Estimation of Diameter at Breast Height in Tropical Forests Based on Terrestrial Laser Scanning and Shape Diameter Function

Abstract

Estimating forest carbon content typically requires the precise measurement of the trees’ diameter at breast height (DBH), which is crucial for maintaining the health and sustainability of natural forests. Currently, Terrestrial Laser Scanning (TLS) systems are commonly used to acquire forest point cloud data for DBH estimation. However, traditional circular fitting methods face challenges such as a reliance on forest elevation normalization and underfitting of large trees. This study explores a novel approach, the Shape Diameter Function (SDF) algorithm model, leveraging the advantages of three-dimensional point cloud information to replace traditional circular fitting methods. This study employed a parallel approach, combining the Digital Elevation Model (DEM) with Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to segment tree point clouds at breast height. Additionally, a point cloud SDF algorithm based on an octree structure was proposed to accurately estimate individual tree DBH. The research data were obtained from tropical secondary forests located in Cameroon, Peru, Indonesia, and Guyana, with forest ground point cloud data acquired via TLS. The experimental results demonstrated the superior performance of the SDF algorithm in estimating DBH. Compared with the Random Sample Consensus (RANSAC) and Hough transform methods, the Root Mean Square Error (RMSE) decreased by 28.1% and 47.8%, respectively. Particularly in estimating DBH for large trees, the SDF algorithm exhibited smaller errors, indicating a closer alignment between the estimated individual tree DBH values and those obtained from manual measurements. This study presented a more accurate DBH estimation algorithm, contributing to the exploration of improved forest carbon content estimation methods.

1. Introduction

Forest ecosystems are fundamental components of terrestrial ecology, and continuous monitoring of wildlife and plant growth and structural changes is crucial. In forestry resource assessment, Diameter at Breast Height (DBH) refers to the diameter size at 1.3 m above-ground. It is commonly used to measure tree size and growth status within forests. DBH is closely related not only to the crown size and wood volume of trees but also to estimating their accumulation and biomass [1]. Emerging measurement equipment such as electronic theodolites [2], total stations [3], and CCD total stations [4] have been applied in the field of DBH measurement. However, measuring each tree individually poses challenges for achieving batch automation in DBH estimation.

In recent years, rapid advancements in Three-Dimensional (3D) laser scanning technology have enabled the non-contact acquisition of the structural parameters of forest trees. Terrestrial Laser Scanning (TLS) devices emit laser pulses towards objects’ surfaces, which, upon diffuse reflection, return almost along the same path to the receiver, acquiring a 3D point cloud of the object. This innovative method extends high-precision spatial analysis into the third dimension, providing point coordinates within either local or global coordinate systems [5]. Terrestrial platforms have become one of the platforms for LIDAR, forming a laser scanning system, with the primary instrument being TLS [6].

TLS obtains the 3D shape of trees by scanning their surfaces, offering the advantages of high-speed performance and high spatial resolution. Consequently, it provides better coverage of tree trunks when estimating woody components [7]. Tree reconstructions within this system come from dense point clouds and have been widely applied in various research fields such as natural disasters [8,9,10], geographic sciences [11,12], vegetation monitoring [13,14], map generation [14,15], and forest planning [16,17]. This process ultimately achieves automation in data collection, aiding in eliminating potential human errors or adverse conditions that could occur in fieldwork [18].

In recent years, scholars have extensively researched the utilization of TLS point clouds to obtain accurate estimations of DBH, demonstrating their remarkable precision in measurements. Numerous researchers have suggested diverse methods for estimating tree DBH parameters, primarily employing Hough transform algorithms.

The preprocessed forest point cloud data are typically provided to the DBH estimation algorithm. Core steps include point cloud registration, forest elevation normalization [19], individual tree point cloud clustering, and stratified rasterization. The Hough transform [20] determines the DBH value by fitting circular features in individual tree point clouds based on set criteria. Nevertheless, converting point cloud data to raster data in these methods invariably leads to accuracy loss, affecting the final extraction results.

Notably, Calders et al. [21] and Tansey et al. [22] employed a least squares circle fitting method for individual tree point cloud extractions to estimate DBH. However, their methods rely heavily on effective elevation normalization in forest areas, necessitating the removal of terrain-induced tilts in tree point clouds. In these approaches, the lowest point in the segmentation results of individual trees serves as the starting point for DBH measurement, potentially reducing DBH calculation accuracy.

