1. Introduction
Light Detection and Ranging (LiDAR) is an active remote sensing system whose output consists of a three-dimensional point cloud representing the Earth’s surface and all the objects standing on it.
Starting from the 1990s, LiDAR became commercially available, thus allowing for an acceleration of its technical improvement and field applications [
1,
2]. Nowadays, applications involve terrestrial, airborne, and spaceborne systems and concern agriculture [
3,
4], geomatics [
5,
6], and forestry [
7,
8], to mention just a few. The ability of LiDAR systems to capture the complex structure of trees and forests is related to the different returns provided by the surfaces when they are intercepted by the LiDAR signal. Vegetation partially reflects and transmits the signal, so multiple returns from a single shot may occur before the last one from the ground is received. Therefore, the vertical characterization of the vegetation structures is possible [
2,
8,
9] and LiDAR-derived data can be efficiently used to determine forest inventory parameters [
10].
Thanks to its features, LiDAR is complementary to or more advantageous than other methods, such as photogrammetry and ground-based data collection, for the characterization of some forest attributes. Monoscopic photogrammetry allows for coarse-scale investigations but does not provide three-dimensional information. Stereoscopy can return a three-dimensional point cloud, but this cloud just describes the upper surface of the canopy in forested areas, thus avoiding the investigation of the under-canopy vegetation structures [
11]. Ground-based methods, despite providing numerous information about individual trees and tree plots, are time-consuming, labour-intensive, expensive, and circumscribed to relatively small areas [
8].
Forest inventories are fundamental for natural resources management. For instance, a record of the past and present status of forests can be generated on the basis of inventory parameters, and used to evaluate forest damage [
12,
13], plan environmental and commercial activities, and model future forest evolution [
14]. Furthermore, data of forest inventory are essential for carbon accounting and fire-related risk assessment [
15,
16], and for the development of a sustainable bio-economy that grounds on renewable resources [
2]. Forest information can be derived by LiDAR data according to two main approaches, namely the area-based and the individual tree-based approaches (see [
16,
17,
18] for detailed information about the features, advantages, and disadvantages of the two approaches). The former approach generally predicts the mean features at the stand level (e.g., mean tree height diameter, basal area, volume, and biomass) from the percentiles of the LiDAR-derived height distribution [
19,
20]. The individual tree-based approach, instead, aims to collect specific information from which deriving other attributes, such as the biomass and the diameter-at-breast height, of each tree by means of existing models [
21]. When the estimation parameters (area-based) or the LiDAR-derived metrics (individual tree-based) are calibrated on the basis of ground data, both of the methods generate accurate forest structural information that can support forest inventory over large areas [
22,
23].
Within the frame of individual tree-based forest inventories, the identification of trees and the assessment of their height and position play a fundamental role as they constitute the basis to derive other tree attributes [
24]. Although the literature provides a large number of works dedicated to the identification of individual trees from LiDAR data, most of the proposed methodologies rely on the adoption of similar approaches, which can be roughly classified into two families, namely the canopy height models-based (CHM) and the cloud-based approaches.
Canopy Height Model (CHM)-based approaches identify the treetops by applying algorithms to the canopy height model, namely the surface model representing the top layer of canopies through its relative height with respect to the ground. This family of approaches can be further divided into classes according to their underlying algorithm: (i) the local maxima methods, which are the most frequently found in literature [
12,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40]; (ii) the local curvature methods [
41]; (iii) the watershed methods, which find the tree crowns through a pouring mechanism [
42,
43,
44]; (iv) the morphological methods, which apply opening operations to isolate the tree crowns within the CHM [
13,
14,
45], and (v) other methods, which delineate potential crown material so that the individual trees can be distinguished [
18,
46,
47,
48]. The main difference among these classes is that the former two carry out the crown segmentation after the treetop identification, whereas the latter three perform the tree identification by looking for the treetop within the segmented crown boundaries. The CHM-based approach has proven to be quite effective in very regular vegetation pattern, especially when only one layer of the tree canopy is present, and in coniferous stands. Nevertheless, this approach may provide lower-accuracy results when applied under particular conditions [
37,
49,
50,
51,
52,
53]: the interpolated surfaces can be affected by the noise of the LiDAR data they derive from and by the complexity of the terrain and canopy geometry so that the tree counting process can be misleading; moreover, the presence of mixed-species forests, random tree patterns, and shade-tolerant species can affect the identification process.
