Towards accurate individual tree parameters estimation in dense forest: optimized coarse-to-fine algorithms for registering UAV and terrestrial LiDAR data

Figures & data

Figure 1. Location of the study area: (a) location of Maoershan in Heilongjiang Province, P.R. China (China Map Examination No. is GS (2019) 1823); (b) Sentinel-2 image (R: Band3; G: Band2; B: Band1) of Maoershan, and the locations of sample plots; (c) distribution of sample plots; and (d) LiDAR point cloud (i.e. TLS and ULS) of one plot. The projection coordinate system for (b) and (c) is WGS 1984 UTM Zone 52N.

Table 1. Essential parameters of the UAV and terrestrial LiDAR data.

	TLS	ULS
Laser scanning instrument	RIEGL-VZ400i	RIEGL mini VUX-1UAV
Wavelength (nm)	1550	905
Beam divergence (mrad)	0.35	0.5
Effective measurement rate (meas/sec)	420,00–500,000	150
Maximum range (m)	0.5–800	>250
Zenith and azimuth range (◦)	360°	NA
Average point density(points/m^2)	190,000–270,000	220–300

Figure 2. Stand conditions for (a) coniferous; (b) mixed broadleaf-coniferous; and (c) broadleaf forests.

Table 2. Description statistics for individual tree parameters of all the 15 plots.

Type	Plot	N	Stem density	DBH (cm)					Tree height (m)
			(stems/ha)	Min	Max	Mean	Median	Std	Min	Max	Mean	Median	Std
Coniferous	C-1	41	440	5.7	38.4	23.3	26.8	10.7	5.5	26.3	19.5	24.0	7.9
	C-2	57	630	5.6	42.3	18.4	9.4	13.1	5.1	26.3	15.0	11.3	8.3
	C-3	71	770	6.0	40.8	17.7	11	10.1	5.0	25.9	15.9	11.8	7.9
	C-4	84	930	5.1	33.4	19.2	22	8.1	5.2	25.6	17.9	20.2	6.4
	C-5	104	1200	6.4	33.6	18.1	17.2	6.6	7.2	23.6	18.7	19.6	4.1
	Mean	-	790	5.8	37.7	19.3	17.3	9.7	5.6	25.5	17.4	17.4	6.9
Mixed	M-1	109	900	5.6	40.5	14.8	12.9	7.2	4.5	23.7	12.6	11.4	4.2
	M-2	116	1000	5.5	48.6	14.8	13.9	7.1	4.3	20.5	12.7	11.7	3.8
	M-3	115	1100	5.4	37.7	15.8	14.4	6.5	5.3	24.2	13.0	13.1	3.9
	M-4	119	1300	6.0	30.9	16.0	15.2	5.8	4.6	23.7	12.1	11.7	3.7
	M-5	145	1500	5.1	30.9	14.8	14.3	5.7	4.5	21.2	12.7	12.3	3.8
	Mean	-	1160	5.5	37.7	15.2	14.1	6.5	4.6	22.7	12.6	12.0	3.9
Broadleaf	B-1	59	660	6.0	42.3	17.3	16.8	7.7	5.2	24.9	15.6	16.0	5.5
	B-2	60	660	7.9	56.5	21.3	16.5	11.1	8.2	28.1	19.2	18.5	5.6
	B-3	69	770	6.9	39.5	20.9	21.7	8.7	7.1	28.4	18.3	19.1	6.3
	B-4	71	770	7.0	49.2	16.8	14.1	7.9	6.8	29.0	16.7	17.1	4.7
	B-5	86	940	7.0	35.9	16.3	15.5	6.3	6.8	28.5	17.5	18.7	5.1
	Mean	-	760	7.0	44.6	18.5	16.9	8.3	6.8	27.8	17.5	17.9	5.4

Note: Coniferous represents coniferous forests; mixed represents mixed broadleaf-coniferous forests; broadleaf represents broadleaf forests. N is the number of trees in each plot. Std is the abbreviation of standard deviation.