In addressing these challenges, Olofsson et al. [23] enhanced the Random Sample Consensus (RANSAC) model-based algorithm, refining the fitting of two-dimensional circles and extracting tree DBH values accordingly. However, in cases where data collection encompasses complex terrains, terrain normalization may not adequately adapt to these variations, causing point cloud tilts. Traditional circular fitting methods are sensitive to these tilts when projecting tree stem DBH in two dimensions, introducing accuracy errors. Moreover, for trees with complex shapes, such as irregularly shaped trunks, circular fitting methods exhibit substantial accuracy errors.

To address these limitations, we proposed a novel approach for estimating individual tree DBH, leveraging the 3D point cloud SDF. The method first estimates surface normals, then for each point, computes the penetration length along the negative normal direction, which is towards the inside of the object. The SDF value of the point cloud is calculated based on a weighted voting rule and represented as the DBH of the tree. Compared to traditional circular fitting methods, the SDF algorithm effectively addresses point cloud tilt arising from elevation distortion and is adaptable to irregularly shaped tree trunks, particularly in forest plots featuring tropical large-tree forests.

2. Materials and Methods

2.1. Datasets

Large trees within tropical environments exhibit intricate morphologies and various terrain structures, emphasizing the significance of accurate diameter estimation methods. This study utilized datasets from two tropical rainforests, acquired using different TLS scanners. Dataset 1 was collected from a tropical forest in Cameroon, Africa, employing the Leica Scanstation C10 (manufactured by Leica Geosystems AG, Heerbrugg, Switzerland). Dataset 2 comprised large tropical trees from Peru, Indonesia, and Guyana, captured using the RIEGL VZ-400 3D^® scanner (manufactured by RIEGL Laser Measurement Systems Ltd. in Horn, Austria). Both datasets comprised TLS point clouds and measurement data obtained after tree felling, detailed in Figure 1. These trees represent substantial species indigenous to tropical regions.

2.1.1. The Dataset of Large Tropical Trees in Cameroon, Africa

Takoudjou et al. [24], from the University of Yaoundé in Cameroon, provided this dataset. The trees come from the eastern part of Cameroon, Africa (Latitude 4°02′20.77″ N, Longitude 14°55′49.15″ E). The forest in this region belongs to a semi-deciduous type, primarily consisting of trees from the Malvaceae and Musaceae families. The average annual temperature is approximately 24 °C. The area experiences an annual precipitation ranging from 1500 to 2000 mm, with distinct dry seasons. The elevation ranges between 600 and 700 m. The dataset comprises the TLS point clouds of 61 trees, along with corresponding measurements post-felling. These trees underwent scanning, felling, and weighing. Among all samples, the maximum individual tree DBH reached 180.3 cm. There was no obstruction or interference from vines or other vegetation hindering the observation of the trees.

(1)

TLS Point Clouds

The dataset includes the TLS point clouds of 61 trees, with each tree’s point cloud existing independently. The tree scanning process utilized the Leica Scanstation C10. This scanner operates on a time-of-flight scanning system with a working wavelength of 532 nanometers. The scanning speed achieves 50,000 points per second, maintaining a scan resolution configured for a point spacing of 0.05 m at a distance of 100 m. The minimum allowed scan point spacing is less than 1 mm. After clearing some understory vegetation and removing obstructing shrubs, the scanner conducted at least three scans for each tree.

(2)

Manual Measurement Data

These trees were scanned, felled, and manually measured for DBH, and the results were recorded in the dataset, indicating an average DBH of 58.37 cm.

2.1.2. The Dataset of Large Tropical Trees in Peru, Indonesia, and Guyana

De Tanago et al. [25] from Wageningen University provided a tree TLS point cloud dataset collected in Peru, Indonesia, and Guyana. These regions experience an annual precipitation between 2000 to 2700 mm, and the elevation ranges between 22 and 312 m. The dataset comprises the TLS data of 29 large individual tropical trees, along with manual measurement data and forest survey data.

(1)

TLS Point Clouds

The dataset offers the TLS point clouds of 29 large tropical trees. The tree point clouds were collected using the RIEGL VZ-400 3D^® terrestrial laser scanner. The laser scanner conducted scans across 29 sample plots, and subsequently, the largest tree within each plot was felled for measurement, with the maximum DBH measured at 127.6 cm. Spatial designs of the plots aimed to cover the anticipated areas of harvested trees: 30 × 50 m in Peru and 30 × 40 m in Indonesia and Guyana.

