Registration of TLS and ULS Point Cloud Data in Natural Forest Based on Similar Distance Search

Abstract

Multiplatform fusion point clouds can effectively compensate for the disadvantages of individual platform point clouds in forest parameter extraction, maximizing the potential of LiDAR technology. However, existing registration algorithms often suffer from insufficient feature extraction and limited registration accuracy. To address these issues, we propose a ULS (Unmanned Aerial Vehicle Laser Scanning)-TLS (Terrestrial Laser Scanning) point cloud data registration method based on Similar Distance Search (SDS). This method enhances coarse registration by accurately retrieving points with similar features, leading to high overlap in the rough registration stage and further improving fine registration precision. (1) The proposed method was tested on four natural forest plots, including Pinus densata Mast., Pinus yunnanensis Franch., Pices asperata Mast., Abies fabri (Mast.) Craib, and demonstrated high registration accuracy. Both coarse and fine registration achieved superior results, significantly outperforming existing algorithms, with notable improvements over the TR algorithm. (2) In addition, the study evaluated the accuracy of individual tree parameter extraction from fusion point clouds versus single-platform point clouds. While ULS point clouds performed slightly better in some metrics, the fused point clouds offered more consistent and reliable results across varying conditions. Overall, the proposed SDS method and the resulting fusion point clouds provide strong technical support for efficient and accurate forest resource management, with significant scientific implications.

1. Introduction

Forests play a dominant role in the terrestrial ecosystem. They are an important part of the biosphere and have a close material exchange with the surrounding ecosystem. Forests also play a key role in maintaining the ecosystem balance, known as the “lungs of the earth” [1,2]. LiDAR (Light detection and ranging) can gather information on the intensity, elevation, and coordinates of objects on land, making it valuable for detecting forest structures and managing forest resources effectively [3,4].

Airborne Laser Scanning (ALS) rapidly captures extensive forest point clouds, aiding multi-scale forest monitoring. The emergence of Unmanned Aerial Vehicles (UAVs), noted for their agility and efficiency, has seen them being used extensively for forest structure analysis [5,6,7]. Due to the “top-down” scanning approach of ALS and the limitations in penetration ability, the point cloud density is relatively low. This is especially true in natural forest areas, where ALS cannot capture complete information on tree trunks, and more of the point cloud data originate from the forest canopy. For example, parameters such as the diameter at breast height (DBH) and the subbranches of tall trees cannot be directly extracted from ALS point cloud data and need to be estimated by building models with other parameters [8,9]. TLS compensates well for this shortcoming. Mounted on tripods or other carriers at ground level, TLS operates with a “bottom-up” scanning approach to acquire point cloud data, allowing it to capture comprehensive information on the lower trunk and understory shrub structures beneath the canopy. Of course, the scanning approach of TLS also results in the loss of some canopy information [10,11,12]. It can be seen that the data of ALS and TLS platforms have inherent advantages and disadvantages. The fusion of ULS and TLS will help to compensate for the respective disadvantages of the two kinds of data, obtain more perfect forest point cloud data, accurately extract forest structure parameters, and provide support for improving the efficiency and accuracy of forest resource investigations [13].

To solve the problem of point cloud registration of natural forestland, many scholars have proposed registration methods according to the characteristics of natural forest sample land. Guan et al. [14] utilized point cloud individual tree segmentation results to construct Triangulated Irregular Networks (TIN) for matching and selecting homonymous tree points, and combined this with the ICP (Iterative Closet Point) algorithm [15] to achieve point cloud registration. However, the registration results were significantly affected by the individual tree segmentation outcomes. Paris et al. [16] segmented individual trees from ALS point cloud data, extracted the boundaries of individual tree crowns, and overlaid them with TLS data for registration. However, when stand density is high, the uncertainty of canopy segmentation increases, reducing the applicability of the registration method. Dai et al. [17] realized key point extraction of ULS and TLS platform point cloud data using the mean shift algorithm, combined with the ICP algorithm and CPD (Coherent Point Drift) algorithm [18] to complete registration. The average accuracy was 0.05 m–0.08 m. Polewski et al. [19] detected the position of an individual tree using ULS and TLS point clouds, took the vertical and horizontal distance of an individual tree as the constraint condition, and completed the registration through image matching. However, using the DBH center as the position of an individual tree in the TLS point cloud created certain deviations, and it was not applicable to some specific tree species. Polewski et al. [20] later achieved registration between ALS and backpack LiDAR point clouds based on tree distances. However, they did not consider that trees do not grow perfectly vertically, thus the applicability of this method in complex forest scenarios remains to be further verified. Liu et al. [21] used the rasterized high point of the CHM tree, took the tree height value and the distance between an individual tree and the center of the sample as constraint conditions to find the same name point pairs, and combined the nearest-neighbor iterative algorithm to complete the point cloud registration. The registration accuracy was between 0.18 m and 0.69 m. Previous studies provide a reference for forest area point cloud registration research; however, there are still areas for further improvement: (1) the quantity of point cloud data is large, and the overall registration time cost based on point clouds is too high; (2) some existing registration algorithms rely on good initial positions and high initial overlaps, which cannot be guaranteed in practical applications; (3) registration methods based on the same name feature points are difficult to capture in natural forests, and it is easy to fall into local optima; and (4) the positions of individual trees are rigid characteristic points worth using, but due to the different conditions of actual natural forests and the differences in specific tree species, the applicability of various methods is still worth discussing, and the registration accuracy still has room for improvement.

