Extraction of Arbors from Terrestrial Laser Scanning Data Based on Trunk Axis Fitting

Abstract

Accurate arbor extraction is an important element of forest surveys. However, the presence of shrubs can interfere with the extraction of arbors. Addressing the issues of low accuracy and weak generalizability in existing Terrestrial Laser Scanning (TLS) arbor point clouds extraction methods, this study proposes a trunk axis fitting (TAF) method for arbor extraction. After separating the point cloud data by upper and lower, slicing, clustering, fitting circles, obtaining the main central axis, filtering by distance, etc. The canopy point clouds are merged with the extracted trunk point clouds to precisely separate arbors and shrubs. The advantage of the TAF method proposed in this study is that it is not affected by point cloud density or the degree of trunk curvature. This study focuses on a natural forest plot in Shangri-La City, Yunnan Province, and a plantation plot in Kunming City, using manually extracted data from a standardized dataset of samples to test the accuracy of the TAF method and validate the feasibility of the proposed method. The results showed that the TAF method proposed in this study has high extraction accuracy. It can effectively avoid the problem of trunk point cloud loss caused by tree growth curvature. The experimental accuracy for both plots reached over 99%. This study can provide certain technical support for arbor parameter extraction and scientific guidance for forest resource investigation and forest management decision-making.

1. Introduction

Forest resources are important natural assets that play an important role in maintaining national ecological security and are crucial in promoting economic development [1]. The accurate extraction of arbors is an important prerequisite for detailed forest surveys and ecological environmental assessments [2]. It can provide accurate basic data for assessing biomass, carbon storage, timber volume, and other studies [3,4]. However, natural forest growth environments are complex, interspersed with arbors, shrubs, and grasses [5]. The presence of shrubs and grasses can affect the extraction of arbors; therefore, designing methods to filter out the scrub point clouds and extract the arbors accurately and completely is the key to a fine forest survey.

From field reconnaissance to aerial visual surveys and the later use of high-resolution remote sensing imagery, the methods used to conduct forest resource surveys in China have changed substantially [1]. As field surveys are conducted on a sampling basis, they are not feasible when testing the growth of trees over a large area [6]. High-resolution remote sensing images, however, are limited by angle and resolution, making it challenging to accurately extract understory parameters [7]. The emergence of Light Detection and Ranging (LiDAR) has sparked a new wave of technological innovation in forest resource surveys [1,8]. LiDAR is an active remote sensing technology [9] that features non-destructive measurements. It allows for richer 3D information [10]. Moreover, point cloud data could potentially enable automated processing [11]. Therefore, it has broad prospects for application in plot surveys. Terrestrial Laser Scanning (TLS) is a new type of remote sensing instrument that mounts a sensor on the ground. It can generate high-precision, three-dimensional data with coordinates. It can accurately and clearly acquire spatial information and vertical structure within the plots [12]. As an emerging remote sensing technology, TLS has been widely used in detailed forest resource surveys [13,14].

The prerequisite for forest surveys is the accurate extraction of arbors. The morphological parameters of arbors are crucial for understanding forest structures in depth. However, interference from undergrowth grass point clouds can significantly affect the extraction of arbors. To achieve the goal of separating arbors from undergrowth grass, scholars have proposed methods such as the ISTTWN algorithm [15], the iForest algorithm [16], and using raster images generated from trunk slices to perform the Hough transform for trunk detection [17]. However, experimental data are often sourced from neatly arranged artificial forests or roadside trees. These methods are suitable for extracting regularly grown trees and may face challenges when applied to irregularly grown natural forest plots. Some scholars have also attempted to extract arbors by creating cylinder models, but this method may not provide precise trunk extraction and may result in the loss of some trunk point cloud data [18,19,20]. Some researchers have proposed the CEC method [21] and the use of the vector of point clouds for arbor extraction. However, these methods involve many parameters and require multiple iterations, making the process quite complex. Furthermore, they are prone to incorrectly excluding parts of the trunk, and they have certain limitations when applied to plots where individual trees grow in a curved manner. Methods such as point cloud shrinking [22], clustering [23], or combining RGB images [24] to construct tree skeletons have also been studied for arbor extraction. However, these methods mostly use experimental data from straight-trunked poplar or fruit trees, leading to incomplete tree extraction when the main trunk is curved. When using classification-based methods such as Support Vector Machine (SVM) [25], Random Forest, and Decision Trees [26] for tree–shrub separation, the major issue lies in the need for manually selecting training samples. Hence, human subjectivity can significantly influence the results.

