Improved progressive triangular irregular network
densification filtering algorithm for airborne LiDAR data based on a
multiscale cylindrical neighborhood
Xiankun Wang, Xincheng Ma, Fanlin Yang, Dianpeng Su, Chao Qi, and Shaobo Xia
Laser point
cloud filtering is a
fundamental step in various applications of light detection and
ranging (LiDAR) data. The progressive triangulated irregular network
(TIN) densification (PTD) filtering algorithm is a classic method and
is widely used due to its robustness and effectiveness. However, the
performance of the PTD filtering algorithm depends on the quality of
the initial TIN-based digital terrain model (DTM). The filtering
effect is also limited by the tuning of a number of parameters to cope
with various terrains. Therefore, an improved PTD filtering algorithm
based on a multiscale cylindrical neighborhood (PTD-MSCN) is proposed
and implemented to enhance the filtering effect in complex terrains.
In the PTD-MSCN algorithm, the multiscale cylindrical neighborhood is
used to obtain and densify ground seed points to create a high-quality
DTM. By linearly decreasing the radius of the cylindrical neighborhood
and the distance threshold, the PTD-MSCN algorithm iteratively finds
ground seed points and removes object points. To evaluate the
performance of the proposed PTD-MSCN algorithm, it was applied to 15
benchmark LiDAR datasets provided by the International Society for
Photogrammetry and Remote Sensing (ISPRS) commission. The experimental
results indicated that the average total error can be decreased from
5.31% when using the same parameter set to 3.32% when optimized.
Compared with five other publicized PTD filtering algorithms, the
proposed PTD-MSCN algorithm is not only superior in accuracy but also
more robust.
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Descriptions of Four Accuracy Metrics Used in This Paper
Accuracy
Metric
Variable Abbreviation
Description
Omission error (type I
error)
Percentage of ground points
incorrectly classified as non-ground points
Commission error (type II
error)
Percentage of non-ground
points accepted as ground points
Total error
Percentage of all incorrectly
classified points
Kappa coefficient
Alternative measure of the
overall classification accuracy, which subtracts the
effect of accidental consistency and quantifies the
effect of the specific classification
Table 3.
Calculation Descriptions: and are the Numbers of Correctly
Identified Ground and Object Points, Respectively; and are the Numbers of
Misclassified Ground and Object Points, Respectively
Filtered
Metrics of Quantitative
Evaluations
Ground
Object
Reference
Ground
Object
Table 4.
Performance Evaluations of the Improved Algorithm on Type I
Error (), Type II Error (), Total Error (), and Kappa Coefficient () for the Reference Datasets
Provided by ISPRS and the Corresponding Parametersa
Optimized
Single Parameter
Samples
samp11
17
0.45
0.85
8.31
8.01
8.18
83.35
9.05
7.78
8.51
82.71
samp12
25
0.35
0.45
3.02
2.63
2.83
94.33
1.67
5.51
3.55
92.89
samp21
20
0.3
0.4
0.42
2.92
0.97
97.17
0.02
10.19
2.28
93.16
samp22
20
0.5
0.65
3.15
6.84
4.31
89.97
3.26
6.75
4.35
89.88
samp23
18
0.65
0.4
3.6
7.32
5.36
89.23
5.97
5.55
5.77
88.42
samp24
9
0.6
0.3
2.85
12.05
5.38
86.31
4.1
10.98
5.99
84.95
samp31
15
0.25
0.4
0.89
1.89
1.35
97.28
0.2
12.59
5.91
88.0
samp41
23
0.65
0.95
6.96
3.66
5.31
89.39
15.14
2.59
8.85
82.29
samp42
23
0.15
1.1
0.83
1.87
1.56
96.27
1.3
8.67
6.51
85.14
samp51
8
0.25
0.45
0.6
5.29
1.63
95.18
0.11
15.82
3.54
89.03
samp52
7
0.5
1.2
1.95
27.9
4.68
73.83
5.81
18.63
7.15
66.52
samp53
3
0.45
0.95
2.22
26.28
3.2
63.43
7.78
19.01
8.24
40.8
samp54
8
0.25
0.7
1.61
3.39
2.57
94.84
0.6
7.52
4.32
91.36
samp61
4
0.45
0.8
0.53
7.88
0.79
88.54
2.4
7.21
2.56
70.07
samp71
10
0.4
0.75
0.77
8.42
1.64
91.76
0.25
17.34
2.19
88.32
Mean
2.51
8.42
3.32
88.73
3.84
10.41
5.31
82.24
Median
1.95
6.84
2.83
89.97
2.4
8.67
5.77
88.0
Min
0.42
1.87
0.79
63.43
0.02
2.59
2.19
40.8
Max
8.31
27.90
8.18
97.28
15.14
19.01
8.85
93.16
For the single parameter set results, the parameters are
selected as $\textit{IR}
= {{18}}\;{\rm{m}}$, $\textit{ST}
= {0.5}$, and $\textit{FT}
= {0.6}\;{\rm{m}}$.
