稳健的回光反射平面靶心定位算法

doi:10.12082/dqxxkx.2018.170486

摘要/Abstract

摘要：

针对因回光反射平面标靶点云数据缺失或冗余而难以准确计算靶心坐标的问题,本文提出一种基于距离标靶重心最远点的边缘点提取和靶心定位算法。首先,进行点云数据预处理,先人工大概选取出标靶点云所在位置,并根据回光反射强度信息提取出标靶点云,对标靶点云进行粗差剔除、投影以及坐标旋转等工作;然后,进行边缘点提取,应用所提的边缘点提取算法对投影到二维平面的标靶点云进行边缘点提取;最后,进行靶心定位,先应用抗差最小二乘对边缘点进行拟合计算圆心坐标,然后将其旋转回三维空间作为靶心坐标计算值。实验结果表明,本文提出的边缘点提取算法能高效、准确地提取出标靶边缘点,比文献[12]中的边缘点提取算法节约了大量时间,并且应用所提取出的边缘点能稳健地计算出靶心坐标,与基准值的偏差在亚毫米以内,优于文献[11]、[12]算法靶心计算精度,有效地解决了残缺或冗余的回光反射平面标靶点云靶心定位问题。

关键词: 回光反射, 平面标靶, 边缘点提取, 抗差最小二乘, 平面拟合

Abstract:

To solve the problem of calculating the center of retro-reflective planar target when the point clouds are deficient or redundant, an algorithm of extracting edge points and calculating target center is proposed. The algorithm includes three steps: (1) point clouds preprocessing; (2) edge points extracting; (3) target center calculating. In step (1), the rough region of the target points is artificially segregated from the points scanned by the laser scanner first. Then, the target points are accurately extracted from the rough region according to the intensity of return light. The noise points are removed from the target points to get the high-quality target point clouds. Finally, the high-quality target point clouds are projected into a plane, called the best fitting plane, and then the plane is rotated to be parallel with the XOY coordinate plane. In step (2), the barycenter of the target point clouds is calculated, and then all the points are translated to a new coordinate plane with the barycenter as its origin. The new coordinate plane is divided into several fan-shaped regions. The point is regarded as the edge one only when it is farthest away from the origin in one region. In step (3), the equation of the target circle is calculated by fitting the edge points, using the robust least square method. The fitting circle center is rotated back to 3D space used for target point cloud. The resulted circle center in 3D space is regarded as the estimated value of the planar target center. In order to test the effectiveness of the proposed algorithm, three tests were conducted. Firstly, the target center of high-quality target point clouds was separately calculated by the proposed algorithm and centroid method, and the accuracy of target center locations was compared. Secondly, the edge points were extracted by the proposed algorithm and the method in Ref. [12], and the time efficiency of the algorithms was compared. Thirdly, the center of low-quality target point clouds is calculated by the proposed algorithm, and methods introduced in Ref. [11] and Ref. [12], and the bias and location accuracy from these methods were compared. The experimental results show that the proposed algorithm of extracting the edge points can get good results in shorter computing time than that by Ref. [12] method. And the proposed algorithm can quickly and accurately calculate the target center, and the location accuracy is better than 1mm, better than that of Ref. [11] and Ref. [12] method. The proposed method is effective and practical.

Key words: retro-reflective, planar target, edge points extracting, robust least square, plane fitting

付永健, 李宗春, 何华. 稳健的回光反射平面靶心定位算法[J]. 地球信息科学学报, 2018, 20(4): 422-429.DOI:10.12082/dqxxkx.2018.170486

FU Yongjian,LI Zongchun,HE Hua. A Robust Algorithm of Retro-reflective Planar Target Center Positioning[J]. Journal of Geo-information Science, 2018, 20(4): 422-429.DOI:10.12082/dqxxkx.2018.170486

图/表 8

图1

图2

图3

表1

本文算法和重心法靶心坐标计算值及二者差值（mm）"

标靶编号	重心法			本文算法				二者差值
标靶编号	X		Y	Z	X	Y	Z	$ΔX$	$ΔY$	$ΔZ$	$ΔP$
001	-4244.6	3085.7	1168.4	-4244.7	3085.5	1168.4		0.1	0.2	0.0	0.2
002	4494.3	3158.2	43.5	4494.0	3158.3	43.3		0.3	-0.1	0.2	0.4
003	-1946.4	-2553.4	446.0	-1946.4	-2553.4	446.1		0.0	0.0	-0.1	0.1
004	1739.8	2065.4	-43.5	1739.8	2065.4	-43.5		0.0	0.0	0.0	0.0
005	-6837.4	3749.9	-1167.3	-6837.2	3749.5	-1167.9		-0.2	0.4	0.6	0.7
006	-7441.6	4170.1	-155.3	-7441.3	4170.0	-155.9		-0.3	0.1	0.6	0.7
007	-5278.4	-1372.8	101.0	-5278.4	-1372.9	100.8		0.0	0.1	0.2	0.2
008	424.7	4048.6	215.7	425.0	4048.4	215.4		-0.3	0.2	0.3	0.5