Figure 3. Flowchart of automated registration based on TLS and ULS and performance assessment using the optimized coarse-to-fine algorithm for coniferous, mixed broadleaf-coniferous, and broadleaf forests.

Figure 4. Procedures of the optimized ICP algorithm. The KD-tree was utilized to calculate the nearest point and final point location; the inner loop determined the corresponding point, while the outer loop determined the final point cloud location.

Figure 5. Visual evaluation of the optimized coarse-to-fine algorithms (i.e. F-OICP, R-OICP, N-OICP) for (a) coniferous, (b) mixed broadleaf-coniferous, and (c) broadleaf forests, taking C-5, M-1, and B-2 plot as examples. The white points represent the registered ULS data and the color-rendered points represent the TLS data. Slices I, II, and III represent the sections 1.3 m (DBH) above the ground, tree trunk, and tree crowns, respectively.

Table 3. Accuracy assessment of transformation in horizontal and vertical directions.

Stand type	Stem density	Statistics	F-OICP		R-OICP		N-OICP
	(stems/ha)		MAE (cm)	RMSE (cm)	MAE (cm)	RMSE (cm)	MAE (cm)	RMSE (cm)
Coniferous	790	Mean	3.30/2.56*	4.29/3.38*	4.93/3.19*	6.02/4.31*	5.02/4.00*	6.55/6.78*
		Std	1.94/1.41*	2.43/1.72*	1.45/1.09*	1.69/1.41*	0.87/1.75*	1.01/2.53*
Mixed	1200	Mean	6.59/5.16*	7.58/6.34*	6.96/5.64*	8.04/6.84*	6.70/5.73*	7.86/6.93*
		Std	1.21/1.14*	1.01/1.15*	1.01/1.44*	1.00/1.39*	1.06/1.24*	0.99/1.24*
Broadleaf	760	Mean	9.72/8.40*	13.22/12.37*	11.49/10.86*	15.04/14.21*	10.95/10.34*	14.75/13.42*
		Std	1.22/1.01*	1.51/1.41*	0.89/0.94*	1.13/1.42*	1.13/0.97*	1.06/1.39*
Mean	-	-	6.54/5.37*	8.36/7.37*	7.79/6.56*	9.70/8.45*	7.56/6.69*	9.72/9.04*
Std	-	-	3.05/2.71*	4.14/4.10*	3.03/3.49*	4.18/4.55*	2.75/3.05*	3.84/3.61*

Note: “*” represents the transformation error in the vertical direction. F-OICP, R-OICP, N-OICP represent FPFH-, RANSAC-, NDT- optimized ICP algorithms, respectively. Std represent the standard deviation of the accuracy indices for all the plots.

Table 4. Accuracy assessment of ITCD using CSP algorithm based on U-TLS data registered by different algorithms.

Stand type	Stem density	Statistics	F-OICP			R-OICP			N-OICP			ICP
	(stems/ha)		r	p	F-score	r	p	F-score	r	p	F-score	r	p	F-score
Coniferous	790	Mean	0.81	0.76	0.78	0.81	0.75	0.78	0.79	0.75	0.76	0.79	0.74	0.76
		Std	0.06	0.05	0.07	0.06	0.06	0.06	0.07	0.05	0.06	0.07	0.08	0.08
Mixed	1200	Mean	0.74	0.68	0.71	0.74	0.67	0.70	0.72	0.65	0.68	0.71	0.65	0.68
		Std	0.03	0.03	0.03	0.03	0.02	0.03	0.03	0.03	0.03	0.04	0.04	0.04
Broadleaf	760	Mean	0.83	0.74	0.78	0.81	0.73	0.76	0.81	0.69	0.74	0.79	0.71	0.74
		Std	0.01	0.03	0.03	0.04	0.03	0.03	0.03	0.01	0.03	0.03	0.01	0.01
Mean	-	-	0.79	0.73	0.77	0.79	0.72	0.75	0.77	0.70	0.73	0.76	0.70	0.73
Std	-	-	0.05	0.06	0.05	0.05	0.04	0.05	0.06	0.06	0.05	0.06	0.06	0.06

Note: coniferous: coniferous forests, mixed: mixed broadleaf-coniferous forests, broadleaf: broadleaf forests. Std represent the standard deviation of the accuracy indices for all the plots.

