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本文中提出的基于机载激光点云的电力线自动提取和矢量化重建方法技术流程如图 1所示。该方法首先通过空间分割方法将输电线路点云划分为多个小尺度子空间网格,然后通过本文中提出的基于子空间网格点云密度的高程滤波算法完成电力线粗提取。接着采用基于倾斜角度平均值的滤波算法精提取电力线,最后通过统计滤波算法对电力线精提取结果去噪,得到电力线整体点云,提高电力线提取准确度。采用基于随机采样一致性(random sample consensus,RANSAC)算法的电力线分条提取算法对各档电力线进行电力线分离,并根据最小二乘法则拟合单条电力线的直线和抛物线模型,生成电力线矢量。
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传统高程阈值分割算法沿x轴方向[11]或者输电线路主方向[12]对输电线路进行空间分割,并不适用于地形起伏较大,线路走向呈折线状的输电线路,此外输电线路激光点云数据中可能存在点云密度不均匀的情况,影响电力线的提取精度。因此本文中提出了改进后的电力线提取算法,具体实现方法见下。
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根据输电线路地形起伏变化情况设置分割尺度dx,将线路原始点云空间S沿x轴方向等距分割为n个单元网格Si(i=1, 2, …, n),xmin和xmax表示原始点云的x坐标最值, ⌈⌉表示向上取整。
$ n = \left\lceil {\frac{{{x_{\max }} - {x_{\min }}}}{{{d_x}}}} \right\rceil $
(1) 根据线路地形实际情况设置分割尺度dy,将单元网格Si沿y轴方向等距分割为mi个子空间网格Si, j(i=1, 2, …, n; j=1, 2, …, mi),ymin和ymax表示单元网格Si中点云的y坐标最值。
$ {m_i} = \left\lceil {\frac{{{y_{\max }} - {y_{\min }}}}{{{d_y}}}} \right\rceil $
(2) 线路点云空间分割时网格分割尺度dx和dy取值范围一般从几米到几十米,通常情况下地形起伏变化越小分割尺度越大,地形起伏变化越大分割尺度越小。输电线路点云的子空间网格分割如图 2所示。
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子空间网格中可能有以下5种点集:地面点集;地面点和植被点集;地面点和电力线点集;地面点、植被点和电力线点集;电力线点集。根据电力线点在相同空间内相比于非电力线点通常具有高程较高和点云密度较小的特征,对子空间网格进行点云密度分析,然后通过高程滤波算法尽可能多地过滤非电力线点。
$ \begin{array}{l} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;f(z) = \\ \left\{ \begin{array}{l} {z_{\min }}, {z_{{\mathop{\rm mean}\nolimits} }} + a, (d > 0.6D)\\ {z_{\min }}, {z_{\min }} + b, (0.03D \le d \le 0.6D)\\ 0, (d < 0.03D) \end{array} \right. \end{array} $
(3) 式中,d表示每个子空间网格的点云平均密度,D表示输电线路总体点云的点云平均密度(输电线路总体点云个数/输电线路水平投影面积),a和b表示常数,zmin和zmean分别表示每个子空间网格点云高程的最小值和平均值,f(z)表示不同条件下子空间网格中需要被滤除的非电力线点的高程区间。
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电力线点在小范围内的高程变化具有远小于植被点和电塔点的特征,因此对于电力线粗提取结果中的植被点和电塔点,本文中采用基于点云间倾斜角度平均值的滤波算法[10]进行电力线精提取,算法原理如下:对点云中每个点给定半径r进行K维树(K-dimensional tree,KdTree)范围搜索,计算搜索区域其它点到搜索点的倾斜角度的平均值,倾斜角度平均值小于阈值的搜索点视为电力线点,否则视为非电力线点。点pi(xi, yi, zi)与点pj(xj, yj, zj)倾斜角度的计算公式为:
$ {\theta _{i, j}} = \arctan \left[ {\frac{{\left| {{z_j} - {z_i}} \right|}}{{\sqrt {{{\left( {{x_j} - {x_i}} \right)}^2} + {{\left( {{y_j} - {y_i}} \right)}^2}} }}} \right] $
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为了提高电力线点云提取精度,本文中采用统计滤波算法滤除上述提取结果中的噪声点。通过KdTree的最近邻搜索方法遍历点云获取其邻域,统计分析搜索点与邻域内各点的距离,计算平均距离和方差,假设结果呈高斯分布,那么与搜索点距离在标准区间外的点视为噪声点,从电力线精提取点云中删除,最终得到电力线整体点云。
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将提取的电力线整体点云按相邻两座电塔之间的电力线为一档进行电力线分档。根据两座电塔之间的电力线的水平投影呈直线且相互平行的特性,通过本文中提出的基于RANSAC的电力线分条提取算法拟合出投影点云中的直线,进而分离各条电力线。基于RANSAC的电力线分条提取算法思路如下:(1)从单档电力线的水平投影点云中随机抽取两个点确定直线,设置距离阈值,计算其它投影点到直线L1的距离,距离小于dth的点加入直线点集P1,并统计点集元素个数N1;(2)设置随机采样次数m,重复m-1次随机采样,得到直线L2,L3,…,Lm及对应的直线点集p2,p3,…,pm;(3)根据最小二乘法则求取最大直线点集的最佳拟合直线,将投影点还原为3维点云,并从单档电力线点云中删除该条电力线;(4)根据单条电力线高程呈连续性分布的特征,对提取的电力线点云进行高程排查,通过KdTree遍历搜索电力线点,剔除与周围点有高程突变的噪声点,以确保电力线点云提取的准确率;(5)重复步骤(1)~步骤(4),提取下一条电力线,直到所有电力线分离完成。
