A Multiscale Filtering Method for Airborne LiDAR Data Using Modified 3D Alpha Shape
"> Figure 1
<p>Workflow of the proposed method for filtering airborne LiDAR data.</p> "> Figure 2
<p>Illustration of 3D alpha shape: (<b>a</b>) the original point cloud of a rabbit; (<b>b</b>) the convex hull of the original point cloud; (<b>c</b>,<b>d</b>) the alpha shapes of the original point cloud; the <math display="inline"><semantics> <mi>α</mi> </semantics></math> used in (<b>c</b>) is 0.05 m, and the <math display="inline"><semantics> <mi>α</mi> </semantics></math> used in (<b>d</b>) is 0.01 m.</p> "> Figure 3
<p>Comparison between 3D alpha shape and the modified 3D alpha shape: (<b>a</b>) the original point cloud (red for nonground points and bule for ground points); (<b>b</b>) result of the 3D alpha shape; (<b>c</b>) result of the modified 3D alpha shape. The green translucent surfaces in (<b>b</b>,<b>c</b>) are the resulting shapes.</p> "> Figure 4
<p>Overview of the modified 3D alpha shape algorithm.</p> "> Figure 5
<p>The extraction of point cloud layers. (<b>a</b>) the top layer extracted using a sufficiently large <math display="inline"><semantics> <mi>α</mi> </semantics></math> (radius of the ball); (<b>b</b>–<b>d</b>) the lower layers extracted using gradually decreasing <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p> "> Figure 6
<p>Procedure for multiscale TIN densification. (<b>a</b>) the top layer that provides seed points; (<b>b</b>–<b>d</b>) extraction of ground points in the lower layers of the data pyramid; (<b>e</b>) extraction of final ground points.</p> "> Figure 7
<p>Illustration of distance threshold determination. (<b>a</b>) <span class="html-italic">d</span> is the distance between the point <span class="html-italic">P</span> and its nearest TIN facet; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>D</mi> <mi>T</mi> </mrow> </semantics></math> is the distance threshold and <math display="inline"><semantics> <mi>θ</mi> </semantics></math> is the relative slope.</p> "> Figure 8
<p>Filtering results for samp11: (<b>a</b>) the reference DTM, (<b>b</b>) filtered DTM, and (<b>c</b>) distribution of type I and type II errors. Most of the buildings were accurately filtered, and the road on the slope was accurately extracted (indicated with a green rectangle). The yellow rectangles indicate the areas where the roof of terraced buildings was misclassified.</p> "> Figure 9
<p>Filtering results for samp22: (<b>a</b>) the reference DTM, (<b>b</b>) filtered DTM, and (<b>c</b>) distribution of errors. The buildings and bridge were accurately filtered (indicated with green rectangle). The yellow rectangles indicate the areas where type II errors occurred due to the misclassification of some edges of the terraced floor, resulting in the roadside edge being cut off in the DTM.</p> "> Figure 10
<p>Filtering results for samp31: (<b>a</b>) the reference DTM, (<b>b</b>) filtered DTM, and (<b>c</b>) distribution of errors. The large buildings in the middle were accurately filtered. The yellow rectangles indicate the areas where an edge of the terraced floor was misclassified, resulting in the oversmoothing of the DTM in the corresponding part.</p> "> Figure 11