In summary, the natural forest area of Shangri-La City in Yunnan Province of China was the research subject to carry out research on the registration method of ULS and TLS point clouds without control points in natural forest areas. This paper proposes a point cloud registration method that uses the tree height points of individual trees as proxies for their positions, searches for similar distances between trees, and achieves ULS-TLS cloud fusion in natural forest areas.

2. Data and Method

2.1. Overview of the Study Area

Shangri-La City is located in the northeast of the Diqing Tibetan Autonomous Prefecture, Yunnan Province, with geographic coordinates of 26°52′~28°52′ N, 99°22′~100°19′ E, and an average elevation of about 3459 m [22] (Figure 1). The region experiences a small annual temperature variation, distinct dry and wet seasons, and lacks a clear summer, with an average annual temperature of 5.5 °C. Intense solar radiation leads to sharp temperature increases during the day and significant cooling at night, with the daily temperature range in the dry season reaching up to 30 °C [23].

Shangri-La is located in the transition zone from the subtropical evergreen broad-leaved forest vegetation area of Yunnan Province to the alpine vegetation area of the Qinghai-Tibet Plateau. It is rich in forest resources, with a forest coverage rate of 78.61%. The city contains Pinus densata Mast., Pinus yunnanensis Franch., Pices asperata Mast., Abies fabri (Mast.) Craib, and Quercus aquifolioides Rehd. & E. H. Wilson [9]. Among them, the first three kinds of trees occupy 74.27% of the land area in the arboreal forest.

This study selected four natural forest sample plots featuring four typical tree species in Shangri-La City to gather TLS and ULS, and measured data as research subjects. It conducted multi-platform point cloud registration research in these natural forest areas. Sample plot information appears in

Table 1. Sample area information.

Sample Area	Coordinates	Tree Species	Average Tree Height/m	Average DBH/cm	Elevation/m	Slope/Aspect
1	99°44′ 51.85″ E 27°37′0.90″ N	Pinus densata Mast.	10.88	14.87	3267.10	1°/Southwest 195°
2	99°41′16.35″ E 27°37′5.15″ N	Pices asperata Mast.	13.11	18.06	3612.70	2°/Northwest 335°
3	100°04′48.43″ E 27°27′54.34″ N	Pinus yunnanensis Franch.	9.31	18.40	2415.08	4°/Northwest 340°
4	99°55′50.63″ E 28°00′57.93″ N	Abies fabri (Mast.) Craib	16.36	28.63	3686.00	5°/Southeast 148°

.

2.2. Data

2.2.1. TLS Point Cloud

The study utilized the Leica P40 3D laser scanner as the TLS point cloud data acquisition tool, with a collection system including a tripod, laser scanner, and targets of control points. Complete natural forest sample plot point cloud data were obtained through multi-station stitching. The specific parameters of the instrument are shown in

Table 2. Leica P40 3D Laser scanner parameter.

Index	Specification
Dimensions	238 mm × 358 mm × 395 mm
Distance accuracy	1.2 mm + 10 pmm
Angle accuracy	Horizontal: 8″; Vertical: 8″
Point accuracy	3 mm @ 50 m; 6 mm @ 100 m
Target acquisition accuracy	2 mm @ 50 m
Laser angle	<0.23 mrad
Scan range & Reflectivity	Min distance: 0.4 m; Max range & Reflectivity: 120 m (8%), 180 m (18%), 270 m (34%)
Scan rate	1,000,000 points/s
Noise range	0.4 mm rms @ 10 m; 0.5 mm rms @ 50 m
Field angle	Horizontal: 360°; Vertical: 270°
Laser line	1550 nm (Visible); 658 nm (Invisible)
Front window laser spot diameter	<3.5 mm

.

2.2.2. ULS Point Cloud

The acquisition system consists of a global navigation satellite system (GNSS), an inertial measurement unit (IMU), and a laser sensor. The study employed a UAV point cloud data collection system composed of a DJI Matrice M600 Pro drone equipped with a VUX-1UAV laser scanner developed and produced by the Austrian company RIEGL (Horn, Austria), as seen in Figure 2. The specific parameters of the loading platform and sensor are shown in

Table 3. DJI Longitude and Latitude M600 Pro UAV platform parameters.

