Estimating Forest Structure from UAV-Mounted LiDAR Point Cloud Using Machine Learning

: Monitoring the structure of forest stands is of high importance for forest managers to help them in maintaining ecosystem services. For that purpose, Unmanned Aerial Vehicles (UAVs) open new prospects, especially in combination with Light Detection and Ranging (LiDAR) technology. Indeed, the shorter distance from the Earth’s surface signiﬁcantly increases the point density beneath the canopy, thus offering new possibilities for the extraction of the underlying semantics. For example, tree stems can now be captured with sufﬁcient detail, which is a gateway to accurately locating trees and directly retrieving metrics—e.g., the Diameter at Breast Height (DBH). Current practices usually require numerous site-speciﬁc parameters, which may preclude their use when applied beyond their initial application context. To overcome this shortcoming, the machine learning Hierarchical Density-Based Spatial Clustering of Application of Noise (HDBSCAN) clustering algorithm was further improved and implemented to segment tree stems. Afterwards, Principal Component Analysis (PCA) was applied to extract tree stem orientation for subsequent DBH estimation. This workﬂow was then validated using LiDAR point clouds collected in a temperate deciduous closed-canopy forest stand during the leaf-on and leaf-off seasons, along with multiple scanning angle ranges. The results show that the proposed methodology can correctly detect up to 82% of tree stems (with a precision of 98%) during the leaf-off season and have a Maximum Scanning Angle Range (MSAR) of 75 degrees, without having to set up any site-speciﬁc parameters for the segmentation procedure. In the future, our method could then minimize the omission and commission errors when initially detecting trees, along with assisting further tree metrics retrieval. Finally, this research shows that, under the study conditions, the point density within an approximately 1.3-meter height above the ground remains low within closed-canopy forest stands even during the leaf-off season, thus restricting the accurate estimation of the DBH. As a result, autonomous UAVs that can both ﬂy above and under the canopy provide a clear opportunity to achieve this purpose.


Context
Forests are critical natural resources for human life and wildlife, as they sustain and protect biodiversity, supply multiple ecosystem services, and mitigate the impacts of climate change [1][2][3][4][5]. Hence, monitoring this terrestrial ecosystem is of utmost importance, as deforestation releases significant amounts of greenhouse gases, alters the surface energy and the water balance, and causes a loss of species diversity [6]. To ensure the preservation of such habitats, their monitoring and management have been of public interest for both political decision-makers and conservationists in the assessment of implemented measures along with resource-dependent companies and localities (in the quantitative estimation of harvests) [7].
In that respect, remote sensing (since the middle of the 20th century) has been a tremendous asset, as it drastically reduces fieldwork, which is inherently labor-and costintensive [8]. Furthermore, it goes beyond the sampling plot-based measurement strategy and therefore ensures a spatially continuous forest monitoring [9]. Afterwards, it provides information across a wide range of temporal and spatial scales through the great variety of sensors and carrying platforms [10]. Thereon, the Unmanned Aerial Vehicle (UAV), commonly referred to as a "drone", is a promising technology in more than one respect. First of all, it can use both active and passive sensors [11]. Then, it delivers data with a very high spatial resolution due to the low altitude at which the aircraft flies [12]. This is even emphasized with a higher flexibility in data acquisition, as UAV supports lower flying speeds and accommodates almost any trajectory requirements (especially with its single and multi-rotor configurations) [13]. In addition, it paves the way to analyses with a very high temporal resolution, since it reduces operational and legal flying constraints, thus increasing the data acquisition frequency [14,15]. Finally, UAVs are a relatively lowcost solution and can therefore meet a wide diversity of application fields [16].