<p>Filtering results for samp42: (<b>a</b>) the reference DTM, (<b>b</b>) filtered DTM, and (<b>c</b>) distribution of errors. The large buildings of the railway station were well-filtered. However, several points on the roof in the lower-left corner were misclassified due to a lack of nearby ground points.</p> "> Figure 12
<p>Filtering results for samp53: (<b>a</b>) the reference DTM, (<b>b</b>) filtered DTM, and (<b>c</b>) distribution of type I and type II errors. The slopes and cliffs were successfully extracted. The yellow rectangles indicate the areas where low vegetations were misclassified, resulting in small protuberance in the DTM.</p> "> Figure 13
<p>Filtering results for samp61: (<b>a</b>) the reference DTM, (<b>b</b>) filtered DTM, and (<b>c</b>) distribution of type I and type II errors. The vegetation on terrain with large gaps and steep slopes was accurately filtered.</p> "> Figure 14
<p>Filtering results for samp71: (<b>a</b>) the reference DTM, (<b>b</b>) filtered DTM, and (<b>c</b>) distribution of type I and type II errors. The bridge was correctly filtered (indicated with green rectangle), whereas some points on the roadside were misclassified due to small scale undulations (indicated with yellow rectangles).</p> "> Figure 15
<p>Filtering results on test samples in OpenGF: (<b>first column</b>) Test I; (<b>second column</b>) Test II (without outliers); (<b>third column</b>) Test III. (<b>a</b>–<b>c</b>) The DSMs of the test samples; (<b>d</b>–<b>f</b>) the DTMs constructed with the filtering results; (<b>g</b>–<b>i</b>) distribution of type I and type II errors (red for type I errors and blue for type II errors).</p> "> Figure 16
<p>Calculation time (seconds) of MASF, CSF, and PMF.</p> "> Figure 17
<p>Ground seeds of representative samples (samp11 for urban areas and samp53 for rural areas): (<b>a</b>,<b>e</b>) overlay result of reference DTM and ground seeds (the red points) extracted using cell lowest point; (<b>b</b>,<b>f</b>) DTM generated with these seeds; (<b>c</b>,<b>g</b>) Overlay result of reference DTM and ground seeds extracted with our method, and (<b>d</b>,<b>h</b>) DTM generated with these seeds.</p> "> Figure 18
<p>Analysis of sensitivities to parameter <math display="inline"><semantics> <msub> <mi>α</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> </msub> </semantics></math>: (<b>a</b>) total errors for samples in urban areas; (<b>b</b>) total errors for samples in rural areas; (<b>c</b>) mean total errors of samples; (<b>d</b>) standard deviation of the total error for each sample.</p> ">
Abstract
:1. Introduction
2. Methods
2.1. Data Preprocessing
2.2. Modified 3D Alpha Shape
Algorithm 1 The modified 3D alpha shape algorithm. |
Require: Preproposed result points . Require: Parameter ;
|
2.3. Data Pyramid Construction
2.4. Multiscale TIN Densification Filter
3. Experiment and Results
3.1. Experimental Setup
3.2. Accuracy Metrics
3.3. Testing Results
3.3.1. Testing with ISPRS Dataset
3.3.2. Testing with OpenGF Dataset
3.4. Algorithm Efficiency Comparison
4. Discussion
4.1. Accuracy of Ground Seeds
4.2. Analysis of Parameter Settings
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Filtered | |||
---|---|---|---|
Ground Points | Nonground Points | ||
Reference | Ground points | a | b |
Nonground points | c | d |
Environment | Site | Sample | Features |
---|---|---|---|
Urban | 1 | 11 | Mixture of vegetation and buildings on the hillside |