Index	Specification 1
Dimensions	1668 mm × 1518 mm × 727 mm
Recommended maximum take-off weight	15.5 kg
Hover accuracy (GPS)	Vertical: ±0.5 m, Horizontal: ±1.5 m
Maximum angular velocity of rotation	Pitch axis: 300°/s, Course axis: 150°/s
Maximum pitch angle	25°
Maximum ascent speed	5 m/s
Maximum descent speed	3 m/s
Maximum wind speed	8 m/s
Maximum horizontal flight speed	65 km/h (No wind)
Maximum take-off altitude	Airscrew blade 2170/2195: 2500 m/4500 m
Hover time	Without load: 38 min; Load 5.5 kg: 18 min

¹ www.dji.com accessed on 14 June 2023.

and

Table 4. VUX-1UAV LiDAR sensor parameter.

Index	Specification 1
Field angle	360°
Farthest range	1050 m
Maximum laser emission frequency	520,000 points/s, 550 kHz
Repeated accuracy	5 mm
Maximum echo	15
Weight	3.5 kg

¹ www.ilidar.com accessed on 14 June 2023.

. The flight parameters are shown in

Table 5. The flight parameters.

Sample Area	Flight Time	Number of Flights	Flight Height (m)	Flight Speed (m/s)	Longitudinal Overlap (%)	Lateral Overlap (%)	Scanner Transmitting Frequency (KHz)
1	17:43 18 August 2021	1	60	5.3	90	60	400
2	14:51 18 August 2021	1	80	5.2	90	60	400
3	09:56 19 August 2021	1	80	5.2	90	60	400
4	11:04 19 August 2021	1	60	5.4	90	60	400

.

2.2.3. The Measured Data of the Plot

In order to further study the influence of different platform data on the extraction of single tree height, the study also artificially measured the tree height of each single tree in the sample field by using the ‘Berulay’ height meter. Each single tree was measured three times, and the average value was taken as the final single tree height.

2.3. Method

To solve the above registration problem, this paper takes advantage of the constant position between individual trees in natural forest areas, uses the point cloud data of different platforms to detect the tree height points of individual trees as approximate individual tree locations, and extracts the same name point pairs of TLS point clouds and ULS point clouds through distance sorting and similar distance searches. The coarse registration of the ULS point cloud and TLS point cloud is completed based on the SVD (Singular Value Decomposition) method of the same name point pair, and the final registration of the TLS and ULS forest area point clouds is completed by combining the nearest point fine registration method. The research technical route shown in Figure 3 includes three parts: data preprocessing, point cloud rough registration, and point cloud fine registration.

2.3.1. Data Preprocessing

The main preprocessing steps included data cropping and coordinate transformation. To facilitate subsequent data registration and mitigate computational inefficiencies due to computer hardware during the data processing phase, the study trimmed ULS data into a circular plot with a radius of 25 m and TLS data into a circular plot with a radius of 20 m, based on the center coordinates of the sample plots. The center of the sample area was determined using GPS (Global Positioning System). For the ULS data, we calculated the distance from each point in the dataset to the sample area center using the distance formula. Points within a specified radius R from the center were then selected for further analysis. We also recorded the actual center point’s projected coordinates using GPS, which facilitated the integration with ULS data. By utilizing GPS, the TLS data could be transformed into projected coordinates, which facilitated a more accurate overlap of the datasets. This approach helped ensure that the datasets aligned correctly, even in the absence of coarse registration. If the datasets do not achieve 100% overlap, we recommend using registration algorithms to resolve the issue. This is a key aspect of our research; the proposed algorithm is specifically designed to address scenarios where the datasets do not fully overlap. Through this algorithm, precise registration of the data is ultimately achieved, ensuring accurate alignment despite initial discrepancies.

Airborne laser scanning data consist of point clouds with projection coordinates. Terrestrial laser scanning data use the position of the scanner at the first measurement station as the center of the sample plot (0.0), and the scanned point cloud data contain local coordinate information [24]. Therefore, the two kinds of data have different initial coordinate systems. To merge and register the point cloud data of the two platforms, the two kinds of data should be converted to a unified coordinate system. Obviously, more parameters are needed to convert the TLS coordinate system to the ULS point cloud coordinate system [16]. The study first attempted to register the ULS data on the TLS coordinate system using the proposed method, and also explored registering the TLS data on the ULS coordinate system. Both approaches were tested, and the effectiveness of the proposed method was validated.