Challenges and Research Objectives
In the past ten years, several scientific studies have been conducted to optimize UAV flight planning (e.g., for the detection and avoidance of physical obstacles, increasing a 3D object's coverage, taking into account airplane restrictions and drone energy consumption [17][18][19][20][21][22][23]) and to assess the feasibility and accuracy of UAV-mounted sensors for multiple research fields (e.g., forest inventory and management [24][25][26][27][28]). In this particular context, UAV-mounted LiDAR technology is a promising solution, since it can go deeper into the canopy, thus opening new prospects for detecting and characterizing 3D objects. Furthermore, having a closer distance between the scanner and the reflected points as compared to manned aircraft and satellite LiDAR solutions reduces the transverse width of the pulse, which can provide more accurate metrics from the point cloud [29,30]. Additionally, this allows the signal to pass through smaller gaps. As a result, tree trunks can now be captured with sufficient detail, which is a gateway to accurately locate trees and directly estimate the Diameter at Breast Height (DBH) without the need for allometric equations [31][32][33][34][35][36].
However, we noted that the conventional practices used to segment tree trunks usually require numerous site-specific parameters-e.g., the a priori knowledge of the DBH (Hough transformation) [61,[63][64][65]; the flatness criterion (Eigen decomposition) [66,67]; the predefined number of clusters (k-means) [60]; the radius and density thresholds of clustering with the Density-Based Spatial Clustering of Application of Noise (DBSCAN)namely, the neighborhood parameters [50,62,68,69]. Additionally, some methods are more sensitive to point density and gaps in the data [70][71][72][73]. This can lead to data containing a high proportion of outliers (from nearby understory vegetation) or segmented tree stems, thus affecting the completeness and accuracy of the estimated DBHs.
Therefore, this research project aims to segment tree stems. reckoning that (1) the user may have little knowledge of the study site, (2) tree stems may be surveyed with large gaps, and (3) the understory vegetation cover may interfere with tree trunks (Figure 1). For that, this study benefits from the machine learning Hierarchical Density-Based Spatial Clustering of Application of Noise (HDBSCAN) clustering algorithm proposed by [74], which is further improved to segment tree stems without having to set up any site-specific parameters. In summary, the main contributions of this research are:

•
The design and implementation of a workflow that segment tree stems without the need for site-specific parameters; • A solution which is both suitable for tree stems surveyed with gaps in the data and nearby understory vegetation; • A method that could further minimize the omission and commission errors when detecting trees along with assisting further tree metrics extraction (e.g., tree stem curve). This paper is structured as follows. Section 2 describes the study site and the data acquisition procedure. Section 3 deals with the methodological framework used to detect and segment tree stems. The results are then presented in Section 4 and discussed in Section 5 along with the research limitations. Ultimately, perspectives are addressed for further studies.

Study Area and Data Acquisition
The study was carried out within a temperate deciduous closed-canopy forest located at the Research Centre Jülich in Germany (WGS84 geographic coordinates: 50 • 54 23 N, 6 • 24 14 E). The study site of a total area of around one hectare was mainly composed of beech and birch trees on a relatively smooth terrain, with elevations ranging from approximately 88 to 91 m. In September 2020, 110 trees were surveyed with the Leica TPS1200 total station and georeferenced (in UTM 32N) with ground control points using a Trimble R10 GNSS receiver. The DBH at approximately 1.3 m in height above the ground of all surveyed trees was measured in order to assess the DBH estimation from the LiDAR point cloud. Figure 2 illustrates the spatial distribution of trees, their recorded attributes (tree species and DBH), and a photograph of the study site.

Sensor, Flight Parameters, and Data Processing
The study site was flown over with the YellowScan ® Surveyor LiDAR sensor mounted on a battery-driven DJI ® Matrice 600 Pro hexacopter with the assistance of DJI (Shenzhen, China) Ground Station Pro as the flight planning software. Two series of flights were conducted during the leaf-on (September) and leaf-off (November) seasons in a doublegrid survey at a mean altitude of 50 m Above Ground Level (AGL) and a 3 m/s flying speed. The overlapping percentage among swaths was set at 70% considering a Maximum Scanning Angle Range (MSAR) of 12 degrees from the nadir on one side, thus creating a total Field of View (FOV) of 24 degrees. Then, the Applanix's POSPac software was employed to create two Smooth Best Estimated Trajectory (SBET) files (one per season) using the Virtual Reference Station (VRS) technology from Trimble. Afterwards, YellowScan's CloudStation software was used for strip alignment and georeferencing purposes, thus applying corrections for GNSS offset (lever-arms), angles (boresight), and GNSS observation post-processing (using the SBET file) [75]. Ultimately, four point-clouds per season were produced considering returns of up to 12 • MSAR (24 • FOV), 25 • MSAR (50 • FOV), 50 • MSAR (100 • FOV), and 75 • MSAR (150 • FOV). Table 1 summarizes the above specifications.

