Progressive Morphological Filtering Algorithm Combined with Thin-Plate Spline Interpolation for Airborne LiDAR

Fig. 3. Filtering results. (a) Digital surface models of raw data; (b) digital elevation models of ground points processed by traditional morphological filtering; (c) digital elevation models of ground points processed by proposed algorithm

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Fig. 4. Spatial distribution of the I-type and the II-type errors for S23 and S51. (a) Classical algorithm; (b) proposed proposed

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Fig. 5. Comparison of average overall accuracy of the different filtering algorithms

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Fig. 6. Comparison of the total error of three filtering algorithms for 12 samples

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Table 1. Sample data characteristics

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Table 1. Sample data characteristics

Environment	Sample	Feature
Urban	S11	Vegetation and buildings on hillside
Urban	S21	Large buildings and bridge
Urban	S22	Irregular shaped buildings
Urban	S23	Large irregular buildings
Urban	S24	Steep slopes
Urban	S31	Large complex buildings
Urban	S41	Data gaps
Rural	S51	Lots of vegetation on hillside
Rural	S52	Low vegetation on steep slopes
Rural	S54	Irregular shaped buildings
Rural	S61	Discontinuous steep slopes
Rural	S71	Data gaps and bridge

Table 2. Precision evaluation indicators
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Table 2. Precision evaluation indicators
Parameter Filtering result Total
Terrain point Non-terrain point
Terrain point $a$ $b$ $e = a + b$
Non-terrain point $c$ $d$ $f = c + d$
Total $g = a + c$ $h = b + d$ $n = e + f$
Error $T_{Ⅰ} = b / (a + b)$ $T_{Ⅱ} = c / (c + d)$ $T_{e} = (b + c) / n$

Table 3. Precision evaluation indicators of different algorithms

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Table 3. Precision evaluation indicators of different algorithms

Sample	Classical algorithm			Proposed algorithm
Sample	I-type error	II-type error	Total error	I-type error	II-type error	Total error
S11	16.16	16.38	16.25	10.22	17.60	13.37
S21	15.14	23.04	16.89	1.73	4.09	2.27
S22	14.74	43.30	23.34	4.32	9.31	5.85
S23	12.46	8.52	10.59	7.51	8.90	8.17
S24	14.80	18.12	15.71	3.42	12.66	5.96
S31	8.48	12.81	10.47	4.85	6.92	5.81
S41	21.00	15.70	18.35	11.33	9.71	10.52
S51	5.02	24.62	9.30	3.19	13.27	5.39
S52	8.62	30.19	10.89	6.02	16.08	7.07
S54	13.26	15.22	14.31	2.41	7.70	5.28
S61	3.56	37.03	4.71	3.10	34.11	4.16
S71	8.85	39.62	12.34	5.09	18.39	6.58

Table 4. Total error of different algorithms

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Table 4. Total error of different algorithms

Sample	Sohn	Axelsson	Pfeifer	Elmqvist	Li	Zhang	Wack	PM
Ave	9.15	4.87	8.38	20.89	6.17	11.99	11.42	6.69
S11	20.49	10.76	17.35	22.40	12.85	18.49	24.02	13.37
S21	8.80	4.25	2.57	8.53	2.55	4.95	4.55	2.27
S22	7.54	3.63	6.71	8.93	4.06	14.18	7.51	5.85
S23	9.84	4.00	8.22	12.28	6.16	12.06	10.97	8.17
S24	13.33	4.42	8.64	13.83	5.67	20.26	11.53	5.96
S31	6.39	4.78	1.80	5.34	2.47	2.32	2.21	5.81
S41	11.27	13.91	10.75	8.76	6.71	20.44	9.01	10.52
S51	9.31	2.72	3.71	21.31	3.92	5.31	11.45	5.39
S52	12.04	3.07	19.64	57.95	15.43	12.98	23.83	7.07
S54	5.68	3.23	5.47	21.26	3.93	6.40	7.63	5.28
S61	2.99	2.08	6.91	35.87	5.81	16.13	13.47	4.16
S71	2.20	1.63	8.85	34.22	4.58	10.44	16.97	6.58

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Wang Xu, Yunlan Guan, Zhao Zhang, Zihui Zhang. Progressive Morphological Filtering Algorithm Combined with Thin-Plate Spline Interpolation for Airborne LiDAR[J]. Laser & Optoelectronics Progress, 2022, 59(10): 1028002

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