The Cloth Simulation Filter (CSF) method [25] extracted the ground points. We subtracted the nonground point cloud from the central value of the ground point cloud and updated the converted ULS point cloud coordinates. The specific formula appears in Formula (1).

$$ULS{\left(x,y,z\right)}_i=UL{S}_{nonground}{\left(x,y,z\right)}_i-mean\left(UL{S}_{ground}\left(x,y,z\right)\right), i=1,2,\dots ,n$$

(1)

where $ULS{\left(x,y,z\right)}_i$ represents the nonground point of the ULS point cloud after coordinate conversion, $UL{S}_{nonground}{\left(x,y,z\right)}_i$ represents the ith nonground point of the ULS point cloud before coordinate conversion, and $mean\left(UL{S}_{ground}\left(x,y,z\right)\right)$ represents the ground center point of the ULS point cloud before coordinate conversion. At this point, the ULS point cloud and the TLS point cloud have been converted to the same coordinate system, and the data range of the two platforms has a certain overlap.

2.3.2. Coarse Registration

Point Cloud Rasterization and Tree Height Point Detection

The point cloud is transformed into a two-dimensional raster image, and the individual tree position is further extracted by using the sliding window to detect the local maximum value of the two-dimensional image. The main steps to convert point clouds to raster images are as follows: (1) select the raster image resolution, (2) divide the grid and establish the index relationship between the grid and point cloud, (3) determine the interpolation method and fill the attribute values into the grid, (4) flip the grid, and (5) add coordinates for each grid crossing point [21]. We use the R language (Version: x64 4.0.4) to generate a raster image with a resolution of 0.1 m by means of maximum interpolation. Because the nonground point cloud is selected and the z value of the point cloud is filled into the grid as an attribute value, the maximum value of the raster image is detected through a 3 × 3 sliding window, and the detected point is the tree high point TH_ULS, TH_TLS, that is, the individual tree position point. Figure 4 shows the detected highest point of the tree.

Similar Distance Search

Figure 4 shows that the tree heights detected by TLS and ULS are not the same due to the different scanning methods of other platforms and different field conditions at the sample sites. However, there are still some tree highs with local similarities to the surrounding tree highs. The tree height represents the location of an individual tree, and the same individual tree should be approximately the same distance from the center of the plot in both the ULS and the TLS.

The distance between the tree and its neighboring trees and the distance between the neighboring trees and the center of the plot should be approximately the same both in the ULS and in the TLS (Formula (2)).

$$\left\{\begin{array}{c}{D}_{TL{S}_{center}}=\sqrt{{(x_{{TH}_{{TLS}_i}}}^2+{y_{{TH}_{{TLS}_i}}}^2)}\approx D_{UL{S}_{center}}=\sqrt{{(x_{{TH}_{{ULS}_i}}}^2+{y_{{TH}_{{ULS}_i}}}^2)}\\ D_{THTLS}=\sqrt{{\left(x_{{{TH}_{TLS}}_i}-y_{{{TH}_{TLS}}_n}\right)}^2+{\left(x_{{{TH}_{TLS}}_i}-y_{{{TH}_{TLS}}_n}\right)}^2}\\ \approx D_{THULS}=\sqrt{{(x_{{{TH}_{ULS}}_i}-y_{{{TH}_{ULS}}_n})}^2+{(x_{{{TH}_{ULS}}_i}-y_{{{TH}_{ULS}}_n})}^2}\end{array}\right.$$

(2)

Based on this idea, a point pair extraction method with the same name based on a similar distance search (SDS) is proposed. The main process is shown in

Table 6. Coarse registration (SDS) procedure code.

	Input: ${TH}_{TLS}$, ${TH}_{ULS}$, $D_{{UL{S}_{center}}_{ }}$, $D_{{TL{S}_{center}}_{ }}$
Step 1	For each tree height ${{TH}_{TLS}}_i$ in $D_{{TL{S}_{center}}_{ }}$     nearest_ULS = find_nearest(${TH}_{ULS}$, $D_{{TL{S}_{center}}_i}$)     If nearest_ULS exists, then selected_pair = (${{TH}_{TLS}}_i$, nearest_ULS)       add_to_selected_pairs(selected_pair)     end if end for
Step 2	For each selected_pair in selected_pairs, enter     nearest_neighbor_TLS = find_nearest_neighbor(selected_pair, ${TH}_{TLS}$) nearest_neighbor_ULS =     find_nearest_neighbor(selected_pair, ${TH}_{ULS}$)     If nearest_neighbor_TLS and nearest_neighbor_ULS are similar, then high_point_distance =       calculate_distance_to_center(nearest_neighbor_TLS, nearest_neighbor_ULS)       If high_point_distance is similar, then         match_point_pair = (nearest_neighbor_TLS, nearest_neighbor_ULS)         add_to_match_point_set(match_point_pair)       Or else         go back to Step 3       end if     Or else       go back to Step 3     end if end for
Step 3	Output match_point_set