In summary, current arbor extraction methods still have issues in terms of low precision and poor generalizability, meaning that they are difficult to apply to complex natural forest samples with single-tree growth curvature or staggered tree–shrub–grass growth. Therefore, this study proposes a trunk axis fitting (TAF) algorithm to achieve precise arbor extraction.

2. Materials and Methods

2.1. Data Acquisition and Preprocessing

The two study sites selected are located in Shangri-La City, Yunnan Province, and Kunming City, Yunnan Province. Shangri-La is located in the northwest of Yunnan Province, in the hinterland of the Hengduan Mountains on the Tibetan Plateau, in the east of Diqing Tibetan Autonomous Prefecture, at the junction of the Yunnan, Sichuan, and Tibetan provinces. The overall terrain trend in the county is northwest high and southeast low, with an average elevation of 3459 m. The climate is diverse, with a narrow climate zone and distinct vertical climatic features. There are more than 10 vegetation types, mainly including temperate coniferous, cold temperate coniferous, warm temperate coniferous, deciduous broad-leaved, shrubs, and meadows. Representative coniferous tree species include Yunnan pine, high mountain pine, spruce, and fir [27]. Kunming is located in the central part of the Yunnan–Guizhou Plateau; the terrain is generally high in the north and low in the south, high in the center and low in the east and west, with an average elevation of 1891 m, belonging to the northern subtropical low-latitude highland mountain monsoon climate, with the smallest annual temperature difference in the country, forming the climatic feature of “four seasons like spring”, and enjoying the reputation of “Spring City”. In addition, Kunming City boasts rich botanical resources with various vegetation types, including subtropical evergreen broad-leaved forests, mixed coniferous and broad-leaved forests, and temperate coniferous. Over 400 species of flowers are cultivated in the city [28].

A Leica P40 3D laser scanner, manufactured in Heerbrugg Switzerland, was used to obtain the data. Data collection took place in September 2020 within the territory of Shangri-La City and in June 2021 within the Chenggong District of Kunming City. When using TLS to acquire point cloud data, in order to obtain more detailed information on the vertical structure of the forest and avoid the problem of missing data due to shading between trees, this experiment set up several scanning stations and targets in the sample plot. The aim was to provide accurate base station scan data and registration point coordinates for the subsequent stitching of point clouds. The principle for setting up targets is to ensure that the targets are mutually visible and that each scanning station can clearly see at least two targets. The first scanning station was generally set up at the center of the sample plot, where visibility of all targets could be achieved. Subsequent scanning stations need only have visibility of at least two targets [29]. The scan data from multiple stations were aligned using the targets as references and processed with Cyclone software version 9.1 to ultimately create a complete point cloud dataset of the sample plot. Compared to single-station scanning, the multi-station scanning method adopted in this study, despite increasing the time spent in terms of on-site measurements and subsequent processing steps, allows for the acquisition of more comprehensive three-dimensional data from the sample plot [30]. Detailed information for each study site is shown in

Table 1. Details of the study sites.

	Advantages Tree Species	Collection Date	Center Location of the Sample Site		Elevation Height/m
			Longitude	Latitude
Sample site 1	Natural forests of Yunnan pine	26 September 2020	99°40′34.97″ E	27°21′53.01″ N	2106
Sample site 2	Eucalyptus plantation	29 June 2021	102°46′23.64″ E	24°49′45.37″ N	1859

.

Sample plot 1 is a natural forest of Yunnan pine in Shangri-La with low undergrowth scrubs and clearly curved tree trunks. Sample plot 2 is situated in an artificial eucalyptus plantation in Kunming City, with slightly taller undergrowth shrubs and relatively straight tree trunks. The reason for selecting these two sample plots is that they contain different characteristics, including varying heights of undergrowth shrubs and degrees of curvature in the main tree trunks. This helps avoid the problem of uniformity in sample plots. The point cloud count for sample plot 1 is 1,099,072, while sample plot 2 has 352,057 points. The substantial difference in point cloud counts between the two plots allows for the validation of the stability of the TAF trunk extraction method proposed in this study.