(2)

Manual Measurement Data

Following the TLS of forest trees, the specimens underwent felling. Preceding this procedure, researchers meticulously gauged the DBH of each tree by utilizing forestry calipers, yielding an average DBH measurement of 73.5 cm.

2.2. Methods

2.2.1. Estimation of Tree DBH Algorithm Implementation

Figure 2 depicts the algorithmic workflow. The algorithm comprises two main modules: the TLS point cloud pre-processing module and the tree DBH measurement module. The TLS point cloud pre-processing module is responsible for projecting the laser equipment onto the tree surface, capturing point clouds of both the forest area and individual trees, and removing the forest ground points using elevation normalization to extract the specific point cloud data. The primary task of the tree DBH measurement module involves segmenting and processing data, including trunk extraction using a method parallel to the forest DEM, employing DBSCAN [26] for segmenting and clustering the point cloud at the Tree’s Breast Height (TBH), and computing the tree DBH using the SDF algorithm. This process yields accurate tree DBH parameters.

2.2.2. Extraction and Clustering of Point Clouds at the TBH

The study utilized a point cloud processing software called CloudCompare (version: 2.12.4) to import and visualize TLS point cloud data, normalized the elevation of the point cloud, and generated a DEM to determine the ground positions and tree trunk positions within the forest, as shown in Figure 3.

We proposed a method combining parallel DEM [27] and DBSCAN clustering for extracting the point cloud at the TBH. Initially, a parallel surface was established based on the forest DEM, positioned 1.3 m above the forest DEM surface, with a set surface thickness d. The area where this surface intersected with the tree point cloud was extracted, indicating the tree DBH region. As shown in Figure 4, the gray plane represents the constructed forest DEM grid, while the green plane represents a parallel plane located 1.3 m away from it.

After extracting the point clouds at the tree DBH positions within the forest, DBSCAN clustering was applied for point cloud segmentation. This step assists in segmenting the point cloud at the TBH of different trees in the forest, thereby facilitating subsequent DBH calculations. Figure 5 illustrates the clustered point cloud at the TBH, with different colors indicating varying heights from the ground. Blue indicates near-ground, while red represents far-ground.

2.2.3. Tree DBH Algorithm Based on SDF

SDF [28] is a mathematical tool used to describe the local thickness and shape attributes of 3D objects. However, the SDF algorithm cannot be directly applied to point cloud data, mainly because the algorithm requires input data to obtain the characteristics of closed surfaces in order to precisely determine the intersection points needed for the ray tracing process. However, discrete point cloud data lack these closed surface features, often resulting in rays that do not intersect with the surface during computation. Therefore, improvements to the SDF algorithm [29] are necessary. As a solution, a point cloud octree-based SDF algorithm was proposed to effectively estimate DBH.

After completing the outlined procedures in Section 2.2.2, point clouds corresponding to the TBH were obtained. This dataset underwent organization into an octree structure, depicted in Figure 6, to construct an octree model tailored to the specific point cloud data of each tree. Progressively, the iterative depth of the octree expanded from a to e, culminating in the formation of a closed surface that represents the point cloud.

Each octree node was searched; whenever a node contained at least one point cloud data point, that node and its child nodes were created. Every octree grid (octree leaf node) is designated by an identification value known as a “key”, utilized to ascertain a point’s location within the octree grid. Next, the normal vector at point P was estimated, acquiring the normal vector N_p at point P. A ray, denoted as L, was emitted in the opposite direction of the N_p vector from point P. The coordinates of the endpoint of ray L are calculated according to Formula (1), where N_p represents the unit vector of the surface normal at point P, step denotes the distance of each ray extension, and m indicates the number of ray extensions.

$$P^{’}(x,y,z)=P(x,y,z)+N_p\times step\times m$$

(1)

The step value, as defined in Formula (2), is contingent on the cell size C, which denotes the edge length of the grid cube within the octree leaf node. Here, L_p refers to the ray precision coefficient, determining the rate at which the ray L extends along the normal direction. It ensures that with each extension, the ray endpoint remains within the subsequent adjacent octree grid without surpassing a displacement of one grid body. Within an octree grid body, the maximum distance amounts to √3 times the cell size. Consequently, the precision coefficient for the ray should be set between 0 and √3. Optimal precision typically ranges around 0.8, as smaller values might decrease ray search efficiency, while excessively high values might slightly compromise search accuracy.

$$step=C\times L_p$$

(2)

Continuously monitor the identifier key of the octree leaf node where the endpoint P’ of the ray resides to ascertain if P’ enters the subsequent node. As the ray L extends, its progression involves checking whether the endpoint P’ remains enclosed within the octree nodes, thereby determining if ray L reaches the opposite surface of the point cloud.