:

Coarse Registration of TLS and ULS

Point cloud registration rotates and translates the ULS to achieve maximum coincidence with the reference cloud (TLS). Based on the set of point pairs with the same name extracted in “SDS”, the paper analyzes the rotation matrix R and the translation vector t by SVD, thus achieving the coarse registration of the ULS point cloud and TLS point cloud in the forest area. The principle of SVD is as follows:

Assume Q = {q1, q2, …, qn} and P = {p1, p2, … p3} are the corresponding point sets in two groups of D-dimensional space, corresponding to the high point set of the same name tree in the research, Q represents the TLS tree high point set, and P represents the ULS tree high point set. Calculating the rigid transformation information between these two point sets is a problem using the least square method [26], which can be described as Formula (3).

$$\left(R,t\right)=\underset{R,t}{\mathit{argmin}}{\sum }_{i=1}^n{w}_i‖{\left(R{p}_i+t\right)-q_i‖}^2$$

(3)

where R represents the rotation matrix, t represents the translation vector, $w_i$ is the weight of the ith point in the point set, and $w_i>0$.

The steps to solve the optimal rotation matrix and translation vector include the following:

(1) Calculate the weighted centroid of the two sets of points

$$\overline{p}={\displaystyle \frac{{\sum }_{i=1}^n{w}_i{p}_i}{{\sum }_{i=1}^n{w}_i}}, \overline{q}={\displaystyle \frac{{\sum }_{i=1}^n{w}_i{q}_i}{{\sum }_{i=1}^n{w}_i}}$$

(4)

(2) Calculate the center vector

$$x_i:=p_i-\overline{p}, y_i:=q_i-\overline{q}, i=1,2,\dots ,n$$

(5)

(3) Calculate the d × d covariance matrix

$$S=XW{Y}^T$$

(6)

where X and Y are $d\times n$ matrices with $x_i$ columns and $y_i$ columns, $W=diag\left(w_1,w_2,\dots ,w_n\right)$

(4) Calculate the singular value decomposition $S=U\Sigma V^T$ and obtain the rotation matrix $R$

$$R=V\left(\begin{array}{ccccc}1& & & & \\ & 1& & & \\ & & \ddots & & \\ & & & 1& \\ & & & & det\left(V{U}^T\right)\end{array}\right)U^T$$

(7)

(5) Calculate the optimal translation vector t

$$t=\overline{q}-R\overline{p}$$

(8)

The calculated rotation matrix R and translation vector t are substituted into the on-board point set to be configured (ULS point cloud dataset) to calculate the registered on-board point cloud dataset ($UL{S}_{tr}$).

$$UL{S}_{tr}=p_i\times R+t$$

(9)

The initial registration of the ULS point cloud and TLS point cloud is coarse registration by detecting the highest point of the tree instead of the individual tree position and then searching for similar distances to find the same feature points. Figure 5 (red points represent ULS tree heights and green points represent TLS tree heights) shows that the tree heights before rough registration are disorganized, and the same list of tree points cannot be identified with the naked eye. After rough registration, the ULS point cloud tree heights and TLS point cloud tree heights in the four sample sites selected by the research show similar spatial distribution patterns. The tree heights of the same name for the data of the two platforms can be clearly identified (Figure 5). However, not all ULS tree heights have corresponding TLS tree heights because the top-down scanning mode of ULS and the bottom-up scanning mode of TLS, resulting in tree height detection, cannot completely detect the corresponding tree height. The range of the ULS point cloud in the study is larger than that of the TLS point cloud, so there is no matching TLS point cloud at the edge tree height of the ULS point cloud.

2.3.3. Fine Registration Method Based on Nearest Points

Through the rough registration method of searching for the same feature point pairs, the ULS point cloud and the TLS point cloud after coarse registration already have a high overlap degree, the number of the same name point pairs obtained in the end is different, and the registration results are prone to local optimal solutions. To achieve higher registration accuracy, further fine registration is required [21]. The basic idea of fine registration is to minimize the distance between the same name points by iterative calculation of the nearest points (ICP) [15]. The main steps of fine registration include: (1) searching for the nearest space point to each point on $UL{S}_{tr}$ after coarse registration in the TLS cluster, (2) performing SVD decomposition on the nearest point pairs to solve for the rotation matrix and translation vector, which are then applied to the ULS point cloud for precise registration, and (3) iteratively calculating errors until finding the rotation matrix and translation vector that minimize the mean square error of the distance between nearest points. Substituting the rotation matrix R and the translation vector t from the precise registration of nearest points into Formula (9) yields the ULS point cloud after final registration. The precisely registered ULS point cloud is merged with the TLS point cloud to create a complete, integrated TLS and ULS fusion point cloud.