The collected data need to be pre-processed using Cloud Compare software version 2.6.3 to perform subsample, cropping, and elevation normalization operations on the spliced data. To improve computational efficiency, this study employed the random method to subsample the point cloud data. The results of a random subsample are representative, allowing the samples to capture the characteristics of the entire dataset. Moreover, it helps reduce errors and improve the accuracy of the data. The sampling parameter was set to 50%, meaning that 50% of the points from the original point cloud were randomly selected for retention without discrimination, aiming to reduce the point cloud density [31], and by performing the aforementioned operations, we can obtain the decimated point cloud data. Since the scanned point cloud data range far exceeds the area of the study site, and forest plots are typically circular with radii ranging from 4 to 15 m [29], in order to improve the computational speed, the experiments were performed after data cropping. At this point, the data contained ground and off-ground points, and further filtering and normalization operations were needed to remove ground points and normalize the elevation of the off-ground points to facilitate subsequent experiments. Commonly used filtering methods include Irregular Triangular Network Progressive Enclosure Filtering [32], Morphological Filtering [33], and Cloth Simulation Filtering [34]. Among these methods, Cloth Simulation Filtering is widely used due to its ease of understanding and adaptability to various terrain conditions. This study employed this algorithm to filter the data. Figure 1 shows the schematic diagram of the two study sites and the point cloud data. Sample plot 1 is a natural Yunnan pine forest in Shangri-La, with obvious curved tree trunks and low understory scrub; sample plot 2 is an artificial eucalyptus forest in Kunming, with straight tree trunks and slightly higher understory scrub.

2.2. Research Methods

In the actual forest scene, the arbor trunks are not exactly growing vertically upwards, and the key to extracting the complete arbor trunks is to maximize the fitting of the bending trend of the arbors. Therefore, this study proposes a trunk extraction method by simulating the trend of tree growth. The specific steps include point cloud clustering, circle fitting, trunk searching, and arbor point cloud extraction. First, the point cloud data were segmented. The height of the lowest clear bole height was used as the dividing line to split the point cloud data into upper and lower parts. The upper layer was considered the point clouds of the tree canopy, and the lower layers were considered the point clouds of the main trunk and the point clouds of the understory scrub. To reduce the impact of canopy point cloud data on experimental speed, this study focused on processing the lower part of the point cloud. Next, the lower part of the point cloud was sliced into five equally spaced sections. The aim was to capture discontinuous trunk point cloud data and generate fitting circles at different heights. Next, clustering was performed on the centers of the fitted circles at different heights in the vertical direction. Circles with distances between their centers smaller than a certain threshold were identified as fitting circles for the same trunk at different heights, and they were assigned different numbers. Then, the centers of the fitting circles for the same trunk were connected in sequence, maximizing the fitting of the trunk’s curved growth trend. The average radius of the fitted circle of this trunk was then used as a threshold to filter out the point cloud of trunks whose distance from the central axis of the trunk was less than the threshold value. Finally, the trunk point cloud identified from the lower part of the point cloud dataset was merged with the canopy point cloud from the upper part. This process extracts the arbor trunks. The research route of this method is shown in Figure 2.

2.2.1. DBSCAN Clustering

This study involved two rounds of clustering. The first step involved clustering the sliced point cloud data horizontally. This aims to differentiate the point clouds of different trunks from the same layer of sliced point clouds. The second step involved clustering the centroids of the fitted circles generated after clustering the point clouds at different vertical heights. This aims to identify the centroids of the fitted circles corresponding to the same trunk. Both rounds of clustering used the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering method. It is a density-based spatial clustering algorithm proposed by Martin Ester and Hans-Peter Kriegel et al. [35] in 1996. This algorithm assumes that clusters can be defined based on the density of data points. By assigning closely connected samples to the same cluster, a clustering category was obtained. By further assigning all separately closely connected samples to different clusters, the final clustering result was obtained.