As shown in Figure 7a, the ray extends from point P during the computation of the DBH. It continuously searches for grids containing the point cloud. If the ray fails to locate a grid containing the point cloud, it counts the number of grids traversed by the ray as n. Formula (3) is employed to compute the penetration distance R_i of the ray.

$$R_i=n\times C$$

(3)

To enhance the precision of SDF computations and improve robustness against noise, a collection of rays within a cone is introduced as a replacement for a single ray L. In Figure 7b, originating from point P, this collection of rays falls within a cone. Each ray L within this set extends from point P, with the angle θ between L and N_p being less than half the cone angle α. Smaller-angle rays contribute more significantly to the SDF calculation at point P.

Utilizing Formula (4), a dynamic weight allocation is performed for the penetration distances of the ray set based on the magnitude of their angles. The weight of the ray is represented as:

$${\omega }_i={\left(cos{\theta }_i\right)}^{\mu }$$

(4)

The apex angle α of the cone centered at point P is divided into ten equal parts, and different weights are assigned to rays falling into various regions on the cone base, as depicted in Figure 8. The region numbers indicate where rays land as the angle θ increases. Considering α = π/3 and various values,

Table 1. Weighting schemes for different μ values when α = π/3.

μ	SDF Ray Weighted Region
	1	2	3	4	5	6	7	8	9	10
0.5	0.9993	0.9973	0.9938	0.989	0.9828	0.9752	0.9662	0.9558	0.9439	0.9306
1.0	0.9986	0.9945	0.9877	0.9781	0.9659	0.9511	0.9336	0.9135	0.891	0.866
1.5	0.9979	0.9918	0.9816	0.9674	0.9493	0.9275	0.902	0.8732	0.841	0.8059
2.0	0.9973	0.9891	0.9755	0.9568	0.933	0.9045	0.8716	0.8346	0.7939	0.75

presents four weight schemes.

Finally, utilize Formula (5) to calculate the SDF value of point P, where m represents the number of SDF rays for point P.

$${SDF}_p=\frac{\sum _{i=1}^m({\omega }_i\times cos{\theta }_i\times R_i)}{m}$$

(5)

For each point, calculate the SDF value of the point cloud at the TBH. Obtain the mean SDF value of this point set as the DBH, as expressed in Formula (6).

$$DBH=\frac{\sum _{i=1}^n{SDF}_i}{n}$$

(6)

2.2.4. Estimation of DBH

The study utilized TLS point cloud data from two datasets as detailed in Section 2.1. The SDF algorithm was applied to compute the DBH of trees within these regions. To validate and compare the calculated results from the SDF algorithm, two DBH calculation methods were employed for comparison. Both Hough transform and the RANSAC algorithm are utilized, employing a circle fitting method to estimate the DBH.

2.2.5. Precision Evaluation Method

Formulas (7)–(9) are employed to calculate the RMSE, R², and absolute error b for estimated DBH against the corresponding reference values.

R² reflects the degree of correlation between the actual values for individual tree DBH and the computed values derived from TLS point clouds. When R² approaches 1, it indicates a stronger correlation between the data sets. Its calculation formula is as follows:

$$R^2=\frac{\sum _{i=1}^n(x_i-{\overline{x}}_i)(X_i-{\overline{X}}_i)}{\sqrt{\sum _{i=1}^n{(x_i-{\overline{x}}_i)}^2}\sqrt{\sum _{i=1}^n{(X_i-{\overline{X}}_i)}^2}}$$

(7)

In Formula (7): $x_i$ stands for the actual values of individual tree DBH from manual measurements; $\overline{x_i}$ denotes the mean value of $x_i$; $X_i$ represents the DBH measured by TLS; ${\overline{X}}_i$ signifies the mean value of $X_i$; and n represents the number of sampled trees studied.

