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| Spatial arc fitting optimization method based on Lagrangian multiplier method |
| HUA Chun-jian1,2, XIONG Xue-mei1,2, CHEN Ying3 |
1. School of Mechanical Engineering, Jiangnan University, Wuxi 214122, China;
2. Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment & Technology, Wuxi 214122, China;
3. School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China |
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Abstract Aiming at the problems that the traditional spatial arc fitting method has poor robustness and low fitting accuracy, a robust spatial arc fitting optimization method is proposed. Firstly, on the basis of Lagrangian multiplier method, the objective function was established based on the constraint of the plane condition, and then the spatial arc fitting equation was derived. Secondly, the error tracking point was eliminated by using the RANSAC (random sample consensus) algorithm, which applied the high stability of RANSAC to the point cloud optimization of spatial arc fitting to improve the fitting accuracy. Finally, the feasibility of the proposed spatial arc fitting optimization method was verified by experimental analysis, and the fitting accuracy of the proposed method was analyzed through comparing with the traditional fitting method. The experimental results showed that the relative accuracy of ordinary arc point cloud fitting was about 0.003, and the relative accuracy of complex arc point cloud fitting was about 0.01. Compared with the traditional fitting method, the proposed method effectively solved the problems of low fitting accuracy and poor robustness. The research results indicate that the proposed spatial arc fitting optimization method can enhance robustness by using Lagrange multiplier method and improve fitting accuracy by using RANSAC algorithm to eliminate the error points, which has a wide range of practical engineering application.
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Received: 18 April 2018
Published: 28 December 2018
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基于拉格朗日乘子法的空间圆弧拟合优化方法
针对传统的空间圆弧拟合方法鲁棒性低、拟合精度不高等问题，提出了一种鲁棒性较强的空间圆弧拟合优化方法。首先，以拉格朗日乘子法为基础，基于平面条件约束建立目标函数，从而得出空间圆弧拟合方程；其次，采用RANSAC（random sample consensus，随机抽样一致）算法剔除错误跟踪点，将RANSAC算法的高稳定性应用到空间圆弧拟合的点云优化中，进而提高拟合精度。最后，通过实验分析验证了所提空间圆弧拟合优化方法的可行性，并与传统拟合方法进行比较，分析所提方法的拟合精度。实验结果表明：普通圆弧点云拟合的相对精度在0.003左右，复杂圆弧点云拟合的相对精度在0.01左右；相较于传统拟合方法，所提方法有效解决了拟合精度低及鲁棒性差等问题。研究结果表明提出的空间圆弧拟合优化方法一方面可运用拉格朗日乘子法增强鲁棒性，另一方面可通过采用RANSAC方法剔除错误点以提高拟合精度，具有广泛的工程实际应用价值。
关键词：
三维测量,
空间圆弧拟合,
拉格朗日乘子法,
RANSAN算法
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| [[1]] |
田艳荣.精密回转型工件的偏心倾斜调整测控技术[D].北京:北京理工大学光电学院,2016:1-30. TIAN Yan-rong. Measurement and control technology of eccentric tilt adjustment for precision rotary workpieces[D]. Beijing:Beijing Institute of Technology, School of Optics and Photonics, 2016:1-30.
|
|
|
| [[2]] |
赵阳.高显现力三目视觉测量关键技术[D].天津:天津大学精密仪器与光电子工程学院,2011:15-50. ZHAO Yang. Key technologies for high-visualization trinocular vision measurement[D].Tianjin:Tianjin University, College of Precision Instruments and Photoelectronics Engineering, 2011:15-50.
|
|
|
| [[3]] |
丁晓晖.圆柱轮廓精密测量中的滤波与调心调倾技术研究[D].哈尔滨:哈尔滨工业大学电气工程及自动化学院,2010:38-60. DING Xiao-hui. Research on filtering and centering tilting technology in precision measurement of cylindrical profile[D]. Harbin:Harbin Institute of Technology, School of Electrical Engineering and Automation, 2010:38-60.
|
|
|
| [[4]] |
杨伟,陈家新,李济顺.基于投影的二阶段空间圆线拟合算法[J].工程设计学报,2009,16(2):117-121. YANG Wei, CHEN Jia-xin, LI Ji-shun. Projection-based two-stage space circular line fitting algorithm[J]. Chinese Journal of Engineering Design, 2009, 16(2):117-121.