This method requires setting only a few parameters and is easy to operate. It includes two key parameters: one is $epsilon$, and the other is $minPts$. $epsilon$ defines the maximum radius, meaning that points within this radius can be recognized as the same cluster. The size of the radius set determines the size of the cluster; $minPts$ represents the minimum number of clustering points, meaning that there must be at least $minPts$ points within a neighborhood radius to be considered a cluster.

2.2.2. Least Squares Circle Fitting

The trunk shape in the point clouds after the first DBSCAN clustering should be approximately circular. According to the equation of a circle, the trunk point cloud slices can be expressed as shown in Equation (1).

$$\begin{array}{c}\begin{array}{c}{\left(x-A\right)}^2+{\left(y-B\right)}^2=r^2\end{array}\end{array}$$

(1)

where $\left(x,y\right)$ are the coordinates of the point cloud in the slice, $\left(A,B\right)$ are the coordinates of the center of the fitted circle, and $r$ is the radius of the fitted circle (in centimeters).

The purpose of least squares fitting is to find a set of samples that minimize the residual of the polynomial fit to that sample. The distance $d_i$ (in centimeters) from each sample data point to the center of the fitted circle can be expressed as shown in Equation (2).

$$\begin{array}{c}{d}_i=\sqrt{{\left(x_i-A\right)}^2+{\left(y_i-B\right)}^2}\end{array}$$

(2)

where the point ${(x}_i,y_i\left)\right(i\in (\mathrm{1,2},3,\cdots ,N))$ represents the coordinates of the point cloud in the slice.

The square of the distance from the point $(x_i,y_i)$ to the edge of the circle minus the square of the radius of the circle, denoted as ${\delta }_i$, is expressed as shown in Equation (3).

$$\begin{array}{cc}{\delta }_i& ={d_i}^2-r^2={\left(x_i-A\right)}^2+{\left(y_i-B\right)}^2-r^2\hfill \\ & ={x_i}^2+{y_i}^2-2A{x}_i-2B{y}_i+c\hfill \end{array}$$

(3)

Using the least squares method, the coordinates of the center $(A,B)$ and the radius $r$ are solved by minimizing the sum of squares of ${\delta }_i$, along with the iterative method. Thus, the fitted circles for each trunk can be obtained.

2.2.3. Scrub Point Cloud Filtering

Due to the presence of understory shrubs, the slicing operation will inevitably cut into the scrub point cloud. If the shrub point cloud is also clustered and fitted into circles, it will affect the accuracy of the subsequent extraction of the main trunk axis. Therefore, this study adopted the F-LS algorithm proposed by Yuncheng Deng et al. [36] to extract breast diameter parameters and remove understory shrub point clouds.

The F-LS algorithm is based on the principle that “the laser emitted by the LiDAR scanner does not penetrate objects, so the shape of the sliced trunk point cloud data should be a hollow circle, and there should be no point cloud within the circle”. It removes falsely detected fitting circles accordingly.

This study also borrowed from the algorithm the concept of removing falsely detected fitting circles for trunks. However, unlike the F-LS algorithm, this study selects based on the radius of the fitting circle. That is, when there are shrub point clouds in the point cloud slice, the radius of the fitted circle for shrub point clouds will be much larger than the radius of the fitted circle for trunk point clouds. When the radius of the fitted circle is larger than a certain threshold, this fitted circle is recognized as a scrub circle instead of a trunk circle, thus achieving the purpose of eliminating the scrub point cloud fitted circle.

2.2.4. Searching for Trunk Point Clouds Using Distance Threshold

After two clusters, five fitted circles of the main trunks of each single tree with different heights were obtained from this sample plot. By connecting the centers of the five fitted circles for each trunk in order of z-value size, the trunk axis of the tree can be obtained. Then, setting a threshold for point cloud selection, points whose distance to the main trunk axis was less than or equal to the threshold were considered trunk point clouds. A diagram showing the distance between the point clouds and the trunk axis is illustrated in Figure 3.

The distance $d$ between the point cloud $P$ and the central axis $l$ of the trunk is calculated as shown in Equation (4).

$$\begin{array}{c}d=\sqrt{{\left|\overrightarrow{AP}\right|}^2-{\left(\frac{\overrightarrow{AP}·\overrightarrow{AB}}{\left|\overrightarrow{AB}\right|}\right)}^2}\end{array}$$

(4)

where $P$ is a known point in space, $A,B$ are the fitted circle centers of two layers of neighboring point cloud slices, and the main trunk median axis $l$ connects points $A$ and $B$. The distance from point $P$ to the median axis $l$ is noted as $d$.