Table 5. The accuracy of estimating individual tree DBH using three optimized algorithms and a traditional ICP algorithm.

Stand type	Statistics	F-OICP			R-OICP			N-OICP			ICP
		R^2	MAE(cm)	RMSE (cm)	R^2	MAE(cm)	RMSE (cm)	R^2	MAE (cm)	RMSE(cm)	R^2	MAE (cm)	RMSE (cm)
Coniferous	Mean	0.93	0.97	1.57	0.94	0.87	1.61	0.92	1.32	1.85	0.91	1.11	1.98
	Std	0.01	0.17	0.49	0.01	0.24	0.63	0.01	0.85	1.03	0.02	0.20	0.48
Mixed	Mean	0.90	1.18	2.19	0.89	1.16	2.05	0.89	1.17	2.18	0.90	1.51	2.14
	Std	0.02	0.24	0.30	0.01	0.17	0.14	0.02	0.10	0.10	0.01	0.36	0.14
Broadleaf	Mean	0.93	0.85	1.74	0.94	1.01	1.47	0.93	0.86	1.52	0.93	1.40	2.08
	Std	0.01	0.10	0.33	0.01	0.14	0.10	0.02	0.17	0.40	0.01	0.30	0.50
Mean	-	0.92	1.00	1.83	0.92	1.01	1.71	0.91	1.12	1.85	0.91	1.34	2.07
Std	-	0.02	0.22	0.44	0.03	0.21	0.46	0.03	0.51	0.64	0.02	0.30	0.38

Note: Std represent the standard deviation of the accuracy indices for all the plots.

Table 6. Accuracy of estimating tree height using three optimized algorithms and traditional ICP algorithm.

Stand type	Statistics	F-OICP			R-OICP			N-OICP			ICP
		R^2	MAE (m)	RMSE (m)	R^2	MAE (m)	RMSE (m)	R^2	MAE (m)	RMSE (m)	R^2	MAE (m)	RMSE (m)
Coniferous	Mean	0.87	0.15	0.21	0.86	0.18	0.26	0.86	0.17	0.26	0.75	0.40	0.58
	Std	0.04	0.06	0.09	0.02	0.04	0.08	0.04	0.04	0.08	0.03	0.14	0.20
Mixed	Mean	0.84	0.26	0.37	0.83	0.26	0.41	0.82	0.28	0.40	0.75	0.39	0.52
	Std	0.01	0.05	0.05	0.03	0.05	0.06	0.03	0.06	0.07	0.02	0.11	0.12
Broadleaf	Mean	0.84	0.34	0.44	0.78	0.40	0.50	0.77	0.40	0.51	0.66	0.65	0.84
	Std	0.02	0.04	0.05	0.03	0.04	0.07	0.03	0.04	0.05	0.05	0.08	0.11
Mean	-	0.85	0.25	0.34	0.82	0.28	0.39	0.82	0.31	0.39	0.72	0.48	0.65
Std	-	0.03	0.10	0.12	0.04	0.11	0.13	0.04	0.11	0.13	0.05	0.16	0.20

Table 7. Two-way ANOVA of the accuracy indices of ITCD and individual tree parameter estimation.