3. Results

3.1. Registration Effect

The initial registration of ULS and TLS point clouds is realized by SVD decomposition through an approximate distance search to detect point pairs with the same features. To further improve the registration accuracy, the final registration of the ULS and TLS point clouds is completed using the nearest point iteration to achieve fine registration. Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 show the registration effect. Figure 6, Figure 8, Figure 10 and Figure 11 show that the ULS point cloud is consistent with the overall range of the TLS point cloud after coordinate conversion ((a), (b), and (c)). No obvious feature points with the same name can be found by artificial visual inspection either from the canopy or from the ground, and the point cloud data of the two platforms present chaotic arrangements. After coarse registration and fine registration, the ULS point cloud and TLS point cloud achieve a certain degree of overlapping fusion ((d), (e), (f)), and the canopy and plane are fitted together. The slopes of plots 3 (Figure 10) and 4 (Figure 12) are significantly higher than those of plots 1 and 2. Soon, missing ground point clouds will occur in areas with complex terrain conditions. However, the method proposed in this study also shows that the ground points of point clouds in the two plots are well registered together because the features extracted in the study are based on canopy point clouds. Of course, even though the tree heights extracted by the point clouds of the two platforms in the stage of feature extraction of tree heights do not exactly correspond one-to-one, the registration results do not affect the final registration results, proving that the proposed extraction method is also applicable to natural forest sample plots with certain slopes and different stand densities.

To further check the registration effect, the research clipped and extracted individual tree point clouds from ULS point clouds and TLS point clouds in each sample plot to check the local registration effect, as shown in Figure 7, Figure 9, Figure 11 and Figure 13. The local single log registration results show that the fusion of the ULS point cloud and TLS point cloud registration can make up for the respective data disadvantages of the two platforms to a certain extent. Compared with a single TLS point cloud, the fused point cloud can obtain more complete canopy information, and some canopy information missing due to scanning angle or special canopy shape can be supplemented, especially canopy height information. Tree species with high tree heights, such as Yunnan pine (Figure 11) and fir (Figure 13), have serious canopy width losses in TLS point clouds. The canopy information in the fusion point cloud is fully expressed, and it is convenient to extract the information of individual trees more accurately. Compared with a single ULS point cloud, the fused point cloud can compensate for the missing understory information and single trunk information. In the plots with higher stand density and larger canopy width, the ULS cannot completely penetrate the canopy layer, resulting in the loss of single trunk information. The fused point cloud accurately retains the information under the TLS point cloud and stores it in the fusion point cloud.

3.2. Registration Accuracy

The research selects the nearest point distance as the index for registration accuracy verification, that is, the nearest point in the ULS point cloud and TLS point cloud after searching registration, and calculates the average p of the sum of the distances, which is the final registration accuracy [14,22,27]. Its calculation formula is shown in Formula (9). The distance distribution of the nearest points of the ULS point cloud in the TLS point cloud after coarse registration and fine registration is studied, calculated, and counted, as shown in Figure 14, Figure 15, Figure 16 and Figure 17, where (a) represents the distance distribution after coarse registration and (b) represents the distance distribution after fine registration. After fine registration, the distribution of the nearest distance tends to be smaller, and the distant points before fine registration are improved.

$$P={\displaystyle \frac{1}{n}}\times \sum _{i=1}^n{d}_{knn\left(i\right)}$$

(10)

where n represents the total number of points and $d_{knn\left(i\right)}$ represents the nearest distance of the ith point.

The mean (μ) and standard deviation (σ) of these distances provide a quantitative measure of the registration quality (

Table 7. Registration Accuracy Statistics.

Plot	Coarse Registration		Fine Registration
	μ/m	σ/m	μ/m	σ/m
1	0.18	0.24	0.10	0.21
2	0.59	0.46	0.27	0.38
3	0.12	0.22	0.08	0.20
4	0.45	0.42	0.09	0.23

). Table 7 shows that coarse registration has already achieved a certain level of accuracy, with relatively low mean nearest point distances and small standard deviations across the plots, indicating that the ULS and TLS point clouds have been effectively merged. However, fine registration further enhances the accuracy, reducing both the mean and standard deviation in each plot, significantly improving the alignment accuracy and consistency, ensuring a tighter match and higher precision fusion of the point clouds.

4. Discussion

4.1. The Accuracy Difference between Different Registration Methods

To prove the validity and reliability of the proposed registration method, two registration methods were selected to compare the registration accuracy. The registration accuracy table is shown in

Table 8. Comparison of the accuracy of each registration method.

