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文中使用两种机载雷达数据集来评估该方法的性能,分别是国际摄影测量和遥感学会(ISPRS)第三委员会/WG3提供的低密度基准数据集和一组高密度的实例数据集。
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该方法需要设置的五个参数: 用于选择初始种子点的移动窗口大小(ws),用于区域增长的法向量之间夹角的角度阈值(θth)和残余阈值(rth),以及用于判断地面点和非地面点的DTM初始分辨率(h)和初始高差阈值(dth)。对这些参数进行反复实验直到滤波结果的总误差最小。优化后的参数值和滤波精度如表1所示。
Sample Optimized parameters Accuracy measures ws/m θth/rad rth/m h/m dth/m T.I T.II T.E. κ 11 16 0.1 0.3 3 0.7 9.02% 10.69% 9.73% 80.15% 12 16 0.1 0.25 2 0.3 2.01% 3.08% 2.53% 94.93% 21 16 0.1 0.1 2 0.2 0.33% 3.13% 0.95% 97.23% 22 28 0.1 0.1 2 0.4 1.47% 8.16% 3.55% 91.61% 23 20 0.1 0.2 3 0.35 3.05% 5.74% 4.32% 91.33% 24 25 0.1 0.1 2 0.35 3.24% 8.65% 4.73% 88.38% 31 23 0.1 0.2 4 0.1 0.44% 1.20% 0.79% 98.40% 41 26 0.1 0.2 3 0.4 2.32% 2.58% 2.45% 95.11% 42 30 0.1 0.05 3 0.35 0.80% 0.77% 0.78% 98.13% 51 15 0.1 0.1 4 0.3 1.11% 4.11% 1.73% 94.92% 52 19 0.1 0.1 6 0.41 1.11% 17.10% 2.79% 84.63% 53 6 0.25 0.4 3 0.33 1.20% 37.87% 2.68% 63.79% 54 16 0.1 0.25 2 0.4 1.31% 3.36% 2.41% 95.17% 61 6 0.3 0.2 2 0.7 0.77% 7.05% 0.98% 86.19% 71 21 0.1 0.05 3 0.6 0.73% 6.33% 1.36% 93.20% Average 1.93% 7.99% 2.79% 90.21% Median 1.20% 5.74% 2.45% 93.20% STD 2.15% 9.27% 2.28% 9.00% Table 1. Optimized parameters and filtering accuracy of the proposed method on the 15 samples
由表1可见,除samp42外,其余样本的I类误差均小于II类误差;平均而言,I类误差大约是II类误差的1/4。这一结果可能是由以下两个原因造成的:(1)由于样本中地面点的数量远大于非地面点的数量,故少数分类错误的非地面点便会导致较大的II类误差;(2)由于文中方法采用了地面点加密策略,当高差阈值较大时,在增加地面点数量的同时也会添加更多的非地面点。
将文中方法与近五年(2015~2019)新提出的15种滤波方法[14]的总误差进行比较,结果如图5所示。文中方法在15个样本中有11个样本的滤波性能优于目前最先进的滤波方法,而在samp11、samp24、samp41和samp52这四个样本中,新方法精度与最佳滤波方法基本一致。文中方法平均总误差为2.79%,与经典滤波算法相比精度至少提高了20.5%,该结果证明了文中方法具有较好的滤波性能。
文中方法在samp11、smp21、samp51和samp52的参考DEM、滤波后DEM和误差分布如图6所示。这四组数据分别对应四种不同的地形环境。其中samp11为陡坡地形且混有大量的植被和建筑物,samp21中有一窄桥,samp51的陡坡上包括有大量的低矮植被,samp52为不连续断裂地形。在这四种地形中,现有的各类滤波算法都很难取得满意的滤波结果。相较而言,新算法的滤波结果较好,滤波后的DEM与参考DEM有很高的相似度。该算法几乎完全滤除了samp21中的桥梁部分,可精确滤除samp51斜坡上全部的低矮植被,能完美保持samp52断裂地形上的断裂线。然而,新方法也包含一些分类错误的非地面点(如图6中的红框标记部分),但这些点很容易通过人工编辑的方式剔除。
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ISPRS数据集的平均点间距为1~3.5 m,远低于现今设备所采集到的点云密度。因此,文中通过三组不同地形(s1,s2和s3)的高密度实例数据对该算法进一步验证,分别为覆盖低矮植被的崎岖山地(s1,图7(a))、覆盖不同高度植被的断裂地形(s2,图7(b))和包含植被和建筑物的斜坡地形(s3,图7(c))。各个区域面积约为23公顷(1公顷=104 m2),平均点间距约为0.5 m。每组参考数据均先通过滤波软件进行初始滤波,然后对滤波结果进行人工检查和编辑,以保证参考数据的质量。
除了文中方法外,还将多分辨率层次滤波(MHC)[6]、布料模拟滤波(CSF)[15]、渐进加密三角网滤波(PTD)[16]和渐进形态学滤波(PMF)[17]应用于实例数据滤波,并与文中方法结果比较。如表2所示,在三种地形中,文中方法的性能均优于其他方法。就平均总误差而言,文中方法较精度最低的CSF算法提高75%,较精度最高的MHC算法提高40%。
Method CSF PTD PMF MHC Proposed Accuracy measure Total Kappa Total Kappa Total Kappa Total Kappa Total Kappa s1 10.38% 67.67% 7.44% 75.49% 7.43% 74.41% 7.44% 76.29% 3.91% 92.15% s2 14.21% 65.09% 7.30% 82.87% 8.03% 81.04% 5.06% 88.20% 2.95% 93.19% s3 15.95% 68.25% 5.40% 89.20% 3.85% 92.31% 4.19% 91.61% 3.19% 93.61% Average 13.51% 69.21% 6.71% 83.07% 6.44% 85.79% 5.56% 84.77% 3.55% 92.62% Table 2. Filtering accuracy of the proposed method against the 4 filtering algorithms
五种滤波方法对s2数据滤波后生成的DEM如图8所示。其中MHC算法得到的DEM最平滑,但同时也损失了一些地形细节。PMF算法滤除了过多的地面点,导致DEM产生过大畸变。PTD和CSF算法II类误差过大,导致DEM表面过于粗糙。相比之下,文中算法滤波后生成的DEM与参考DEM相似度最高。
Interpolation-based filtering with segmentation for airborne LiDAR point clouds
doi: 10.3788/IRLA20200369
- Received Date: 2020-12-20
- Rev Recd Date: 2021-02-25
- Publish Date: 2021-09-23
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Key words:
- airborne LiDAR point clouds /
- filtering /
- interpolation /
- multi-scale /
- segmentation
Abstract: The classical airborne LiDAR filtering algorithms show good results on most landscapes, but they suffer from low-level adaptability on steep slopes. Thus, to improve the filtering performance under different environments, a surface interpolation-based filtering algorithm with segmentation was proposed. Firstly, the original point clouds were grouped into a set of segments and one set of scattered points by an improved region growing method. Then, the segments and the scattered points were classified simultaneously using a weighted least square algorithm. The benchmark dataset provided by International Society for Photogrammetry and Remote Sensing(ISPRS) was used to validate the performance of the proposed method. Results illustrate that the proposed method outperforms the state-of-the-art filtering methods on 11 out of 15 samples, showing its strong adaptability to different terrain environments. Moreover, the proposed method has the lowest average total error. Filtering three samples of high-density with different terrain features also demonstrates the promising performance of the proposed method.