Optimal ellipse fitting method based on least-square principle
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摘要: 基于最小二乘法研究了一种改进的椭圆拟合算法.最小二乘椭圆拟合算法,由于包含误差较大样本点在内的所有样本点都参与运算,所以会对椭圆拟合的最后结果产生偏差.针对这种情况,采用随机理论的思想,先随机选取6个点拟合椭圆,然后计算与此椭圆匹配的所有样本点个数.重复此过程一定次数,采用投票机制,匹配样本点多的椭圆即为最优椭圆,构造了一种快速准确剔除误差较大样本点的改进椭圆拟合算法,并在实际图像应用中验证了算法能够有效地处理包含有较大比例误差点的样本空间,拟合出具有高精度的椭圆,并且算法的速度能够满足实时性的要求.Abstract: The fragmental ellipse fitting algorithm based on least square was studied. The ellipse-constraint algebraic fitting always provides an elliptical solution, but the bias is inevitably added to result because the algorithm involves all the sample data including some much biased data. Based on this situation, the random theory was introduced. First, an ellipse was fitted by six points which were selected randomly. Then the number of points which match the ellipse was calculated. Repeating the process some times, according to the voting mechanism, the best ellipse is the ellipse whose matching point number is largest. A rapid algorithm with the ability to abandon the biased sample data was presented. The application of algorithm in a real-time image processing system demonstrates that this algorithm can efficiently fit an ellipse to experimental data including a significant percentage of gross errors and the rapidity of the algorithm can meet the requirement of real-time system.
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Key words:
- least square fitting /
- curve fitting /
- ellipse fitting
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[1] Gander W,Golub G H, Strebel R, et al. Least-squares fitting of circles and ellipses[J]. BIT Numerical Mathematics, 1994,34(4):558-578 [2] Rosin P L. Ellipse fitting by accumulating five-point fits[J]. Pattern Recognition Letters,1993,14(8):661-669 [3] 钮毅.部分遮挡条件下椭圆目标识别 .上海:上海交通大学自动化学院,2007 Niu Yi. Detection of partially occluded elipses . Shanghai: School of Electronic,Information and Electrical Engineering, Shanghai Jiaotong University,2007(in Chinese) [4] Forbes A B. Least-squares best fit geometric elements Algorithms for Approximation II.London: Chapman and Hall,1990:311-319 [5] 曹芳.计算机视觉中的各点异性回归技术 .上海:上海海事大学信息工程学院,2004 Cao Fang. The heteroscedastic regression technology in computer vision . Shanghai: Information Engineering College, Shanghai Maritime University,2004(in Chinese) [6] 周磊.椭圆拟合方法及其应用于土星光环的边缘 .广州:暨南大学计算机学院,2006 Zhou Lei. Application of ellipse fitting methods to the edge of Saturn’s ring . Guangzhou: College of Information Science and Technology,Ji’nan University,2006(in Chinese) [7] 陈凯.双核细胞显微图像的自动分割与识别 .武汉:华中科技大学计算机科学与技术学院,2004 Chen Kai. The automatics segmentation and recognition of microscope image of binuclear cell . Wuhan: Computer Science and Technology, Huazhong University of Science and Technology,2004(in Chinese) [8] Fischler M A,Bolles R C.Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography[J].Communications of the ACM,1981,24(6):381-395 -
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