As reported by Richardson and Moskal [
50], some attempts have been made to overcome the aforementioned intrinsic weaknesses of the CHM-based approaches. For instance, the CHM has been used together with full-waveform LiDAR datasets [
54], combined to a new inventory index [
15] or improved by computing correlation surfaces [
55,
56]. Since these improvements have not led to a satisfactory rise of the accuracy [
50,
57], at the beginning of the 2010s, a new paradigm for treetop detection promoted the rise of the second family of approaches, labeled as cloud-based. These methods do not just work on the CHM, but on the entire three-dimensional point cloud and are further classified in: (i) the top-bottom methods, where treetops are firstly detected and then all the points belonging to the same tree are identified on the basis of tree spacing [
24,
50,
51,
52,
58,
59,
60,
61,
62,
63], and (ii) the bottom-top methods, where the stems are firstly detected from the lower layer and then all the points belonging to the same tree are identified while moving upwards [
53,
57]. To our knowledge, the only cloud-based methods that cannot be listed in the aforementioned classes were provided by Rahman and Gorte [
64], Rahman et al. [
65], Ferraz et al. [
66], Paris et al. [
67] and work either on point density or point clustering. Although the cloud-based approach generally achieves higher accuracy than the CHM-based [
57], it requires a greater computational effort. Therefore, the CHM-based approach is still the most commonly adopted [
44,
48].
The described classification is summarized by
Figure 1. It grounds on the extensive, albeit not exhaustive, literature review that is reported in
Table S1 of the Supplementary Material. The review begins from the 2000s, when active remote sensing devices began to be widely used in forestry [
59,
68], and only considers the applications of the traditional airborne discrete-return LiDAR systems, neglecting the multi-spectral e.g., [
69] and the full-waveform ones e.g., [
54,
70,
71]. Furthermore, it does not include the recent branch of Terrestrial Laser Scanning (TLS) systems. While Airborne Laser Scanning (ALS) systems provide complementary information for forest inventory in terms of tree number, areal stem density, and tree height over large areas (up to the regional scale), TLSs give high point density data and allow for three-dimensional tree reconstruction but can investigate relatively small areas (see [
72,
73,
74,
75] for further details).
The tools and algorithms that have been proposed so far for the individual tree identification usually lead to more accurate results when applied to coniferous stands than to deciduous ones. This is mainly due to the particular features of coniferous trees since their conical shape makes their tops easy to identify [
12,
50], but it is also due to the regular pattern of coniferous stands that avoids the inaccuracies related to the presence of understory trees. Conversely, deciduous trees assume an umbrella-like shape so that their crowns are usually very rounded and tend to overlap each other. Moreover, except for the regular spatial configuration of plantations, trees in natural deciduous stands are usually located according to random patterns with a strong presence of understory vegetation, thus affecting the tree detection [
30,
50,
57,
76].
Aiming to improve the individual tree detection for the case of deciduous stands, this work provides a novel, flexible, and simple tool that falls into the category of point cloud-based approaches and relies on a density-based algorithm.
In the following, we describe the structure of the algorithm and assess its accuracy by applying it to twelve deciduous stands along the Orco River (Italy). Seven of these areas show regularly-arranged trees, whereas the others are characterized by trees that are randomly located. Therefore, the algorithm is tested for, respectively, more and less favorable tree configurations. The performance of the algorithm is evaluated both in terms of tree count and stem position by comparing its outcome with a tree census that was carried out by the authors in February 2019. The influence of input parameters on the presented algorithm is then investigated through a sensitivity analysis and its results are discussed. Finally, the algorithm is applied to the datasets that have undergone a re-sampling process. The evaluation of the outcome accuracy at different re-sampling rates is then used to define the minimum point density that is required for the input datasets in order to meet an overall accuracy higher than 0.70.