|
|
|
| [[5]] |
邹进贵,陈健.基于空间向量的空间圆拟合算法研究及其应用[J].测绘地理信息,2013,37(6):3-5. ZOU Jin-gui, CHEN Jian. Research and application of the arithmetic based on space vectorin 3D circle fitting[J]. Journal of Geomatics, 2013, 37(6):3-5.
|
|
|
| [[6]] |
张晶,黄琴,兰红军,等.工程测量中空间圆的拟合方法研究[J].计量与测试技术,2011,38(9):31-32. ZHANG Jing, HUANG Qin, LAN Hong-jun, et al. Fitting method of 3D circular object in engineering surveying[J]. Metrology and Measurement Technique, 2011, 38(9):31-32.
|
|
|
| [[7]] |
潘国荣,陈晓龙.空间圆形物体数据拟合新方法[J].大地测量与地球动力学,2008,28(2):92-94. PAN Guo-rong, CHEN Xiao-long. A new method for 3D circular object fitting[J]. Journal of Geodesy and Geodynamics, 2008, 28(2):92-94.
|
|
|
| [[8]] |
AHN Sung Joon, RAUH Wolfgang, WARNECKE Hans-Jürgen. Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola[J]. Pattern Recognition, 2001, 34(12):2283-2303.
|
|
|
| [[9]] |
田猛,王先培,董政呈,等.基于拉格朗日乘子法的虚假数据攻击策略[J].电力系统自动化,2017,41(11):26-32. TIAN Meng, WANG Xian-pei, DONG Zheng-cheng, et al. Fake data attack strategy based on Lagrangian multiplier method[J].Automation of Electric Power Systems, 2017, 41(11):26-32.
|
|
|
| [[10]] |
郭志军.拉格朗日乘子法在有约束条件的最优化问题研究[J].邢台学院学报,2013,28(4):170-171. GUO Zhi-jun. Study on the optimization problem of Lagrange multiplier method with constraints[J].Journal of Xingtai University, 2013, 28(4):170-171.
|
|
|
| [[11]] |
陈敬华.拉格朗日乘子法及其推广[J].湖北师范学院学报(自然科学版),2010,30(4):108-111. CHEN Jing-hua. Lagrange multiplier method and its extension[J].Journal of Hubei Normal University (Natural Science Edition), 2010, 30(4):108-111.
|
|
|
| [[12]] |
华东师范大学数学系.数学分析[M].北京:高等教育出版社,2010:70-80. Department of Mathematics, East China Normal University. Mathematical analysis[M]. Beijing:Higher Education Press, 2010:70-80.
|
|
|
| [[13]] |
曲天伟,安波,陈桂兰.改进的RANSAC算法在图像配准中的应用[J].计算机应用,2010,30(7):1849-1851. QU Tian-wei, AN Bo, CHEN Gui-lan. Application of improved RANSAC algorithm in image registration[J]. Journal of Computer Applications, 2010, 30(7):1849-1851.
|
|
|
| [[14]] |
许烨璋,王鑫森,郑德华,等.一种改进的RANSAC算法提取多模型圆弧特征点云[J].测绘工程,2015,24(1):28-32. XU Ye-zhang, WANG Xin-sen, ZHENG De-hua, et al. An improved RANSAC algorithm for extracting multi-model arc feature point cloud[J].Geographic Engineering, 2015, 24(1):28-32.
|
|
|
| [[15]] |
赵烨,蒋建国,洪日昌.基于RANSAC的SIFT匹配优化[J].光电工程,2014,41(8):58-65. ZHAO Ye, JIANG Jian-guo, HONG Ri-chang. SIFT matching optimization based on RANSAC[J].Opto-Electronic Engineering, 2014, 41(8):58-65.
|
|
|
| [[16]] |
甄艳,刘学军,王美珍.一种改进RANSAC的基础矩阵估计方法[J].测绘通报,2014(4):39-43. ZHEN Yan, LIU Xue-jun, WANG Mei-zhen. An improved RANSAC based fundamental matrix estimation method[J]. Bulletin of Surveying and Mapping, 2014(4):39-43.
|
|
|
| [[17]] |
李宝,程志全,党岗,等.一种基于RANSAC的点云特征线提取算法[J].计算机工程与科学,2013,35(2):147-153. LI Bao, CHENG Zhi-quan, DANG Gang, et al. An algorithm of point cloud feature extraction based on RANSAC[J]. Computer Engineering & Science, 2013, 35(2):147-153.
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