表1

图4

表2

本文算法和文献[12]算法靶心定位偏差（mm）"

标靶编号	本文算法靶心定位偏差					文献[12]算法靶心定位偏差
标靶编号	$ΔX$		$ΔY$	$ΔZ$	$ΔP$	$ΔX$	$ΔY$	$ΔZ$	$ΔP$
004_1	0.1	-0.1	-0.4	0.4		-1.9	-0.2	0.2	1.9
004_2	0.0	0.0	-0.2	0.2		0.4	-0.6	0.5	0.9
004_3	0.0	0.0	-0.1	0.1		-0.8	-0.5	-0.1	0.9
004_4	0.0	0.0	-0.2	0.2		-0.6	-0.5	-0.2	0.8
004_5	0.1	0.0	-0.1	0.1		-2.9	-6.6	2.3	7.5
004_6	0.1	-0.1	-0.2	0.2		-6.3	-7.7	2.5	10.1

表2

表3

本文算法和文献[11]算法定位精度对比（mm）"

标靶编号	本文算法					文献[11]算法
标靶编号	$ΔX$		$ΔY$	$ΔZ$	$ΔP$	$ΔX$	$ΔY$	$ΔZ$	$ΔP$
004_1	0.1	-0.1	-0.4	0.4		-1.9	-1.4	-0.7	2.5
004_2	0.0	0.0	-0.2	0.2		0.7	0.5	2.0	2.2
004_3	0.0	0.0	-0.1	0.1		-0.8	0.6	-0.4	1.1
004_4	0.0	0.0	-0.2	0.2		0.2	-0.2	0.4	0.5
004_5	0.1	0.0	-0.1	0.1		0.0	0.0	-2.2	2.2
004_6	0.1	-0.1	-0.2	0.2		-0.8	0.6	2.7	2.9