RMSE quantifies the discrepancy between the actual DBH values and the DBH estimated by TLS data. A smaller RMSE value indicates that the DBH measurement is closer to the actual values, reflecting a more accurate estimation of DBH by the algorithm. It is calculated as follows:

$$RMSE=\sqrt{\frac{\sum _{i=1}^n{(x_i-X_i)}^2}{n}}$$

(8)

In Formula (8): RMSE stands for Root Mean Square Error; $x_i$ represents the manual measurements of individual tree DBH; $X_i$ represents the DBH measured by TLS; n represents the total number of trees.

The absolute error b is the absolute difference between the true DBH obtained through manual measurements and the DBH estimated from the TLS point cloud. A smaller b value signifies a stronger predictive capability of the algorithm. The calculation is as follows.

$$b=|x-x’|$$

(9)

In Formula (9): b represents the absolute error; x stands for the actual value obtained from manual measurements; x’ denotes the DBH estimated from TLS point cloud.

The relative error r is defined as the ratio of the absolute error b to the true DBH obtained by manual measurement. The average relative error r’ represents the average of the total absolute errors in the dataset. Both r and r’ indicate the degree of deviation from the true values, with smaller values indicating a stronger predictive capability of the algorithm. The calculation methods are as follows.

$$r=\frac{b}{X}$$

(10)

$$r\prime =\frac{\sum _{i=1}^n{r}_i}{n}$$

(11)

In Formula (10): b represents the absolute error; X represents the manually measured DBH value.

In Formula (11): r_i represents the relative error value in the dataset, where i is the index number, and n represents the total number of trees.

3. Results and Discussion

3.1. Comparison and Analysis of Errors

During the execution of the SDF algorithm, the surface thickness d of the parallel forest DEM was set to 0.04 m. This indicates that with the forest ground DEM as a reference, the tree point cloud within a distance of 1.28 to 1.32 m has been selected. The search neighborhood radius of the DBSCAN clustering was defined as 0.08 m, while the core point parameter ‘min_samples’ was set to 50. A dataset comprising measurements of DBH from 90 felled tropical trees was used as a reference to validate the accuracy of SDF in extracting DBH. Deviation analysis of the calculated tree diameter at breast height (DBH) results using three different methods was conducted across two datasets. Absolute error b was computed and analyzed according to Formula (9), while relative error r was calculated based on Formulas (10) and (11). The results depicted in

Table 2. Comparison of DBH estimation deviations among algorithms.

Datasets	Methods	Absolute Error/cm			Relative Error
		Max	Min	Mean	Max	Min	Mean
1	Hough Transform	22.7	0.59	5.77	14.80%	0.89%	11.77%
	RANSAC Algorithm	16.9	0.2	3.52	22.94%	1.42%	8.78%
	SDF Algorithm	7.79	0.19	3.14	11.01%	0.41%	7.56%
2	Hough Transform	8.79	0.5	4	15.49%	1.23%	6.01%
	RANSAC Algorithm	18.2	0.4	4.2	16.22%	0.55%	5.72%
	SDF Algorithm	7.39	0.09	3.42	9.20%	0.13%	5.25%

reveal significant discrepancies in the deviation among the three methods.

In dataset 1, the Hough transform [22] showed an absolute error of 22.70 cm, which was the largest among the three methods across datasets. The relative error of the maximum bias of the RANSAC [30] algorithm is the largest in both datasets. In contrast, the SDF algorithm consistently exhibited the smallest maximum deviation across both datasets. The minimum deviation values of the three methods across both datasets were relatively consistent, all remaining under 0.6 cm. The mean deviations of these methods were all less than 6 cm, while the point cloud-based SDF method’s mean deviation was less than 3.5 cm. Meanwhile, in terms of relative error outcomes, it becomes evident that the SDF algorithm notably mitigates errors associated with larger trees, demonstrating an overall superior performance when compared to the remaining two algorithms.

