摘要
机载激光雷达(Light Detection and Ranging,LiDAR)可快速、高效的获取大范围地形信息,已成为高精度地形建模的重要数据获取手段。然而,针对复杂地形的机载LiDAR点云构建数字高程模型(Digital Elevation Model,DEM)的插值误差研究缺乏,严重限制了其在土壤侵蚀、开采沉陷等地表过程研究中的应用。该研究基于黄土高塬沟壑区典型地形的机载LiDAR数据,对比了反距离加权(Inverse Distance Weighted,IDW)、克里金(Kriging)、样条函数(Spline)、自然邻域(Natural Neighbor,NN)、趋势面(Trend)、不规则三角网(Triangulated Irregular Network,TIN)等插值算法的插值误差。首先优选了IDW、Kriging、Spline、Trend等4种算法的关键参数,其次分析了不同点云密度和地形下IDW、Kriging、Spline、NN、TIN等5种算法的插值误差及其空间分布。结果表明:1)IDW最优插值参数为权指数1和搜索点数12,Kriging为无方向、高斯函数和搜索点数12,Spline为规则样条函数和搜索点数32,Trend误差达米级,不适用于地形复杂区域。2)当点云密度较小时(1~19点/m^(2)),IDW、Kriging、NN、TIN4种插值方法较为准确地描述地形。当点云密度较大时(39~77点/m^(2)),各个插值方法的DEM空间分布差异不大。3)针对黄土高塬沟壑区复杂地形区域,点云密度越大,DEM的误差越小。陡坡区域DEM的平均绝对误差明显高于缓坡区域,随着点云密度增大,陡坡区域误差明显减小,而缓坡区域变化较小。当点云密度较小时(1~19点/m^(2)),缓坡和陡坡最优插值插值方法分别为NN和TIN;当点云密度较大时(39~77点/m^(2)),缓坡和陡坡最优插值方法均为Spline。研究结果可为机载LiDAR用于地形复杂区域的高精度地形建模与地表过程研究提供依据。
Airborne Light Detection and Ranging(LiDAR)technology has widely been used to efficiently acquire terrain data over large areas,particularly providing data sources for the generation of high-resolution Digital Elevation Models(DEMs).However,little was known about the errors in the interpolation of airborne LiDAR point clouds for topographically complex areas,thereby resulting in the less application of airborne LiDAR in the earth surface process.In this study,the errors of six commonly-used DEM interpolations were assessed using the airborne LiDAR point clouds acquired from a topographically complex area in the gullied Loess Plateau,China.Six DEM interpolations included the Inverse Distance Weighted(IDW),Kriging,Spline,Natural Neighbor(NN),Triangulated Irregular Network(TIN),and Trend.Firstly,four parameters were optimized,including IDW,Kriging,Spline,and Trend.Secondly,the optimized algorithms were applied to produce DEMs.Lastly,the errors of DEMs were quantitatively evaluated using mean absolute error(MAE),root mean square error(RMSE),and coefficient of determination(R2).Results showed that:1)The optimal values of IDW weights and searching points were 1 and 12,respectively.The optimal parameters for Kriging included non-orientation,Gauss function,and 12 searching points.Spline performed best in regular spline functions and 32 of searching points.Nevertheless,Trend was unsuitable for the topographically complex area,due to the produced DEMs with meter-level errors.2)In terms of quality,IDW,Kriging,NN,and TIN produced relatively sound DEMs at the 1%-25%subsampling rate(1-19 points/m^(2)),whereas,unreasonable outliers were found in the DEMs produced by Spline.Additionally,there were similar spatial patterns in the DEMs produced by IDW,Kriging,NN,TIN,and Spline,when the subsampling rate was 50%-100%(39-77 points/m^(2)).3)Excellent relations(R2>0.99)were found between the elevation measurements and the DEMs produced using point clouds of different subsampling rates.The average MAE and RMSE of produced DEMs firstly decreased rapidly,and then stabilized,as the point density increased,demonstrating that the reduction of interpolation errors varied slowly,as the point density reached a certain level.TIN produced the lowest error at a 1%subsampling rate(1 points/m^(2)),with the MAE and RMSE of 0.208 and 0.298 m,respectively.At the 5%-12.5%subsampling rate(4-10 points/m^(2)),NN produced the lowest error,where the MAE and RMSE were 0.170-0.175 m and 0.259-0.262 m,respectively.At the>25%-100%subsampling rate(>19-77 points/m^(2)),Spline yielded the lowest error with the MAE and RMSE of 0.164-0.168 and 0.249-0.255 m,respectively.More importantly,the interpolation errors for steep areas were considerably higher than those for gently-sloping areas.The errors for steep areas decreased markedly,while those for gently-sloping areas changed slightly,as the point density increased.NN and TIN were the most suitable interpolation for gently-and steep-sloping areas at the point density of 1-19 points/m^(2),with the MAE of 0.049-0.171 and 0.062-0.776 m,respectively.Spline yielded the lowest interpolation errors for both steep-and gently-sloping areas with the MAE of 0.010-0.123 and 0.051-0.593 m,respectively when the point density was between 39-77 points/m^(2).The findings can provide promising potential support to the earth surface process,thereby generating high-resolution DEMs for the topographically complex areas.
作者
李朋飞
张晓晨
严露
胡晋飞
李豆
丹杨
Li Pengfei;Zhang Xiaochen;Yan Lu;Hu Jinfei;Li Dou;Dan Yang(College of Geomatics,Xi’an University of Science and Technology,Xi’an 710054,China)
出处
《农业工程学报》
EI
CAS
CSCD
北大核心
2021年第15期146-153,共8页
Transactions of the Chinese Society of Agricultural Engineering
基金
国家自然科学基金(41807063,41977059)。
关键词
激光雷达
DEM
插值算法
复杂地形
黄土高原
LiDAR
DEM
interpolation algorithms
complex topography
Loess Plateau