Table 5.
Performance Comparison Between Our Algorithm and Publicized
Improved PTD Filtering Algorithms in Terms of the Total Error
(%)
Descriptions of Four Accuracy Metrics Used in This Paper
Accuracy
Metric
Variable Abbreviation
Description
Omission error (type I
error)
Percentage of ground points
incorrectly classified as non-ground points
Commission error (type II
error)
Percentage of non-ground
points accepted as ground points
Total error
Percentage of all incorrectly
classified points
Kappa coefficient
Alternative measure of the
overall classification accuracy, which subtracts the
effect of accidental consistency and quantifies the
effect of the specific classification
Table 3.
Calculation Descriptions: and are the Numbers of Correctly
Identified Ground and Object Points, Respectively; and are the Numbers of
Misclassified Ground and Object Points, Respectively
Filtered
Metrics of Quantitative
Evaluations
Ground
Object
Reference
Ground
Object
Table 4.
Performance Evaluations of the Improved Algorithm on Type I
Error (), Type II Error (), Total Error (), and Kappa Coefficient () for the Reference Datasets
Provided by ISPRS and the Corresponding Parametersa
Optimized
Single Parameter
Samples
samp11
17
0.45
0.85
8.31
8.01
8.18
83.35
9.05
7.78
8.51
82.71
samp12
25
0.35
0.45
3.02
2.63
2.83
94.33
1.67
5.51
3.55
92.89
samp21
20
0.3
0.4
0.42
2.92
0.97
97.17
0.02
10.19
2.28
93.16
samp22
20
0.5
0.65
3.15
6.84
4.31
89.97
3.26
6.75
4.35
89.88
samp23
18
0.65
0.4
3.6
7.32
5.36
89.23
5.97
5.55
5.77
88.42
samp24
9
0.6
0.3
2.85
12.05
5.38
86.31
4.1
10.98
5.99
84.95
samp31
15
0.25
0.4
0.89
1.89
1.35
97.28
0.2
12.59
5.91
88.0
samp41
23
0.65
0.95
6.96
3.66
5.31
89.39
15.14
2.59
8.85
82.29
samp42
23
0.15
1.1
0.83
1.87
1.56
96.27
1.3
8.67
6.51
85.14
samp51
8
0.25
0.45
0.6
5.29
1.63
95.18
0.11
15.82
3.54
89.03
samp52
7
0.5
1.2
1.95
27.9
4.68
73.83
5.81
18.63
7.15
66.52
samp53
3
0.45
0.95
2.22
26.28
3.2
63.43
7.78
19.01
8.24
40.8
samp54
8
0.25
0.7
1.61
3.39
2.57
94.84
0.6
7.52
4.32
91.36
samp61
4
0.45
0.8
0.53
7.88
0.79
88.54
2.4
7.21
2.56
70.07
samp71
10
0.4
0.75
0.77
8.42
1.64
91.76
0.25
17.34
2.19
88.32
Mean
2.51
8.42
3.32
88.73
3.84
10.41
5.31
82.24
Median
1.95
6.84
2.83
89.97
2.4
8.67
5.77
88.0
Min
0.42
1.87
0.79
63.43
0.02
2.59
2.19
40.8
Max
8.31
27.90
8.18
97.28
15.14
19.01
8.85
93.16
For the single parameter set results, the parameters are
selected as $\textit{IR}
= {{18}}\;{\rm{m}}$, $\textit{ST}
= {0.5}$, and $\textit{FT}
= {0.6}\;{\rm{m}}$.
Table 5.
Performance Comparison Between Our Algorithm and Publicized
Improved PTD Filtering Algorithms in Terms of the Total Error
(%)