Introduction
This section gives an overview of the methodological framework for segmenting and classifying tree stems along with estimating the DBH. As summarized in Figure 3, points were firstly classified into ground and non-ground points through the Progressive Morphological Filter (PMF) [76]. Then, a normalized point cloud (i.e., converting Z coordinates into heights above the ground) was created and used to individually detect and delineate trees based on the field measures and buffer zones. Section 3.2 explains this process in more detail. Next, the tree stem stratum was retrieved for each tree and used to segment and classify the tree trunk using the machine learning HDBSCAN clustering algorithm paired with a binary search and a feature vector. Finally, Principal Components Analysis (PCA) was applied to extract the tree stem orientation and estimate the DBH. Section 3.3 fully explains these procedures.

Normalized Point Cloud
Segmenting the LiDAR dataset into ground and non-ground points is a crucial step for both individual tree detection and structural height-based metrics assessment [77]. To this end, many data filtering methods have already been proposed to successfully deal with the variety of natural and urban landscapes [76,[78][79][80][81][82]. In this paper, PMF was used, as it is well suited for smooth terrains and is more time-efficient compared to the Cloth Simulation Filter (CSF). Note that the following PMF parameters were used: the sequences of windows sizes of the filter and threshold heights above the parametrized ground surface (to be considered as ground returns) were, respectively, set to 0.5 m and 2.5 m and 0.1 m and 0.5 m. Then, the dataset was normalized to transform the point's elevation (i.e., the Z coordinate) into height above the ground using the spatial Triangular Irregular Network (TIN) interpolation method due to the nature and the size of the surface to be modeled along with the absence of large discontinuities [83][84][85][86][87][88][89][90][91] (Figure 4). It is also noteworthy that, in order to remove the inaccuracy owing to the discrete nature of a digital elevation model (DEM) [92], the point-based normalization approach was applied during the leaf-on season. However, a high proportion of data artifacts attributed to multipath was observed during the leaf-off season, thus requiring an external DEM (raster-based approach) from the leaf-on season to remove falsely located underground points. The DEM was generated at a resolution of 0.1 meters using the point cloud acquired during the leaf-on season and a 75 • MSAR. Figure 5 shows the distribution of ground points after the DEM normalization using the point cloud acquired during the leaf-on season and a 75 • MSAR, where 95% of ground points fall between −0.06 m and 0.06 m.
Then, tree locations obtained using the total station and the GNSS receiver were used to generate circular buffer zones for segmenting trees. For each tree, the radius threshold was set to half the distance among its nearest neighbors ( Figure 6).    . Individual trees detection and segmentation based on the field measures and using circular buffers. For each tree, the radius threshold was set to half the distance among its nearest neighbors. Note that each cross-section is at a different scale in order to increase the visibility of the study site.

Clustering from Machine Learning
The aim of clustering is to split a finite unlabeled dataset into a finite and discrete set of underlying data structures-i.e., clusters [93]. It therefore belongs to the unsupervised learning from machine learning in the same way as the dimensionality reduction purpose [94]. Data clustering is a central task in artificial intelligence as it serves many applications such as data compression and supervised classification to create subsequent labeled datasets [95,96]. In this study, clustering is of utmost importance since it will directly affect the further tree stem classification along with the metrics estimation.
In this context, previous studies have already benefited from machine learning to cluster tree stems, such as k-means [60] and the traditional DBSCAN [50,62,68,69]. However, their application requires to set a series of parameters, which are either unknown (e.g., the predefined number of clusters with k-means) or complex to define (DBSCAN)-e.g., the maximum distance between two points to be considered as part of the same cluster, the ε distance, and the minimum number of points within a cluster, the cluster size. These settings rely heavily on the study site and must therefore be reviewed when applied to untested environments and/or sensors.
To avoid the previous limitations, this research takes advantage of the machine learning HDBSCAN clustering algorithm [74]. Compared to conventional DBSCAN, HDSCAN does not require the definition of the ε distance, thus allowing to cluster a higher variability of tree stems within the study site-i.e., surveyed with different densities. However, the cluster size remains a critical parameter as it may under-or oversegment the tree stem if not correctly configured. Additionally, since the point density may vary for each tree stem, this parameter should be uniquely set up. In the next section, we therefore propose a novel approach that aims to remove this issue by proposing an iterative procedure.