2. Data and Method
2.1. Study Site and Available Data
The study areas are located in the Orco River floodplain (Northwestern Italy, 45
14
22.2
N–7
48
45.2
E), as shown in
Figure 2a–c.
The Orco River is 89.57 km long and has a catchment area of 930 km
2, bounded by the Gran Paradiso National Park, the Stura di Lanzo Valley, the Vanoise National Park, and the Canavese Valley at the Northern, Southern, Western, and Eastern side, respectively. The Orco River floodplain is characterized by a low degree of anthropic activities so that the river channels and meanders can migrate over time. The study sites are located between the town of Cuorgnè and the confluence with the Po River and are occupied by stands of deciduous trees, mainly poplars (
Populus alba, Populus nigra), willows (
Salix alba), black locusts (
Robinia pseudoacacia), oaks (
Quercus robur), and hornbeams (
Carpinus betulus). Some of these stands belong to commercial plantations and are characterized by well-separated trees of similar age and size and organized according to a regular pattern, such as at the study area hereinafter called
(
Figure 2e). Nevertheless, the majority of vegetation follows the natural life cycle of the riparian forests, being populated by trees of different sizes and ages, randomly arranged, often with partially-overlapping crowns. An example of this latter case is shown by the study area hereinafter called
(
Figure 2d).
Table 1 reports the main features of the twelve study areas. No significant topographic variations are reported for the selected areas since they are generally flat or with very gentle slope (average slope range from 1 to 5 degrees except for
, which is close to the river banks).
The LiDAR data associated with these study areas were acquired on 28 February 2019 by the Italian National Council of Research—Research Institute for Geo-Hydrological Protection (CNR-IRPI) with a LiteMapper 6800 installed on a POD DART certificated by EASA with a minor/STC approval for Eurocopter AS350 Heliwest. The scanning process was designed to guarantee: (i) a raw coverage of the twelve surveyed areas equal to nine points·m
on average; (ii) a minimal stereoscopic coverage equal to 60% and 30% for the forward and sideward overlap between adjacent swaths, respectively, and (iii) an average ground sampling distance equal to 10 cm/pixel. The scan frequency was 400 KhZ, whereas the flight height ranged between 675 and 794 m above sea level. The scan angle ranges from 4
to 19
, approximately, for the study areas. The trajectories of the flight are shown in
Figure 2f. The dataset was provided as two separate clouds for the ground and the vegetation, respectively.
During the LiDAR data acquisition, the authors carried out a tree census within the study areas. The tree coordinates were taken by means of a Real-Time Kinematic Global Positioning System (RTK-GPS), model ROVER LEICA 1250, and GNSS smart antenna. The error position of this device is approximately 1.0 m when performing measurements within the tree stands because of the reduced availability of satellites for the GNSS-based positioning and the low signal from the reference station for the kinematic corrections. After the survey, the acquired tree positions were double-checked with a visual inspection of the orthophotos deriving from the LiDAR campaign.
2.2. Presentation of the Algorithm
The algorithm is provided in Matlab® code and freely available in the
supplementary material. Unlike most of the other existing methods, it does not look for local height maxima but local point density maxima, after having defined the point density as the number of the points’ projections on the plane
z = 0 per unit area. The underlying assumption is that the point cloud becomes denser in correspondence with the tree center. Thus, the principles upon which the algorithm is based are that: (i) in the lower layers, LiDAR systems tend to record the highest number of returns when the signal intercepts tree trunks unless too thick understory vegetation is present, and (ii) above a certain reference height the density of tree branches is higher at the center of the crown, decreasing towards its edges. Whereas the former statement is intuitive, the latter has been confirmed by previous studies e.g., [
49,
64,
65], which have also reported that this feature does not depend on the crown shape. Accordingly, this assumption holds for LiDAR data acquired in leaf-off conditions, such as the ones used in this work. We further checked the validity of this hypothesis, by projecting all the points of the cloud on the plane
and computing their areal density. As it can be observed in
Figure 3, the density is maximum at the tree center and gradually decreases towards the tree edges.