Parameter	Factor	Degree of freedom	Sum of square	Mean Square	F- statistics	p-value
ITCD	Stand type	2	0.07	0.04	17.39	0.00*
	Algorithm	3	0.01	0.00	1.35	0.26
	Stand type× Algorithm	6	0.00	0.00	0.04	1.00
DBH	Stand type	2	4.22	2.11	10.76	0.00*
	Algorithm	3	0.11	0.04	0.18	0.91
	Stand type× Algorithm	6	2.52	0.42	2.14	0.07
	Stand type	2	0.62	0.31	32.15	0.00*
Tree height	Algorithm	3	0.88	0.29	30.33	0.00*
	Stand type×Algorithm	6	0.12	0.02	2.11	0.07

Note: “*” represents significant differences at p < 0.05. The response variables are F-score for ITCD and RMSE for DBH and tree height.

Figure 6. Turkey test for the RMSE of DBH and tree height estimated by different registration algorithms for three stand types. (a) F-score of ITCD; main effect: stand type; (b) F-score of ITCD; main effect: registration algorithm; (c) RMSE of DBH; main effect: stand type; (d) RMSE of DBH; main effect: registration algorithm; (e) RMSE of tree height; main effect: stand type; and (f) RMSE of tree height; main effect: registration algorithm. Different lowercase letters indicate statistical differences using Tukey test post-hoc and significant differences between forest stand type or algorithm. “·” represent the outliers.

Table 8. Runtime performance of the registration algorithms.

Stand type	Statistics	Number of Points		Runtime (second)
		TLS	ULS	F-OICP	R-OICP	N-OICP	ICP
Coniferous	Mean	44853920	196118	236.0	230.4	251.4	396.5
	Std	-	-	39.9	22.3	32.7	17.9
Mixed	Mean	52555915	215341	302.5	315.4	331.5	411.7
	Std	-	-	17.0	29.5	21.5	12.1
Broadleaf	Mean	41060974	242423	218.8	222.3	224.1	385.1
	Std	-	-	53.6	53.6	52.9	19.5
Mean	-	46156936	217960	252.4	256.1	269.0	397.8
Std	-	-	-	52.7	59.4	59.1	29.3

Note: The number of TLS point clouds is the total amount of resampled point clouds.

Table A1. All the abbreviations used in this study.

Abbreviation	Explanation	Abbreviation	Explanation
ALS	Airborne Laser Scanning	ANOVA	Analysis of Variance
BLS	Backpack Laser Scanning	CAS (Xu et al. 2020)	Coverage Aware Sampling
CSP (Tao et al. 2015)	Comparative Shortest Path	DBH	Diameter at Breast Height
F-OICP	FPFH-based Optimized ICP	FPFH (Rusu et al. 2009)	Fast Point Feature Histogram
GNSS	Global Navigation Satellite System	ICP (Besl and McKay 1992)	Iterative Closest Point
ITCD	Individual Tree Crown Delineation	KD-tree	K-Dimensional Tree
LiDAR	Light Detection and Ranging	MAE	Mean Absolute Error
MLS	Mobile Laser Scanning	NDT (Magnusson 2009)	Normal Distributions Transform
N-OICP	NDT-based Optimized ICP	PDFs	Probability Density Functions
RANSAC (Raguram et al. 2013)	Random Sample Consensus	RMSE	Root Mean Squared Error
R-OICP	RANSAC-based Optimized ICP	RTK	Real-Time Kinematic
SIFT (Lowe 2004)	Scale-Invariant Feature Transform	SPFH (Rusu et al. 2008)	Simplified Point Feature Histogram
TLS	Terrestrial Laser Scanning	TIN	Triangular Irregular Network
Tukey’s HSD	Tukey’s Honest Significant Difference	ULS	Unmanned Aerial Vehicle Laser Scanning
3D	Three-Dimensional	4PCS (Aiger et al. 2008)	4-Points Congruent Sets

Data availability statement

The data that support the findings of this study are openly available in [figshare] at [https://doi.org/10.6084/m9.figshare.21786140.v1]. The reference data are available on request from the corresponding authors (Z.Z. and Y.Z.).