2.2.5. Accuracy Verification

Overall accuracy (OA) is a simple and commonly used metric to measure the performance of a classification model. It represents the proportion of correctly classified samples to the total number of samples, reflecting the overall performance of the model across all classification tasks. The overall accuracy can be calculated using the following formula:

$$\begin{array}{c}OverallAccuracy=\frac{TP+TN}{TP+TN+FP+FN}\end{array}$$

(5)

where $TP$ (True Positive) represents the number of samples correctly classified as positive. $TN$ (True Negative) represents the number of samples correctly classified as negative. $FP$ (False Positive) represents the number of negative samples incorrectly classified as positive. $FN$ (False Negative) represents the number of positive samples incorrectly classified as negative. The following is the same as here.

Relative error is a metric used to quantify the difference between a measured or predicted value and the true value. It represents the proportion of the error to the true value and is commonly used to assess the accuracy of measurements or predictions. A smaller value of relative error indicates that the measured or predicted value is closer to the true value, indicating higher accuracy. The formula for calculating relative error is as follows:

$$\begin{array}{c}RelativeError=\frac{\left|TrueValue-MeasuredValue\right|}{\left|TrueValue\right|}\end{array}$$

(6)

where $TrueValue$ is the actual value. $MeasuredValue$ is the measured value.

Recall, also known as sensitivity, is a metric that measures the ability of a model to correctly identify positive samples. It reflects the proportion of all actual positive samples that are correctly identified as positive. Recall is a key metric in classification evaluation, especially in scenarios like trunk extraction, where it is crucial to minimize missing positive samples. The formula for calculating recall is as follows:

$$\begin{array}{c}Recall=\frac{TP}{TP+FN}\end{array}$$

(7)

The Kappa coefficient is a statistical measure used to assess the performance of a classification model or classifier. It measures the agreement between the classification results and random classification results while excluding the influence of chance agreement. The Kappa coefficient is suitable for assessing the accuracy of classification tasks, particularly in situations featuring class imbalance. It provides a more reliable evaluation method than overall accuracy. For this study, where there is an imbalance between trunk point clouds and undergrowth point clouds, the Kappa coefficient can provide a more accurate assessment of the robustness of the method. The formula for calculating Kappa is as follows:

$$\begin{array}{c}Kappa=\frac{P_o-P_e}{1-P_e}\end{array}$$

(8)

where $P_o$ (Observed Agreement) represents the observed consistency, $P_e$ (Expected Agreement) represents the expected random agreement.

3. Results and Analysis

3.1. Fitting Results of the Trunk Axis

Firstly, the point cloud data are separated into upper and lower layers based on the height of the clear bole height for each study site. According to the methodology of this study, the lower layer point cloud data, after slicing for both study sites, are processed. The lower layer point cloud data are sliced into five equal intervals with equal thickness to obtain cross-sections of individual trees at different heights. Subsequently, after clustering and fitting circles for each slice of the point cloud, the fitting results of the trunk axis are shown in Figure 4.

From Figure 4, it can be observed that the fitting of the trunk axis accurately captures the trend of tree growth, even when the trunk is curved.

3.2. Results of Trunk Point Cloud Extraction

Based on the fitting results of the trunk center axis, the point cloud is traversed according to a certain threshold; the points whose distance from the trunk center axis is less than the threshold are extracted, and the results of the trunk point cloud extraction in the two sample plots are obtained. Based on the experimental results, it can be seen that this method has better results for the extraction of tree trunk point clouds in both sample plots, and the tree morphology has been completely preserved and can maximize the filtering of shrub and grass point clouds. The results of the main stem point cloud extraction for the two sample sites are shown in Figure 5.

After filtering by distance, the entire trunk point cloud of the trees can be obtained. Overall, the results look good, but quantitative descriptions of extraction accuracy are still lacking. In order to verify the accuracy of this method for extracting tree trunk point clouds, two sample plots were manually extracted in Cloud Compare software, and the number of trunk point clouds extracted from the two sample plots was counted and compared with the method in this study to verify the accuracy. The results are shown in

Table 2. Statistics of trunk point cloud extraction accuracy.

