103-115
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• 2004

A computational algorithm is developed for fitting given data in the plane or in 3-space by implicitly defined quadrics. Implicity implies that the type of the quadric is part of the model and need not be known in advance. Starting with some estimate for the coefficients of the quadric the method will alternatively determine the shortest distances from the given points onto the quadric and adapt the coefficients such as to reduce the sum of those squared distances. Numerical examples are given.

• 한국광학회지
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• 제8권4호
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• pp.267-276
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• 1997

서로 대칭되는 이중 조명을 이용한 홀로그래피 네파간섭계를 구성하여 횡변위와 종변위를 동시에 측정하였다. 물체파와 재생파의 간섭을 일으킨 후 위상이동법으로 변위위상도를 작성하였으며 최소제곱법맞춤으로 위상도의 잡음을 제거하였다. 이러한 방법으로 네파간섭계의 두 광로에 존재하는 위성의 차와 합에 대한 정보를 구하였으며, 파장 632.8 nm인 헬륨-네온 레이저 광선에 대하여 종변위와 횡변위는 각각 정밀도 .lambda./40 및 .lambda./100 이내로 측정되었다.