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理想情况下电力线在理论力学中的空间形态的数学模型为悬链线模型,根据已有研究结果发现抛物线方程可视作电力线悬链线模型的近似表达,且比悬链线模型有更高的模型重建效率和精度,更适合电力线重建[13]。因此将单条电力线的3维重建分为曲线拟合和直线拟合,直线拟合时首先将电力线点云投影到xy平面,然后根据最小二乘法则求取参量k, b,直线方程式如下:
$ y = kx + b $
(5) 曲线拟合时先求取电力线方向,然后将单条电力线投影到电力线方向和Z轴所构成的平面[13],最后根据拟合z值与点云实际z值的残差平方和Q最小求取抛物线模型的最佳参量a0,a1,a2。抛物线方程和最小二乘法则的残差平方和计算公式如下:
$ {z = {a_0}{x^2} + {a_1}x + {a_2}} $
(6) $ {Q = \sum\limits_{i = 1}^n {{{\left( {{a_0}x_i^2 + {a_1}{x_i} + {a_2} - {z_i}} \right)}^2}} = \min } $
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本文中以Microsoft Visual Studio 2013为程序开发平台,使用点云库(point cloud library,PCL)完成算法设计。为了验证电力线自动提取和重建算法的可行性,采用中国能源建设集团广东省电力设计院提供的两段输电线路机载激光点云数据进行实验测试,两段输电线路中植被众多,同档电力线水平投影相隔最短距离为0.38m,走廊内点云密度不均匀,部分地区存在点云密度比较稀疏的情况。数据1:线路总长度为2km,线路走向为直线段,地形起伏变化较大,点云总数为9325655,点云平均密度为68point/m2; 数据2:线路总长度为1.95km,线路走向为折线段,地形起伏变化较小,点云总数为7314818,点云平均密度为71point/m2。原始点云数据如图 3所示。
输电线路空间分割时根据地形起伏情况设置分割尺度,数据1中设置dx=dy=5,数据2中设置dx=25,dy=15。如果不对分割后的子空间网格进行点云密度分析,高程阈值区间都统一为(zmin, zmean+a),会因为子空间内点云密度大小不一,导致电力线粗提取结果中要么存在大量植被点和杆塔点,要么部分电力线点被过滤掉。此外某些子空间网格中可能只有电力线点,此时无论高程阈值区间怎么取值都会造成电力线点被过滤的结果,因此需要对子空间网格进行点云密度分析,以便提高电力线提取的效率和准确率。如图 4所示, 数据1中该处点云比较稀疏。
高程滤波时(3)式中高程阈值区间数据1设置a=b=5,数据2设置a=5,b=4。如图 5所示,两组数据的粗提取结果可靠,没有造成电力线缺失,对输电线路地形、走向和点云密度等因素鲁棒性较好,能滤除绝大多数地面点,大量植被点和电塔点,左侧为数据1的电力线粗提取部分结果,右侧为数据2的电力线粗提取部分结果。
两组点云数据在电力线精提取时KdTree的搜索半径设置为1.5m,角度阈值设置为9°,统计滤波时通过KdTree遍历点云搜索最邻近的50个点,剔除与搜索点距离在3倍标准差外的噪声点。两组点云数据的电力线整体点云提取结果准确完整,精度较高,噪声点少,部分结果如图 6所示。
对电力线整体点云按照相邻两座电塔为一档进行分档处理后,随机选取第2档电力线作为后续电力线分条提取和电力线拟合重建的实验数据。根据本文中提出的基于RANSAC直线拟合的电力线分条提取算法分离各条电力线,RANSAC直线拟合时采样次数为40,距离阈值设置为0.38m,高程排查搜索半径为1.5m,高程差阈值为1m。电力线分条提取精度详见表 1,该档内8条电力线总的提取精度达到99.342%,单条电力线的最低提取精度为98.90%。
Table 1. Extraction accuracy of power line
power
lineoriginal
numberextraction
numberextraction
accuracy/%1 788 784 99.49 2 783 778 99.36 3 787 779 99.48 4 767 763 99.47 5 700 698 99.71 6 675 668 98.96 7 574 570 99.30 8 546 540 98.90 第2档电力线分条提取后,将各条电力线依次投影到xy平面、电力线方向和z轴构成的平面上,根据最小二乘法则计算直线拟合方程和抛物线最佳拟合曲线方程,最后在[xmin,xmax]上每隔0.3m根据直线方程和抛物线方程生成对应的y值和z值,得到电力线3维矢量节点,近似表达电力线矢量。电力线重建结果精度评定采用原始电力线LiDAR点云与3维重建模型的最佳拟合点的欧氏距离的最大值dmax、平均值dmean和最小值dmin 3项指标为评价标准,其中距离平均值为最重要的精度评价指标。该档电力线3维重建精度统计结果如表 2所示,模型拟合的距离平均值最大误差为0.042m。
Table 2. Accuracy evaluation of 3-D reconstruction of power lines
power line dmean/m dmax/m dmin/m 1 0.036 0.134 0.001 2 0.039 0.123 0.002 3 0.041 0.229 0.001 4 0.041 0.129 0.001 5 0.042 0.150 0.003 6 0.040 0.170 0.001 7 0.039 0.113 0.001 8 0.039 0.115 0.001