Theory of the Proposed HDSCAN Implementation
First, each tree is vertically split into N layers of one-meter height in order to produce vertical histograms of individual points [51]. Then, starting from the bottom, all layers that fall under the 30th percentile are kept and classified into continuous series. The longest series of layers is retained and assumed to contain the bole while also including some understory vegetation and tree crown sections. Note that the 30th threshold was chosen to facilitate the tree stem segmentation and classification on the bole-i.e., the lowest point density stratum, thus removing as many as branches from the tree crown. This value was adopted after some visual inspection of the dataset, thus fitting the tree species from the study area. Depending on the features of the forest, this threshold can be easily changed.
Secondly, the machine learning HDBSCAN clustering algorithm is applied into the planimetric space (i.e., using the x and y coordinates) in order to segment the tree stem. To overcome the definition of the minimum number of points within a cluster, an iterative procedure using a binary search is performed to find the upper limit from which a cluster is removed, thus avoiding tree stem over-segmentation. Then, three criteria must be met to classify this cluster as a tree stem based a feature vector:

1.
The maximum 2D spatial extension in each layer is lower than 1.5 m, which is considered to be the maximum realistic DBH within the study area.

2.
The height of the highest point is greater than 4 meters to avoid the understory vegetation.

3.
The cluster contains less than 50% of void with respect to the height of the 3D analyzed space-i.e., the bole section of the tree.
If no cluster simultaneously satisfies these three conditions, then the process continues by removing these points from the dataset. However, if a cluster meets the second and third condition, then all points outside the 1.5 m threshold are removed using the center of the cluster computed from the layers with less than 1.5 m wide. Finally, the cluster with the greatest continuity regarding the vertical histogram of individual points is classified as the tree stem.
When the tree stem is segmented and classified, the PCA method is applied to determine its growth direction [50,59,97]. As a result, the first principal component (PC1) is mainly oriented towards the vertical direction of the tree trunk; the second (PC2) and the third (PC3) components are oriented into a perpendicular plan. Finally, points between 1.2-and 1.4-m heights are used to estimate the DBH. For that purpose, a circle is fit in a least squares fashion by applying the QR decomposition (using an orthogonal matrix Q and an upper triangular matrix R), which is a suitable (i.e., fast) solution for relatively noise free input data [98,99]. Figure 7 summarizes the processing chain.

Introduction
From a methodological and technical point of view, the validation procedure was validated using field measures as ground truth (similarly to [100,101]) within the R software environment and using several packages for point cloud processing (e.g., lidR, TreeLS, and dbscan) and data visualization (plotly). Note that additional verification methods exist, such as the manual delineation from the LiDAR dataset [102,103].

Tree Trunk Detection & Segmentation
The accuracy assessment for individual tree detection was carried out with three indicators-recall (r), precision (p), and F-score (F)-using the following equations [104,105]: where TP stands for true positive, FP for false positive, and FN false positive, which respectively depict correct segmentation, over-segmentation, and under-segmentation. Note that FP is also called commission error (i.e., when a tree stem is segmented but does actually fit another object) and FN is called omission error (i.e., when a tree stem is not segmented while it actually exists). With this in mind, recall (r) quantifies the completeness of detected tree stems regarding the reference dataset; precision (p) represents the correctness of detected tree trunks with respect to the set of found tree stems; and F-score is an overall indicator, taking both commission and omission errors into account [106]. Note that all these indicators vary from 0 to 1, and that the higher the value, the more accurate the segmentation. As shown in Table 2, the ratio of correctly detected tree stems (i.e., the recall factor) varies from 18% (leaf-on season with a MSAR of 12 • ) to 82% (leaf-off season with a MSAR of 75 • ) of the dataset. Overall, independently of the season, the wider the processing scanning angle range, the higher the detection rate. Furthermore, it is noteworthy that the number of correctly detected tree trunks is greater during the leaf-off season with the lowest MSAR (12 • ) compared to the highest MSAR (75 • ) acquired during the leaf-on season. Finally, we also note that the highest precision scores are usually observed at low (12 • ) and high (75 • ) scanning angle ranges.