The adoption of a density-based approach allows the algorithm to overcome the limitations of the other approaches when applied to deciduous stands. The upper panels of
Figure 4 provide a graphical explanation of the influence that the spatial distribution of the trees has on their detection when the local height maxima are looked for, whereas the lower panels highlight the intrinsic advantage of the density-based approaches.
2.2.1. Pre-Processing
The required input is a text file containing the coordinates of the elements constituting the LiDAR point-cloud, where the vertical coordinate z must be expressed as relative height with respect to the ground. The generation of the ground surface model and the computation of the relative heights is required prior to the use of the algorithm.
2.2.2. Workflow
Firstly, the algorithm removes the outliers from the point cloud that are associated with unrealistic vertical coordinates, as well as the points lower than 1.4 m, which may be associated with shrubs, bushes, and grasses. In this way, the computational time is reduced.
Secondly, for each point of the ‘cleaned’ cloud, the algorithm computes the most frequent radius, which is a proxy of the crown radius. To this aim, it sorts the inverse distances from all the surrounding points, applies the periodogram method to obtain the Fourier transform of the inverse distance signal, and switches from the space to frequency domain. The computation of the power spectral density of this signal leads to the identification of the mean spatial frequency of the points, which is the inverse of the most frequent radius.
As the computation of the most frequent radius can be time-consuming for large clouds, the input file is clipped around the
i-th considered point, at a distance equal to
. Then, the algorithm determines the areal density
according to
For the i-th considered point, is the number of the points’ projections on the plane z = 0 that are contained in an area of radius . Finally, the algorithm selects the point associated with the maximum density for each , and generates a list of the coordinates of the detected stems. The outcome is further refined by applying a filter that eliminates double-counting, based on the typical spacing of stems.
The highest point density corresponds to the stem location, but it does not always coincide with the location of the treetop. Optionally, the algorithm detects the closest local height maximum for each stem and creates a new list of coordinates for the treetops’ location and heights. Another (optional) filter identifies trees with an apparent height close to that of other objects (e.g., fences) and decides whether to remove them on the basis of statistical considerations about the surrounding trees (i.e., comparing the mean and standard deviation of the tree heights).
The algorithm’s output can be imported in Geographic Information Systems (GIS) and compared to field data, as shown in
Figure 5.
As further discussed in
Section 4.3, the present algorithm requires two parameters to be set, namely the radius of the circular area that is used to clip the input file (i.e.,
), and the critical length for the double-counted stem filter. In this work, we set the clipping radius equal to 20 m, whereas we used an optional function, included in the algorithm, to automatically compute the latter: the critical length can be interpreted as a proxy of the typical stem spacing that can be observed in the study area; therefore, for each detected stems, the function computes the most frequent spacing with respect to the surrounding trees and then sets the critical length as the median of the resulting spacing values.
The conceptual workflow of the algorithm is reported in
Figure 6, whereas the technical details about the algorithm setup are reported in
Appendix A.
2.3. Accuracy Assessment
The accuracy for the tree count was assessed by following the same criteria adopted in the literature: the algorithm-detected trees were classified as true positive
if correctly identified, and false positive
if they do not correspond to the field-mapped ones; the trees omitted by the algorithm were instead classified as false negative
e.g., [
51,
57]. The rate of tree detection is represented by the
recallr metric, its correctness by the
precisionp, and the overall accuracy by the
F-score F [
77] that were computed as follows:
All of these metrics range from 0 to 1.
The position error, expressed in m, was calculated as the average distance between the field-measured trees and the algorithm-detected ones.
The correct shift from the stem position to the closest height maxima to define the treetops was checked by comparing the resulting stem-to-top distances with the typical values of the crown radius.