基于机载激光点云的电力线自动提取方法
Power line automatic extraction method based on airborne laser point cloud
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摘要: 为了解决地形、走向复杂、点云密度不均匀的输电线路的电力线提取精度低的问题, 提出了一种高效的电力线自动提取和重建方法。首先通过空间分割和点云密度分析方法改进高程滤波算法实现电力线粗提取; 采用基于点云间倾斜角度平均值的滤波算法精提取电力线; 使用统计滤波算法完成电力线整体点云提取; 通过基于随机采样一致性算法的电力线分条提取算法分离电力线, 最后采用直线和抛物线结合的模型完成电力线重建。结果表明, 该方法电力线总的提取精度为99.342%, 单条电力线重建精度最低为0.042m, 对地形、线路走向和点云密度等因素具有较好的鲁棒性。该研究为复杂场景下大规模输电线路的电力线提取和3维重建提供了参考。Abstract: In order to solve the problem of low accuracy of power line extraction of transmission lines with complex terrain and trending, and uneven point cloud density, an efficient method for automatic extraction and reconstruction of power lines was proposed. Firstly, through the space segmentation and point cloud density analysis method, the improved elevation filtering algorithm was used to achieve the rough extraction of power lines; the filtering algorithm based on the average value of the inclination angle between the point clouds was used to extract the power lines precisely; the statistical filtering algorithm was used to complete the extraction of the whole point cloud of the power lines. Then the power lines were separated by the random sample consensus(RANSAC)-based power line striping extraction algorithm, and finally the power line reconstruction was completed by using a model combining straight lines and paraboloids. The results show that the total power line extraction accuracy of this method is 99.342%, and the minimum reconstruction accuracy of a single power line is 0.042m, which is robust to terrain, line direction, point cloud density and other factors. This research provides a reference for power line extraction and 3-D reconstruction of large-scale transmission lines in complex scenarios.
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Key words:
- laser technique /
- power line automatic extraction /
- point cloud density /
- reconstruction /
- filtering /
- RANSAC
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Table 1. Extraction accuracy of power line
power
lineoriginal
numberextraction
numberextraction
accuracy/%1 788 784 99.49 2 783 778 99.36 3 787 779 99.48 4 767 763 99.47 5 700 698 99.71 6 675 668 98.96 7 574 570 99.30 8 546 540 98.90 Table 2. Accuracy evaluation of 3-D reconstruction of power lines
power line dmean/m dmax/m dmin/m 1 0.036 0.134 0.001 2 0.039 0.123 0.002 3 0.041 0.229 0.001 4 0.041 0.129 0.001 5 0.042 0.150 0.003 6 0.040 0.170 0.001 7 0.039 0.113 0.001 8 0.039 0.115 0.001 -
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