Sample Site	Number of Trunk Point Clouds Extracted Manually/pc	Number of Trunk Point Clouds Extracted by This Method/pc	Overall Accuracy	Relative Error	Recall	Kappa
1	787,284	784,262	99.73%	0.38%	99.62%	99.34%
2	319,991	319,534	99.87%	0.14%	99.86%	99.22%

.

According to the statistical results of the number of trunk point clouds extracted from the two sample sites, it can be seen that this method achieves high accuracy in extracting trunk point clouds. Moreover, the proposed TAF method still has certain advantages when the trunk grows in a curved manner. The experimental results of tree extraction obtained from the two sample sites are shown in Figure 6.

4. Discussion

The key aspects of the TAF method proposed here are the separation of the upper and lower layers of the point cloud, point cloud clustering, and the determination of the trunk axis. The basis for separating the upper and lower layers of the point cloud is the lowest clear bole height of the sample plot. The clear bole height is defined as the height from the ground to the first primary branch on the trunk. In this study, the point cloud is separated into upper and lower layers based on the lowest clear bole height determined by actual tree growth. Below this height, the trunk has no significant branches, and its shape is clear. Moreover, the height of the undergrowth is below the lowest clear bole height of the sample plot, which helps avoid intersecting with the undergrowth point clouds during the slicing process. One purpose of this step is to remove the influence of canopy point clouds, thereby reducing the data volume and maximizing computational efficiency. The second purpose is that the separated lower layer data consist of branch-free trunk point clouds and undergrowth point clouds, providing clearer raw data for subsequent steps [5].

For the clustering method, this study used DBSCAN. Compared to other common clustering methods, the DBSCAN clustering method can cluster point cloud data of arbitrary shapes and handle large datasets [37]. It has a weaker subjective influence on the clustering results, with parameters that are easy to set. This method has been applied across multiple disciplines. It has shown better results in building point cloud classification, point target clustering in satellite field of view angles, and clustering other two-dimensional data [38,39,40]. Wang et al. [41] improved the DBSCAN algorithm by automatically calculating key parameters based on the data characteristics. Their research evaluated this method on different point cloud datasets, showing that it achieves high accuracy in point cloud segmentation.

In addition to the DBSCAN algorithm, K-means can also be used for point cloud clustering. However, K-means clustering is more focused on extracting the trunk diameter, while the DBSCAN algorithm is suitable for handling datasets containing noise, irregular shapes, and clusters with large differences in size. The key to the K-means clustering method lies in determining the value of k and selecting the initial cluster centers. The value of k needs to be predetermined based on prior information, while the initial cluster centers are the centroids preset by the K-means algorithm for each cluster. These two parameters greatly influence the effectiveness of clustering. Weifeng Ma et al. [42] proposed an improved K-means algorithm that adaptively determines the number of trees in a plot based on the constraints of tree spacing using the inflection point method. This method is primarily focused on the extraction of high-precision breast height diameter parameters of trees. Since the focus of the two point cloud clustering methods is different, the DBSCAN clustering algorithm used in this study and the parameters were manually adjusted according to the actual scenarios to achieve optimal extraction.

4.1. Horizontal Clustering

When using the DBSCAN method for point cloud clustering, the values of $epsilon$ (the $epsilon$ neighborhood of point $p$) and $minPts$ (the minimum number of points within a certain neighborhood) are crucial. The clusters formed are the maximal sets of density-connected points, meaning that the density of points within a cluster is much higher than outside of it [37]. The $minPts$ parameter affects the size of the clusters. To test the accuracy of the DBSCAN algorithm in clustering point clouds, we conducted multiple experiments to determine the most suitable parameters ($epsilon$ and $minPts$) for clustering point cloud slices horizontally.

Since the main purpose of this step is to cluster the trunk point cloud horizontally, in the point cloud data, the distance between the closest two points on the same tree does not exceed 5 cm. Based on the main trunk diameter and point cloud density characteristics of the two sample plots, $epsilon$ was set to 0.05 and $minPts$ was set to 10, and the experiments on the two sample plots achieved better clustering results. The results of the slice clustering on the two sample plots are shown in Figure 7.