表3

表4

参考文献 2

[2]	[ Wang J M, Yao J L, Jia X Y, et al.An overall assessment method for the target positioning accuracy of multi-station scanning[J]. Science of Surveying and Mapping, 2017,42(8):102-106. ] doi: 10.16251/j.cnki.1009-2307.2017.08.019
[3]	陈俊杰,闫伟涛.基于激光点云的平面标靶中心坐标提取方法研究[J].工程勘察,2011(8):53-57.
	[Chen J J, Yan W T.Research on algorithm for extraction of target center coordinates based on the point clouds[J]. Geotechnical Investigation & Surveying, 2011(8):53-57. ]
[4]	官云兰,程效军,陈晓勇,等.地面Lidar平面标靶稳健定位[J].激光杂志,2015,36(1):13-16.
	[ Guan Y L, Cheng X J, Chen X Y, et al.Robust location for planner target of terrestrial lidar[J]. Laser Journal, 2015,36(1):13-16. ]
[5]	苏晓蓓,郝刚.地面三维激光扫描标靶中心识别算法研究[J].城市勘测,2010(3):68-70. doi: 10.3969/j.issn.1672-8262.2010.03.020
	[ Su X B, Hao G.Research of the target center identifying method about 3D laser scanning[J]. Urban Geotechnical Investigation and Surveying, 2010(3):68-70. ] doi: 10.3969/j.issn.1672-8262.2010.03.020
[6]	Lichit D D, Stewart M P, Ssakiri M.Benchmark tests on a three-dimensional laser scanning system[J]. Geomertrics′Research Australasia, 2000,72:1-23.
[1]	王玉鹏,卢小平,葛晓天.地面三维激光扫描点位精度评定[J].测绘通报,2011(4):10-13.
	[ Wang Y P, Lu X P, Ge X T.Point precision assessment for terrestrial 3D laser scanning[J]. Bulletin of Surveying and Mapping, 2011(4):10-13. ]
[7]	王乐洋,陈汉清,林永达,等.利用稳健WTLS方法进行三维激光扫描标靶球定位[J].大地测量与地球动力学,2016,36(8):745-750.
	[ Wang L Y, Chen H Q, Lin Y D, et al.Spherical target positioning of 3D laser scanning by using robust WTLS method[J]. Journal of Geodesy and Geodynamics, 2016,36(8):745-750. ]
[8]	权力奥,杨荣华,潘蕾西兰,等.基于球体几何关系的球标靶特征提取算法[J].大地测量与地球动力学,2017,37(8):860-863. doi: 10.14075/j.jgg.2017.08.018
	[ Quan L A, Yang R H, Pan X L X, et al. Feature extraction algorithm of spherical target based on sphere geometrical relationship[J]. Journal of Geodesy and Geodynamics, 2017,37(8):860-863. ] doi: 10.14075/j.jgg.2017.08.018
[9]	薛晓璐,林欢.基于RANSAC的残缺平面标靶稳健定位方法[J].测绘工程,2016,25(4):51-54.
	[ Xue X L, Lin H.A robust location method of incomplete planar target based on RANSAC[J]. Engineering of Survey and Mapping, 2016,25(4):51-54. ]
[10]	陈西江,花向红,杨荣华,等.分带K–均值聚类的平面标靶定位[J].武汉大学学报·信息科学版,2013,38(2):167-170.
	[ Chen J X, Hua X H, Yang R H, et al.Planar target location based on the zoning K-means clustering[J]. Geomatics and Information Science of Wuhan University, 2013,38(2):167-170. ]
[11]	王力,李广云,张洪新.基于回光强度的平面标靶自动识别方法[J].红外与激光工程,2011,40(10):1910-1914.
	[ Wang L, Li G Y, Zhang H X.Auto recognition method of planar target based on return light intensity[J]. Infrared and Laser Engineering, 2011,40(10):1910-1914. ]
[12]	朱宁宁,卢小平,李向阳.一种平面靶心的提取算法[J].大地测量与地球动力学,2014,34(3):173-178.
	[ Zhu N N,LU X P, Li X Y.A new algorithm extracting planar target center[J]. Journal of Geodesy and Geodynamics, 2014,34(3):173-178. ]
[13]	吴超,袁永博,张明媛.基于反射强度和K-means聚类的平面标靶定位研究[J].激光技术,2015,39(3):341-344. doi: 10.7510/jgjs.issn.1001-3806.2015.03.013
	[ Wu C, Yuan Y B, Zhang M Y.Plane target positioning based on reflection intensity and K-means clustering method[J]. Laser Technology, 2015,39(3):341-344. ] doi: 10.7510/jgjs.issn.1001-3806.2015.03.013
[14]	孙鹏,闫阳阳,牛路标,等.地面激光扫描仪自制平面标靶中心识别算法研究[J].河南城建学院学报,2014,23(2):54-57. doi: 10.3969/j.issn.1674-7046.2014.02.012
	[ Sun P, Yan Y Y, Niu L B, et al.Research of recognition algorithm for target center home-made plane by ground laser scanner[J]. Journal of Henan University of Urban Construction, 2014,23(2):54-57. ] doi: 10.3969/j.issn.1674-7046.2014.02.012
[15]	王力. 车载三维激光扫描系统集成与QA/QC技术研究[D].郑州:解放军信息工程大学,2014.
	[ Wang L.Study on the key technology of system integration and QA/QC on mobile laser scanning[D]. Zhengzhou: PLA Information Engineering University, 2014. ]
[16]	隋立芬,宋力杰,柴洪洲.误差理论与测量平差基础[M].北京:测绘出版社,2010.
	[ Sui L F, Song L J, Chai H Z.Error theory and foundation of surveying adjustment[M]. Beijing: Surveying and Mapping Publishing House, 2010. ]
[17]	王峰,丘广新,程效军.改进的鲁棒迭代最小二乘平面拟合算法[J].同济大学学报(自然科学版),2011,39(9):1350-1355. doi: 10.3969/j.issn.0253-374x.2011.09.018
	[ Wang F, Qiu G X, Cheng X J.An improved robust method for iterating least-squares plane fitting[J]. Journal of Tongji University(natural science), 2011,39(9):1350-1355. ] doi: 10.3969/j.issn.0253-374x.2011.09.018
[18]	王果. 不同平台激光点云数据面状信息自动提取研究[D].北京:中国矿业大学,2014.
	[ Wang G.Research on automated planar information extraction from 3D lidar point cloud of different platforms[D]. Beijing: China University of Mining and Technology, 2014. ]
[19]	官叶沆,周西振,刘传瑞.一段圆弧上多点坐标拟合圆心位置的可靠性分析[J].勘察科学技术,2012(4):54-57. doi: 10.3969/j.issn.1001-3946.2012.04.013
	[ Guan Y H, Zhou X Z, Liu C R.Reliability analysis of multiple points coordinates on an arc to fitting circle center position[J]. Site Investigation Science and Technology, 2012(4):54-57. ] doi: 10.3969/j.issn.1001-3946.2012.04.013
[20]	刘珂,周富强,张广军.半径约束最小二乘圆拟合方法及其误差分析[J].光电子·激光,2006,7(5):604-607.
	[ Liu K, Zhou F Q, Zhang G J.Radius constraint least-square circle fitting method and error analysis[J]. Journal of Optoelectronics Laser, 2006,7(5):604-607. ]
[21]	杨元喜. 抗差估计理论及其应用[M].北京:八一出版社,1993.
	[ Yang Y X.Robust estimation theory and its application[M]. Beijing: Bayi Publishing House, 1993. ]
[2]	王江妹,姚吉利,贾象阳,等.一种多站扫描中标靶定位精度的整体评估方法[J].测绘科学,2017,42(8):102-106. doi: 10.16251/j.cnki.1009-2307.2017.08.019

	标靶编号
	001	002	003	004	005	006	007	008
点数/个	29 987	23 387	20 120	60 609	21 306	20 045	30 142	30 846
本文算法耗时/s	3.8	1.1	1.8	2.2	0.8	0.8	1.1	1.1
文献[12]算法耗时/s	165.5	119.9	95.5	228.5	119.9	99.7	202.2	200.9