3.2. Regression Analysis of DBH Measurement Results

The distribution of DBH measurement values compared to the actual DBH was statistically analyzed for two datasets, followed by regression analysis. As depicted in Figure 9, Figure 10 and Figure 11, the comparison illustrates the linear regression and error comparison between the DBH extraction values from three algorithms and the manually measured actual DBH. Dataset 1 is represented as blue circles in the graph, indicating the 61 African Cameroon tropical tree dataset mentioned in Section 2.1.1, while Dataset 2 is depicted by red triangle markers, representing the 29 tropical trees from Peru, Indonesia, and Guyana highlighted in Section 2.1.2. The R² values for the DBH regression models are 0.9660, 0.9817, and 0.9898, indicating a strong correlation between the actual DBH from manual measurements and the calculated DBH from TLS. The RMSE for DBH is 7.0234 cm, 5.1041 cm, and 3.6703 cm, respectively. Notably, the SDF algorithm demonstrates an RMSE improvement of 28.1% and 47.8% compared to the other two algorithms.

According to the analysis of deviation results, it was evident that the algorithm of the Hough transform exhibits larger measurement errors in two specific datasets compared to the other two methods. Similar to the RANSAC algorithm, in these two datasets, the measurement errors for larger DBH individual trees show a greater deviation. Particularly in the case of trees with measured DBH ranging from 125 cm to 181 cm, these two algorithms demonstrate larger errors. The SDF algorithm, however, maintains smaller errors in the measurement of larger DBH individual trees, displaying better accuracy and robustness. This could be attributed to the fact that the Hough transform and the RANSAC algorithm employ methods based on two-dimensional projection and circular fitting, causing skewed distortions in the individual tree TLS data when extracting DEM from the forest for elevation normalization.

Additionally, algorithms based on two-dimensional circular fitting exhibit significant errors when dealing with irregularly shaped trees, with these errors increasing as the tree’s DBH grows. However, the SDF algorithm utilizes the 3D spatial neighborhood information of point clouds, avoiding the two-dimensional projection errors caused by elevation normalization-induced point cloud tilt. It adopts a non-circular fitting approach, eliminating errors arising from irregular tree shapes, hence performing better in estimating DBH for irregularly shaped tree trunks.

4. Conclusions

Focused on tropical trees, experimental data were obtained using Leica Scanstation C10 and RIEGL VZ-400 3D terrestrial laser scanners to acquire forest point cloud data. The point cloud data underwent DBSCAN clustering segmentation to extract individual tree point clouds. Addressing the issue of extracting DBH from individual tree point clouds, a Shape Diameter Function algorithm was proposed. The precision performance of two typical circular fitting-based DBH estimation algorithms (Hough transform, RANSAC algorithm) and the point cloud SDF algorithm were evaluated under two tropical tree datasets. Through the analysis of experimental data, a comprehensive exploration was conducted on the precision performance and adaptability of DBH estimation algorithms for various individual tree TLS point cloud data.

The results of the linear regression analysis revealed a significant correlation between the measured data and the data computed by the point cloud algorithms, yielding R² values of 0.9660, 0.9817, and 0.9898, respectively. This suggests that TLS individual tree point cloud DBH extraction technology could effectively replace manual measurements for data collection purposes.

The DBH extraction precision of the proposed point cloud SDF algorithm was least affected by the irregular shapes of large trees and elevation normalization biases. In complex forest terrain and data involving larger DBH trees, the relative error of SDF for large trees’ DBH is 9.2% and 11.01%, which is lower than the other two algorithms. The SDF algorithm consistently achieved higher precision in DBH estimation. Comparisons of the Hough transform algorithm and RANSAC algorithm on a large tropical tree dataset demonstrated that this algorithm’s overall precision performance surpassed the other two methods (R² = 0.9898, RMSE = 3.6703 cm). The point cloud SDF algorithm’s utilization of non-circular fitting addressed issues of errors caused by traditional circular fitting methods when dealing with irregular trunk shapes and potential point cloud skewness due to elevation normalization, as well as performing better in the task of estimating DBH for large trees.

The DBH estimation work based on TLS point cloud data offers new methodologies. However, the study’s results still presented some issues that could be further researched:

(1)

The research results were tailored to datasets of tropical trees; future studies should aim to validate the algorithm’s applicability across a broader range of forest types.

(2)

SDF algorithm-based DBH estimation typically requires relatively complete point cloud data. TLS point cloud data necessitates registration before it can be used for DBH estimation. Future improvements are needed for SDF DBH estimation algorithms targeting incomplete TLS individual tree point cloud data.

(3)

The manual measurements of irregular tree trunks’ DBH are often not sufficiently accurate. Comparing the effectiveness of the point cloud-based SDF algorithm and manual measurements could be a focus of future research.