Plot	Fine Registration Accuracy (m)		Absolute Accuracy Difference (m)	Relative Accuracy Difference (%)
	SDS	TR 1	SDS vs. TR	SDS vs. TR
1	0.10	0.12	0.02	16.67
2	0.27	0.48	0.21	43.75
3	0.08	0.10	0.02	20.00
4	0.09	0.22	0.13	59.10

¹ TR (Tree-height Registration) algorithm.

. Through comparison with other methods, it was found that the coarse registration of the proposed search similarity distance method achieved good results. Compared with the TR (Tree-height Registration) algorithm proposed by Liu et al. [21], which also uses the high point of an individual tree, the precision registration effect of each sample plot improved. Compared with the TR (Tree height Registration) algorithm, the average accuracy improved by 34.88%. The TR algorithm relies on the similarity of the distance between the high point of the tree and the center of the plot and is prone to local optimization. The proposed algorithm not only considers the distance between the individual tree and the center of the plot but also considers the position relationship between the adjacent individual trees. By comparing with the registration results of other methods, the proposed registration method has been proven to have certain validity and reliability, and the registration accuracy improves.

4.2. Difference in Extracting Single-Wood Parameters of Point Cloud Data before and after Fusion

Fusion point cloud data were obtained by merging the ULS point cloud data after registration conversion with the original TLS point cloud data. To further explore the difference between individual platform point cloud and fusion point cloud extraction of individual tree parameters, individual tree height extraction was carried out for single TLS point cloud data, single ULS point cloud data, and point clouds after registration fusion.

The study introduced three metrics: RMSE (Root Mean Square Error), R² (Coefficient of Determination), and MRE (Mean Relative Error) to evaluate the accuracy of tree height extraction. The evaluation results are shown in Figure 18. From the correlation between the measured tree height and the tree height extracted based on the point clouds of each platform, the tree height extracted from the fusion point cloud and ULS point cloud has a high correlation with the measured value, R² reaches 0.955 (RMSE = 1.897 m, MRE = 8.693%), followed by the ULS point cloud, R² reaches 0.965 (RMSE = 1.707 m, MRE = 10.082%), and the difference between the two is not large. The lowest is the TLS point cloud data, where R² is 0.838 (RMSE = 3.344 m, RME = 10.670%) (Figure 18). The reason for the lower accuracy of tree height extraction from the fused point cloud compared with the ULS point cloud may be due to the selected study area where the tree heights range from 7 m to 30 m, resulting in significant variations in RMSE with large differences in tree height. Therefore, when considering the MRE metric, it can be observed that the fused point cloud provides higher overall accuracy and greater stability in tree height extraction. Among the three kinds of data, the high precision of the TLS cloud extraction tree is relatively low, which is caused by the difference between the bottom-up scanning mode of TLS and the top-down scanning mode of ULS LiDAR [28,29]. For some tall trees, the scanning range of the TLS is limited, the laser point cannot reach the true high point of the individual tree canopy, and the maximum value in the Z-axis direction is not the true maximum value, that is, the true tree high point [30]. Although ULS can obtain a more complete individual canopy point cloud, part of the noise attached to the upper layer of the tree will become the source of error, which is also the reason why the height estimate of an individual tree extracted based on the ULS point cloud in the study is relatively high. Fusion point clouds make up for the data disadvantages caused by the different scanning methods of a single platform, making the canopy information of TLS point clouds more complete and the attribution of point clouds more clear. Some point clouds attached to the upper canopy are easier to remove by denoising to obtain more accurate tree height values [31].

In fact, actual tree height measurements also contain human errors. Tree heights were measured using a Blume-Leiss altimeter, which requires visual identification of the tree’s highest and root points. Such subjective judgments, combined with interference from complex forest environments, increase the margin of human measurement error [31]. Especially for some tall trees, extracting tree heights from LiDAR point cloud data is more accurate than manual measurements. Of course, measuring individual trees by felling them would yield different results, but that approach would cause ecological damage and incur higher measurement costs.

4.3. Coordinate System Transformation

In the preprocessing phase, the initial ULS coordinate system is transformed into the same local coordinate system as TLS, with the proposed registration method using TLS as the reference point cloud to register the ULS point cloud within it. This approach has some drawbacks in practical applications. Converting TLS into geographic coordinates offers advantages; however, existing studies indicate that converting TLS to geographic coordinates requires more transformation parameters, making it difficult to operate and presenting significant disadvantages [16,19]. The study did not acquire the necessary transformation parameters during the data acquisition phase, so it ultimately chose to transform ULS into the TLS coordinate system. Additionally, the coordinate transformation principles outlined in Section 2.3.1 were applied. After clipping the point cloud, the centroid of the airborne ground point cloud was computed and added to the ground-based point cloud, thereby updating the coordinates of the transformed ground-based point cloud. This transformation is expressed by Equation (11):

$$\mathrm{T}\mathrm{L}\mathrm{S}{\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)}_{\mathrm{i}}={TLS}_{origin}{\left(x,y,z\right)}_i+\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\left(UL{S}_{ground}\left(x,y,z\right)\right),i=1,2,\dots ,n$$