4.2. Vertical Trunk Axis Determination

After clustering the point cloud horizontally, fitting circles were generated at five different heights for each trunk. Subsequently, vertical clustering of the fitted circle centers was performed using the DBSCAN algorithm on the sliced data to obtain the trunk axis. At this stage, the parameter settings are related to the curvature of individual trees. In sample site 1, where the trunks are more curved, different parameter values may be chosen compared to sample site 2, where the trunks grow relatively straight. Therefore, when clustering in the vertical direction, the values of $epsilon$ are set to 0.15 and 0.1, respectively. Here, the curvature of the main trunk is taken into account. If the main trunk grows straight upwards, the distance between the centers of the fitting circles of the same main trunk in the vertical direction should be similar. However, if the main trunk grows in a curved manner, there will be a certain distance between the centers of the fitting circles in the vertical direction. Considering that the shading of taller shrubs or obstacles, which results in less point cloud data in part of the main trunk, may make a layer of slices lost, resulting in discontinuous point cloud slices, in order to maximize the retention of point cloud data in the rest of the main trunk, the $minPts$ of the two sample plots were set to an integer number less than 5. Since the setting of the $epsilon$ value depends on the curvature of the trees and follows a certain pattern, we will only discuss the influence of $minPts$ on the clustering results here. Since there are five layers of slices and the extraction of the main trunk median requires the connection of the circle centers of each layer of slices, the $minPts$ were set to 2 and 3, respectively, and applied to the two sample plots to discuss the effects of the $minPts$ values on the clustering results, respectively. The results of trunk fitting and point cloud extraction are shown in Figure 8 and Figure 9, and the statistics of the number of sample point clouds are shown in Figure 10.

The experimental results from both sites indicate that when $minPts$ is set to 2 and 3, respectively, the fitting of the main trunk axis is satisfactory. However, when $minPts$ is set to 2, some low shrubs or incomplete main trunks may be fitted as a single tree, which can affect the experimental results during subsequent point cloud filtering. Setting $minPts$ to 3 helps avoid this issue more effectively. Based on the statistical results of the number of main trunk point cloud extractions with different parameters set for the two plots, it can be observed that when $minPts$ is set to 2, the number of point cloud extractions exceeds the standard quantity. The reason is that the $minPts$ setting is too small to recognize a portion of the scrub fitting circle as the main trunk fitting circle, so the scrub point clouds will be retained when performing threshold filtering. Therefore, when $minPts$ is set to 3, the extracted point cloud quantity is closest to the actual value. Hence, setting $minPts$ to 3 is the most suitable choice.

5. Conclusions

Focusing on the difficulties and low accuracy relating to arbor extraction in natural forests, this study achieved arbor extraction in two sample plots with different tree species and different degrees of trunk curvature using TAF method. From the results, the extraction of arbor point clouds in both sample plots achieved an accuracy of over 99%. In sample plot 1, where the trunks grow with significant curvature, the greatest point cloud loss occurred in areas where there was a sudden change in the growth direction between two adjacent slices. Due to the large distance between the centers of the fitted circles in adjacent layers, these points were not grouped into the same cluster. Consequently, this portion of the point cloud was missed during distance-based filtering. In the entire plot, only one tree trunk appears to have some noticeable loss. The TAF tree extraction method proposed in this study is more dominant in samples with curved trunk growth, maximizes the preservation of the trunk point cloud, and has fewer setup parameters.

Accurate arbor extraction results can provide technical support for subsequent tree parameter extraction in natural forests and provide scientific guidance for forest resource investigations and efficient forest management decision-making. However, because it involves clustering, different parameters need to be set according to the characteristics of different sample plots, so when the understory scrub is high in height and grows interspersed with the canopy, the inability to accurately separate the canopy point cloud from the shrub point cloud will have an impact on the clustering results of the point cloud, which, in turn, will affect the extraction results of the point cloud of the main trunk of the tree. Subsequent studies will focus on complex sample plots with interspersed growth of trees and shrubs to improve the applicability of this method for tree trunk extraction experiments under different understory conditions.