DBH
The assessment of estimated DBHs was determined by computing the bias and the Root Mean Square Error (RMSE). They were computed as follows [50]: where N is the number of trees for which a DBH value is estimated (i.e., with at least three points); x i,re f and x i , respectively, denote the reference (i.e., measured in the field) and estimated (i.e., from the point cloud) DBHs. Note that DBHs beyond the expected limit values (i.e., larger than 1.5 m within the study area) were removed from the analysis (only one DBH in this study). First of all, the number of estimated DBHs ranges from eight (leaf-on season using a 12 • MSAR) to 66 (leaf-off season with a 75 • MSAR), which is, respectively, 7% to 60% of the dataset. The bias varies from −0.07 m (leaf-off season using a 75 • MSAR) to −0.38 m (leaf-off season using a 12 • MSAR), while the RMSE varies from 0.15 m (leaf-on season using a 75 • MSAR) to 0.42 m (leaf-off season and 12 • MSAR). Overall, the estimations become more accurate and precise when increasing the MSAR regardless of the season. It is also noteworthy that despite a higher number of estimated DBHs, the bias and RMSE significantly increased when shifting from the leaf-on with a 75 • MSAR to the leaf-off season with a 12 • MSAR. Figure 8 illustrates the most relevant results from the leaf-on and leaf-off seasons-i.e., using a 50 • and 75 • MSAR. A deeper analysis of the outcomes shows that the leaf-off season with a 75 • MSAR correctly detected 66 out of 90 points that were used to estimate the DBH, meaning that 24 trunks were captured with less than three points at approximately 1.2 and 1.4 m heights above the ground (minimum required number to assess the DBH). As shown in Figure 9, 24 out of 66 tree stems (22% of the dataset) were classified into the right category of DBH (considering a 0.2 m boundary); 42 trunks were then misclassified.

Back to the Research Objectives
The purpose of this research was to develop a complete workflow that does not rely on the definition of site-specific parameters in segmenting tree stems. This concern arose from the high complexity in settings that must be configured. For that matter, the machine learning HDBSCAN clustering algorithm was applied to cluster points. This hierarchical version of DBSCAN has the advantage of getting rid of the maximum distance parameter between two points to be considered as part of the same cluster. However, this algorithm preserves the minimum number of points within a cluster, which was overcome by an iterative procedure paired to a binary search. As a result, the user's involvement in extracting tree trunks is limited to the bole and tree stem classification with respect to the canopy and understory.
Then, this workflow was validated within a deciduous forest stand during the leafon and leaf-off seasons while using various MSARs. The results firstly show a high detection robustness with a precision score higher than 90% for all tested configurations. This study also points out that, within the studied forest stand, the tree stem detection was better achieved during the leaf-off season along when incorporating beams from a wide scanning angle range. For that matter, this latter setup also greatly influences the accuracy and precision of the DBH estimation, as the larger the MSAR, the higher the point density is over the trunk surface at around a 1.3 m height above the ground. However, this configuration has some pitfalls, since data artefacts due to multipath simultaneously increase (also mentioned in [107]), especially during the leaf-off season. Indeed, the high foliage density during the leaf-on season reduces the likelihood of receiving reflected pulses. As such, the use of an external DEM from the leaf-on season was required to remove falsely located underground points.