2.4. Sensitivity Analysis and the Parameter Setting
As said above, the algorithm requires the setting of two input parameters: (i) the radius of the area to clip the input file around each element, and (ii) the critical length to detect the double-counted stems. We performed an analysis to assess the parameter sensitivity in the outcomes of the algorithm. For this purpose, we tested 10 values of the clipping radius in the range 10–100 m, and twenty values of the critical length in the range 0.5–10.0 m. In case the clipping radius exceeded the extent of the study areas, all of the input points were considered.
As we mentioned in the previous paragraphs, the algorithm can optionally compute the critical length as a proxy of the typical stem spacing on the basis on the statistics of the distances among the identified stems. We tested the effectiveness of this automatic function by comparing the real spacing, obtained by site-specific observations, with the optimal spacing that emerges from the sensitivity analysis and that leads to the highest accuracy, and the values computed by the algorithm.
2.5. Application to Re-Sampled Point Clouds
Finally, we re-tested the presented algorithm on the same study cases but using lower resolution input data. The new datasets were obtained through the random re-sampling of the vegetation point clouds by employing the free software CloudCompare. The rate of point reduction was of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90%, corresponding to an average density of 8.1, 7.2, 6.3, 5.4, 4.5, 3.6, 2.7, 1.8, and 0.9 points·m. This additional test allowed us to understand the influence of point density on the achieved accuracy and to define a minimum requirement for the resolution of the input LiDAR data.
5. Conclusions
In this work, we proposed a novel algorithm for the identification of individual trees in forest stands from three-dimensional point clouds. The algorithm is designed to process airborne LiDAR point clouds and grounds on the detection of stems according to local maxima of the areal point density. It can give the stem coordinates and the treetop height as output.
The algorithm achieves high accuracy when applied to stands with both regular and random spatial tree distribution. The achieved F-score is higher than 0.70 and position error close to 1.0 m, if the input point cloud has a density of at least 2 points·m. Thanks to its capability to deal with relatively low-density clouds, old LiDAR datasets can be also accurately analyzed, while very dense clouds can be sub-sampled to speed up the process.
A sensitivity analysis highlighted the influence that the parameter describing the critical stem spacing has on the achieved accuracy. However, the algorithm demonstrated to be able to automatically compute it on the basis of statistical considerations about the geometric configuration of the detected trees. This feature allows the algorithm to also be adopted with little information about the study area.
The main advantages and limitations of the algorithm are summarized in
Table 5 along with the precautions that may be taken to obtain better results.
Despite its simplicity, the algorithm can constitute the basis for more complex tools, such as those for crown segmentation. In addition, it may allow for the biomass estimation if coupled to GIS information about the spatial distribution of tree species and site-dependent allometric laws. There are many applications for such a coupled methodology, ranging from forest inventories e.g., [
25,
96] to the characterization of riparian vegetation for hydrodynamic modeling e.g., [
97,
98,
99].
Our results suggest that the accuracy of tree identification relies on the quality of the input point clouds. Although this is not a limitation of the algorithm itself, it must be considered when analyzing the region of interest. It is worth noting that the algorithm performs better in plantations and forest stands with mature vegetation since the mature trees are better represented in the point clouds and generally more spaced apart from each other. The application of the algorithm to natural stands is generally good unless the stem spacing is excessively variable or the crown is very interlaced. We also point out that the presence of high and thick brambles, as often occurs in the riparian zone, can decrease the algorithm accuracy since they may be wrongly identified as trees.
Finally, we note that the algorithm was tested on LiDAR data acquired during leaf-off conditions. Because of a density-based approach, the algorithm is expected to work well in leaf-on conditions too, if applied to coniferous stands (see
Figure 4). In that specific case, indeed, the underlying hypothesis (i.e., the correspondence between the maximum point density and the tree center) still holds thanks to the conical shape of these species. Future works should verify whether this hypothesis holds for point clouds acquired in deciduous stands with leaf-on conditions and whether the presence of interlacing branches or their non-symmetric distribution can mislead the stem identification, as is suggested by some authors e.g., [
64] and the large position error of
.