(11)

where $TLS{\left(x,y,z\right)}_i$ denotes the transformed TLS coordinates, ${TLS}_{origin}{\left(x,y,z\right)}_i$ represents the original TLS coordinates, and $\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\left(UL{S}_{ground}\left(x,y,z\right)\right)$ represents the centroid of the airborne ground point cloud prior to coordinate transformation. Following this transformation, both the airborne and ground-based point clouds were aligned to the WGS1984 coordinate system (Figure 19b). The registration method proposed in this study was then employed, achieving point cloud registration with the registered point cloud aligned to the coordinate system of the original ULS (Figure 19d). The results demonstrate that the choice of coordinate system does not affect the applicability of the proposed registration algorithm, as the registration concept is independent of the geographic or local coordinate system.

4.4. Tree Height Detection

The sliding window technique is utilized to detect local maxima in the CHM, which indicates the positions of individual trees. However, due to different scanning methods used by ULS and TLS, the TLS occasionally fails to capture the true canopy top, resulting in discrepancies in detected local maxima [32,33]. To address this, our proposed method uses tree height as one of the constraints, along with the distance similarity between trees to match detected tree heights, thereby confirming the final point pairs. This approach mitigates errors that could arise from relying solely on parameter extraction and considers the spatial relationships between individual trees, thus avoiding local optimization issues [19]. Quantitative verification demonstrates that this is an effective registration method for point clouds in natural forest areas.

4.5. Deficiency and Prospects

The proposed registration algorithm achieved a good registration effect in natural forest sample plots. Compared with some existing registration algorithms, the accuracy is improved, but there are still some areas that can be further studied and improved. For example, the forest sample plots involved in the research are all natural forest sample plots in the alpine mountains of Shangri-La City; however, they are all natural pure forests with strong homogeneity and individual tree species. To further prove the validity and universality of the proposed registration method or to explore a more suitable registration method, this study will be conducted for mixed forests or more complex stands in future studies.

5. Conclusions

LiDAR technology is an effective means of informed, intelligent and efficient management of forest resources. Various platforms’ point cloud data have advantages and disadvantages. Rapid and accurate registration and fusion of multiplatform point cloud data will better utilize the advantages of each platform point cloud data and further improve the role of LiDAR in forest surveys. Aiming at the shortcomings of current point cloud registration algorithms in natural forests, a ULS-TLS point cloud registration algorithm, SDS, based on a similar distance search, is proposed. The point cloud was generated into a DSM to extract the tree’s high point instead of the individual tree position. The target tree high point and the similar position of the surrounding tree high point were searched to find the same name feature point pair, achieve the point cloud rough registration by SVD solution, and finally complete the point cloud fine registration by the nearest iteration. The registration method was applied to four natural forest sample plots of four typical tree species in different site environments in Shangri-La City, Yunnan Province, China. The average registration accuracy reached 0.13 m, and compared with the TR algorithm, the accuracy increased by 34.88%, proving that the proposed method has certain validity.

To further illustrate the advantage of fused point cloud data over individual platform point cloud data in extracting individual tree parameters, the study extracted tree height parameters from both pre- and post-fusion point clouds. By comparing these with actual measured parameters, it was found that the tree heights extracted from the fused point clouds had higher correlation with the actual measured tree heights, achieving greater extraction precision. The correlation coefficient R² increased by 0.004, making the point cloud data of natural forest areas more complete and the expression of individual tree point cloud information more comprehensive.

From a practical standpoint, the successful application of the SDS algorithm in diverse natural forest environments highlights its robustness and adaptability. Forest managers can now leverage this method to obtain more accurate tree height measurements, which are crucial for inventory assessments, biomass estimation, and ecological monitoring. The improved precision in data fusion also means that large-scale forest surveys can be conducted more efficiently, with reduced need for manual intervention and correction.

Moreover, the enhanced accuracy of the fused data opens up new possibilities for advanced forest management practices, such as dynamic monitoring of forest health, detection of subtle changes in tree growth, and more precise modeling of forest structure. These capabilities are essential for sustainable forest management, enabling more informed decision-making processes that can better address conservation goals, resource allocation, and climate change mitigation efforts.

In summary, this study provides a significant methodological advancement with both scientific and practical implications. By effectively combining ULS and TLS point cloud data, the SDS algorithm not only improves the accuracy and reliability of forest resource assessments but also supports more sustainable and efficient forest management practices. The contributions of this research extend beyond technical improvements, offering a valuable tool for a wide range of applications in forestry and environmental management.