Limitations and Perspectives
This paper only investigates the tree stem delineation and DBH estimation within a single temperate deciduous forest stand. Supplementary tests are thus required to increase the confidence in the methodology and generalize it-for instance, within additional deciduous (of different species composition and structure) and also coniferous forests. Furthermore, it should be noted that the data acquisition for the leaf-off season was conducted during the autumn with some remaining leaves. Additional flights should thus be carried out during the winter to remove this constraint.
Additionally, this research shows, under the study conditions, the limits of the UAVmounted LiDAR solution within temperate deciduous closed-canopy forest stands, especially for accurate DBH estimation. This conclusion is also drawn in [67], where the accuracy of abovecanopy UAV-mounted LiDAR systems was found to be unsatisfactory to estimate the tree stem attributes for accurate field reference data. In this study, only 60% of our dataset could be used (at best) for further DBH estimation-i.e., with at least three points at approximately 1.2 and 1.4 m in height above the ground. This may be explained by the high proportion of occluded areas (unlike open stands) and the tree stem direction regarding the incoming pulse direction. Furthermore, only 22% of the tree stems were classified into the right category of DBH. This low proportion may result from the small number of points at around a 1.3 m height along with the circle fitting method (the QR decomposition) [46,108]. Additionally, the positional drift of the scanner may have affected the modeling accuracy of the tree stem and subsequently the DBH. Thereupon, methods that match displaced tree stem models corresponding to a single tree could be used in the future to alleviate this issue [50,108,109]. As a result, autonomous drones that can both operate above and beneath the canopy are a promising solution for accurately estimating the DBH in such environments. Indeed, their capacity to fly at the same height as the tree stem stratum guarantees a spatially more continuous coverage of the tree stem surface. This would thus allow to combine the advantages of UAV-mounted LiDAR and TLS. For that matter, manually piloted UAVs beneath the canopy have already been tested for DBH estimation along with the tree stem volume estimation if coupled with above-canopy laser scanning [69,110].
Furthermore, from a methodological perspective this study simply takes advantage of the ordinary PCA to extract the tree stem orientation. While it is suitable for tilted tree trunks, this assumption cannot be made for bent tree stems, which would require a nonlinear PCA adjustment to improve the tree stem orientation extraction along with the DBH estimation. However, it is noteworthy that the current proposed tree stem detection method can already improve the individual tree detection accuracy if combined with topdown-based methods (as shown in [68]), along with assisting further tree metrics retrieval (e.g., tree stem curve). In this context, additional hierarchical clustering could also be carried out to link false positives to their mother tree along with splitting clusters that are too large into its children.
Finally, the recent advances in deep learning for Earth observation also brought new prospects in detecting 3D objects [111,112]. As a result, clustering and dimensionality reduction tasks could be further conducted using deep neural network methods [113].

Conclusions
This paper proposes a method to segment tree stems in a deciduous forest stand that does not rely on any site-specific parameters. To achieve that, this research benefits from the HDBSCAN clustering algorithm from machine learning, which was implemented in a way to avoid the definition of the minimum number of points within a cluster. The workflow was then validated in a temperate deciduous closed-canopy forest during the leaf-on and leaf-off seasons. The outcomes of this study show that the proposed methodology can correctly detect up to 82% of tree stems with a precision of 98% (leaf-off season and an MSAR of 75 • ). Additionally, this research points out that the over-canopy UAV laser scanning has limitations in segmenting tree trunks with closed canopy forests during the leaf-on season. During this season, it is therefore recommended to keep beams from a wide scanning angle range in order to maximize the point density over the tree stem. The same is also true during the leaf-off season, except that data artefacts due to multipaths are clearly observed. However, this can be partially solved using a DEM from the leaf-on season, thus removing returns that are falsely located under the ground.
Additionally, this research shows that, inside closed-canopy forest stands and under the study conditions, the point density remains low within an approximately 1.3 m height above the ground even during the leaf-off season, which prevents the use of overcanopy UAV laser scanning to accurately estimate the DBH in such environments. As a result, it might be interesting to fly under the canopy to increase the tree stem coverage. Autonomous drones that can both operate above and under the canopy are a promising solution to tackle this issue, and will be further investigated along with deep neural network methods for clustering and dimensionality purposes.
Author Contributions: R.N. conceived the research question, assisted with data acquisition, designed and implemented the proposed methodology, validated and discussed the results, and wrote the manuscript; F.J. also developed the research question, assisted with data acquisition and the interpretation of results, and revised and edited the manuscript; J.S.B. participated in the LiDAR data acquisition process, produced the raw LiDAR datasets, and revised and edited the manuscript. All authors have read and agreed to the published version of the manuscript.