12 | Mixed vegetation and buildings | ||
2 | 21 | Large buildings and bridge | |
22 | Irregularly shaped buildings | ||
23 | Large, irregularly shaped buildings | ||
24 | Steep slopes with vegetation | ||
3 | 31 | Complex buildings | |
4 | 41 | Data gaps, vegetation on moderate slopes | |
42 | Railway station with trains | ||
Rural | 5 | 51 | Gaps, vegetation on moderate slopes |
52 | Large buildings and bridge | ||
53 | Irregularly shaped buildings | ||
54 | Large, irregularly shaped buildings | ||
6 | 61 | Steep slopes and large gap | |
7 | 71 | Steep slopes and bridge. |
Sample | Parameter | Result | |||||
---|---|---|---|---|---|---|---|
(m) | (m) | ST | T.I (%) | T.II (%) | T.E. (%) | kappa (%) | |
samp11 | 28 | 1 | 0.10 | 6.60 | 11.59 | 8.73 | 82.10 |
samp12 | 25 | 1 | 0.05 | 2.50 | 3.94 | 3.20 | 93.60 |
samp21 | 20 | 2 | 0.05 | 0.49 | 3.48 | 1.15 | 96.65 |
samp22 | 25 | 1 | 0.10 | 2.79 | 8.67 | 4.61 | 89.16 |
samp23 | 15 | 1 | 0.10 | 1.75 | 9.80 | 5.56 | 88.80 |
samp24 | 10 | 1 | 0.10 | 4.10 | 13.12 | 6.58 | 83.37 |
samp31 | 25 | 2 | 0.01 | 0.90 | 1.87 | 1.35 | 97.28 |
samp41 | 25 | 2 | 0.05 | 5.11 | 1.78 | 3.45 | 93.09 |
samp42 | 20 | 9 | 0.10 | 0.99 | 0.80 | 0.85 | 97.95 |
samp51 | 25 | 4 | 0.05 | 0.34 | 5.52 | 1.47 | 95.61 |
samp52 | 20 | 1 | 0.05 | 3.10 | 17.02 | 4.57 | 76.70 |
samp53 | 7 | 1 | 0.25 | 0.99 | 39.45 | 2.54 | 64.49 |
samp54 | 20 | 9 | 0.05 | 2.46 | 3.16 | 2.84 | 94.30 |
samp61 | 6 | 1 | 0.10 | 0.33 | 12.02 | 0.73 | 88.82 |
samp71 | 15 | 2 | 0.05 | 0.94 | 5.70 | 1.48 | 92.66 |
Avg. | 2.23 | 9.19 | 3.27 | 88.97 |
Sample | Axelsson (2000) | Mongus (2012) | Chen (2013) | Pingel (2013) | Hu (2014) | Mongus (2014) | Hui (2016) | Zhang (2016) | MASF |
---|---|---|---|---|---|---|---|---|---|
samp11 | 10.76 | 11.01 | 13.01 | 8.28 | 8.31 | 7.50 | 13.34 | 12.01 | 8.73 |
samp12 | 3.25 | 5.17 | 3.38 | 2.92 | 2.58 | 2.55 | 3.50 | 2.97 | 3.20 |
samp21 | 4.25 | 1.98 | 1.34 | 1.10 | 0.95 | 1.23 | 2.21 | 3.42 | 1.15 |
samp22 | 3.63 | 6.56 | 4.67 | 3.35 | 3.23 | 2.83 | 5.41 | 8.94 | 4.61 |
samp23 | 4.00 | 5.83 | 5.24 | 4.61 | 4.42 | 4.34 | 5.11 | 4.79 | 5.56 |
samp24 | 4.42 | 7.98 | 6.29 | 3.52 | 3.80 | 3.58 | 7.47 | 2.87 | 6.58 |
samp31 | 4.78 | 3.34 | 1.11 | 0.91 | 0.90 | 0.97 | 1.33 | 1.61 | 1.35 |
samp41 | 13.91 | 3.71 | 5.58 | 5.91 | 5.91 | 3.18 | 10.60 | 5.14 | 3.45 |
samp42 | 1.62 | 5.72 | 1.72 | 1.48 | 0.73 | 1.35 | 1.92 | 1.58 | 0.85 |
samp51 | 2.72 | 2.59 | 1.64 | 1.43 | 2.04 | 2.73 | 4.88 | 3.08 | 1.47 |
samp52 | 3.07 | 7.11 | 4.18 | 3.82 | 2.52 | 3.11 | 6.56 | 3.93 | 4.57 |
samp53 | 8.91 | 8.52 | 7.29 | 2.43 | 2.74 | 2.19 | 7.47 | 5.20 | 2.54 |
samp54 | 3.23 | 6.73 | 3.09 | 2.27 | 2.35 | 2.16 | 4.16 | 3.18 | 2.84 |
samp61 | 2.08 | 4.85 | 1.81 | 0.86 | 0.84 | 0.96 | 2.33 | 1.49 | 0.73 |
samp71 | 1.63 | 3.14 | 1.33 | 1.65 | 1.50 | 2.49 | 3.73 | 5.71 | 1.48 |
Avg. | 4.82 | 5.62 | 4.11 | 2.97 | 2.85 | 2.74 | 5.33 | 4.39 | 3.27 |
Samples | Axelsson (2000) | Chen (2013) | Pingel (2013) | Hu (2014) | Hui (2016) | Zhang (2016) | MASF |
---|---|---|---|---|---|---|---|
samp11 | 78.48 | 74.12 | 83.12 | 82.97 | 72.92 | 75.17 | 82.10 |
samp12 | 93.51 | 93.23 | 94.15 | 94.83 | 93.00 | 94.04 | 93.60 |
samp21 | 86.34 | 96.10 | 96.77 | 97.23 | 93.35 | 90.47 | 96.65 |
samp22 | 91.33 | 89.03 | 92.21 | 92.04 | 87.58 | 77.72 | 89.16 |
samp23 | 91.97 | 89.49 | 90.73 | 91.14 | 89.74 | 90.38 | 88.80 |
samp24 | 88.50 | 84.53 | 91.13 | 90.39 | 81.93 | 92.68 | 83.37 |
samp31 | 90.43 | 97.76 | 98.17 | 98.19 | 97.33 | 96.75 | 97.28 |
samp41 | 72.21 | 88.83 | 88.18 | 88.18 | 78.78 | 89.73 | 93.09 |
samp42 | 96.15 | 95.81 | 96.48 | 98.25 | 95.38 | 96.18 | 97.95 |
samp51 | 91.68 | 95.17 | 95.76 | 93.90 | 85.06 | 91.13 | 95.61 |
samp52 | 83.63 | 78.91 | 81.04 | 86.24 | 69.51 | 77.05 | 76.70 |
samp53 | 39.13 | 46.69 | 68.12 | 66.43 | 41.84 | 46.86 | 64.49 |
samp54 | 93.52 | 93.90 | 95.44 | 95.28 | 91.63 | 93.61 | 94.30 |
samp61 | 74.52 | 77.36 | 87.22 | 86.76 | 67.82 | 78.10 | 88.82 |
samp71 | 91.44 | 93.19 | 91.81 | 92.59 | 79.86 | 68.03 | 92.66 |
Avg. | 84.19 | 86.27 | 90.02 | 90.29 | 81.72 | 83.86 | 88.97 |
Test I | Test II (w/o Outliers) | Test III | |||||||
---|---|---|---|---|---|---|---|---|---|
TE (%) | IoU1 (%) | IoU2 (%) | T.E. (%) | IoU1 (%) | IoU2 (%) | T.E. (%) | IoU1 (%) | IoU2 (%) | |
MASF | 2.34 | 94.85 | 95.88 | 3.92 | 92.59 | 92.31 | 1.94 | 89.87 | 97.66 |
PTDF | 5.18 | 89.00 | 91.10 | 6.70 | 87.24 | 87.64 | 2.45 | 87.16 | 97.05 |
PMF | 8.37 | 79.62 | 85.22 | 13.44 | 73.61 | 78.50 | 5.07 | 73.67 | 94.09 |
MCC | 3.71 | 91.86 | 93.63 | 15.56 | 70.27 | 75.39 | 3.03 | 84.12 | 96.40 |
CSF | 6.93 | 85.64 | 88.17 | 10.66 | 80.38 | 81.08 | 4.65 | 78.29 | 94.42 |
PointNet++ | 2.42 | 94.68 | 95.75 | 12.62 | 79.63 | 75.19 | 1.88 | 90.24 | 97.72 |
KPConv | 2.21 | 95.17 | 96.10 | 8.91 | 84.67 | 82.44 | 1.69 | 91.28 | 97.94 |
RandLA-Net | 3.71 | 91.65 | 93.74 | 5.04 | 90.42 | 90.38 | 2.40 | 87.08 | 97.14 |
SCF-Net | 4.25 | 90.43 | 92.90 | 9.09 | 83.32 | 83.35 | 2.77 | 85.18 | 96.70 |
Test I | Test II (w/o Outliers) | Test III | |
---|---|---|---|
MASF | 27.1 | 6.3 | 7.08 |
PTD | 2.8 | 0.2 | 0.8 |
PMF | 0.7 | 1.5 | 0.4 |
CSF | 14.6 | 0.7 | 7.8 |
KPConv | 2.3 | 0.2 | 1.3 |
RandLA-Net | 1.9 | 0.3 | 1.2 |
SCF-Net | 2.1 | 0.3 | 1.2 |
Sample | Lowest Cell | Ours | ||||
---|---|---|---|---|---|---|
CS (m) | Points | OP (%) | (m) | Points | OP (%) | |
samp11 | 20 | 112 | 99.11 | 28 | 4166 | 99.26 |
samp12 | 20 | 154 | 94.81 | 25 | 12,622 | 99.60 |
samp21 | 25 | 25 | 100.00 | 20 | 5420 | 99.83 |
samp22 | 40 | 25 | 100.00 | 25 | 9242 | 99.83 |
samp23 | 25 | 54 | 100.00 | 15 | 6923 | 98.07 |
samp24 | 15 | 45 | 100.00 | 10 | 3068 | 98.57 |
samp31 | 25 | 49 | 93.88 | 25 | 9147 | 99.63 |
samp41 | 25 | 35 | 94.29 | 25 | 2150 | 99.81 |
samp42 | 30 | 25 | 100.00 | 20 | 3631 | 99.75 |
samp51 | 20 | 264 | 98.48 | 25 | 13,043 | 99.42 |
samp52 | 10 | 1325 | 98.26 | 20 | 15,206 | 99.60 |
samp53 | 10 | 1937 | 99.79 | 7 | 31,290 | 99.42 |
samp54 | 15 | 234 | 99.15 | 20 | 3731 | 98.25 |
samp61 | 15 | 870 | 99.88 | 6 | 33,536 | 99.59 |
samp71 | 20 | 221 | 99.55 | 15 | 12,471 | 99.79 |
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Cao, D.; Wang, C.; Du, M.; Xi, X. A Multiscale Filtering Method for Airborne LiDAR Data Using Modified 3D Alpha Shape. Remote Sens. 2024, 16, 1443. https://doi.org/10.3390/rs16081443
Cao D, Wang C, Du M, Xi X. A Multiscale Filtering Method for Airborne LiDAR Data Using Modified 3D Alpha Shape. Remote Sensing. 2024; 16(8):1443. https://doi.org/10.3390/rs16081443
Chicago/Turabian StyleCao, Di, Cheng Wang, Meng Du, and Xiaohuan Xi. 2024. "A Multiscale Filtering Method for Airborne LiDAR Data Using Modified 3D Alpha Shape" Remote Sensing 16, no. 8: 1443. https://doi.org/10.3390/rs16081443