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Modeling Earth Systems and Environment (2024) 10:5225–5240
https://doi.org/10.1007/s40808-024-02060-w
ORIGINAL ARTICLE
A new method forindividual treetop detection withlow‑resolution
aerial laser scanned data
GergőDiószegi1· VandaÉvaMolnár2,3· LorándAttilaNagy1· PéterEnyedi4· PéterTörök3,5· SzilárdSzabó1
Received: 9 March 2024 / Accepted: 2 June 2024 / Published online: 13 June 2024
© The Author(s) 2024
Abstract
In the past decade, the use of three-dimensional forest information from airborne Light Detection and Ranging (LiDAR)
has become widespread in forest inventories. Accurate Individual Treetop Detection (ITD) and crown boundary delineation
using LiDAR data are critical for obtaining precise inventory metrics. To address this need, we introduced a novel grow-
ing tree region (GTR)-driven ITD method that utilizes canopy height models (CHM) derived from very low-resolution
airborne LiDAR data. The GTR algorithm consists of three key stages: (i) preserving all height layers through incremental
cutting and stacking of CHM; (ii) employing a three-layer concept to identify individual treetops; and (iii) refining the
detected treetops using a distance-based filter. Our method was tested in five temperate forests across Central Europe and
was compared against the widely-used local maxima (LM) search combined with an optimized variable window filtering
(VWF) technique. Our results showed that the GTR method outperformed LM with VWF, particularly in forests with high
canopy density. The achieved root mean square accuracies were 74% for the matching rate, 19% for commission errors,
and 27% for omission errors. In comparison, the LM with the VWF method resulted in a matching rate of 71%, commis-
sion errors of 20%, and omission errors of 31%. To facilitate the application of our algorithm, we developed an R package
called TREETOPS, which seamlessly integrates with the lidR package, ensuring compatibility with existing treetop-based
segmentation methods. By introducing TREETOPS, we provide the most accurate open-source tool for detecting treetops
using low-resolution LiDAR-derived CHM.
Keywords CHM-based treetop detection· Growing tree region· Local maxima· Variable window filtering· Low-resolution
LiDAR· Central European forest· R
Introduction
The use of Individual Treetop Detection (ITD) and crown
delineation via active remote sensing technology, particu-
larly Light Detection and Ranging (LiDAR) with Airborne
Laser Scanning (ALS) data, has become essential for
advancing our understanding of forest structure and ecology
(Koch etal. 2006; White etal. 2016; Wulder etal. 2008).
Over the past two decades, ALS technology has become
essential for advancing our understanding of forest structure
and ecology (Hyyppä etal. 2008; Lim etal. 2003; White
etal. 2016). The primary goal of forest management is to
obtain precise individual tree metrics, including tree species,
location, height, diameter at breast height (DBH), and crown
dimensions (González-Ferreiro etal. 2012; Hu etal. 2014;
Koch etal. 2006; Maltamo and Gobakken 2014). These
* Gergő Diószegi
dioszegi.gergo@science.unideb.hu
1 Department ofPhysical Geography andGeoinformatics,
Faculty ofSciences andTechnology, University ofDebrecen,
Egyetem Tér 1., Debrecen, Hungary
2 ELKH-DE Anthropocene Ecology Research Group,
University ofDebrecen, Egyetem Tér 1., Debrecen, Hungary
3 Department ofEcology, Faculty ofSciences andTechnology,
University ofDebrecen, Egyetem Tér 1., Debrecen, Hungary
4 Envirosense Hungary Ltd., Péchy M. U. 46, Debrecen,
Hungary
5 HUN-REN-UD Functional andRestoration Ecology
Research Group, Egyetem Tér 1., Debrecen, Hungary
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5226 Modeling Earth Systems and Environment (2024) 10:5225–5240
metrics are crucial for estimating forest characteristics, such
as tree species composition, growing stock volume, canopy
density, and mean basal area (Ene etal. 2012; Lee etal.
2013; Parkitna etal. 2021; Unger etal. 2014). However,
the accuracy of these parameters is influenced by errors in
various individual tree detection methods, including treetop
detection, crown delineation, and tree segmentation. Conse-
quently, developing the most accurate algorithms for these
tasks remains a significant challenge.
Numerous studies have proposed various ITD methods
for scientific and operational applications (Brosofske etal.
2014; Coops etal. 2021; Popescu and Wynne 2004; Wulder
etal. 2000). Technically, ITD and crown delineation meth-
ods follow two main concepts. The point-based concept
utilizes laser scanned data with high and very high point
densities to detect and segment individual trees directly from
the point cloud by clustering points into objects (Duncanson
etal. 2014; Li etal. 2012; Yao etal. 2014). The raster-based
concept employs low-resolution LiDAR data (low point
density). Initially, it used the point-to-raster algorithm to
create a digitalized square unit (pixel) representation of the
forest surface in a canopy height model (CHM) (Popescu
etal. 2002; Popescu and Wynne 2004). Following this,
treetops are detected using the local maxima (LM) algo-
rithm with a fixed or variable window filtering (VWF) size
(Pitkänen 2001; Popescu and Wynne 2004; Wulder etal.
2000). Finally, marker-controlled watershed segmentation
or marker-controlled decision tree segmentation, utilizing
treetops as markers, is applied for tree boundary delinea-
tion (i.e., crown) (Beucher and Meyer 1993; Dalponte and
Coomes 2016; Lamar etal. 2005; Wang etal. 2004). The
raster-based concept is essentially a CHM-based method.
Traditionally, computing the CHM involves subtracting
the Digital Terrain Model (DTM) from the Digital Surface
Model (DSM). However, it is crucial to approach CHM pro-
cessing with care, as different retrieval methods can produce
qualitatively distinct representations of tree heights compared
to in-situ measured tree heights (Mielcarek etal. 2018). For
optimal CHM accuracy, triangulation-based algorithms are
recommended because they provide the most faithful rep-
resentations of trees within CHMs (Mielcarek etal. 2018;
Roussel etal. 2020). However, triangulation-based model gen-
eration may introduce empty or erroneous pixels, which are
often referred to as pits. This can be effectively mitigated by
employing various post-processing filters (Roussel etal. 2020;
Stereńczak etal. 2020). Additionally, to reduce the number of
Local Maxima (LM) a priori, Gaussian filtering with varying
kernel window sizes, allowing for adjustment of the smooth-
ing effect, can be applied to refine the model (Stereńczak etal.
2020). The processed CHM can then undergo ITD.
Eysn etal. (2015) conducted a thorough comparison of
several CHM-based ITD methods using aerial laser scanned
data collected in Central European alpine forests. They also
introduced an automated matching procedure with highly accu-
rate evaluation metrics for ITD (Eysn etal. 2015; Stereńczak
etal. 2020). Their findings revealed that the Local Maxima
(LM) search with Variable Window Filtering (VWF) achieved
the best results, with a matching rate of 60% for single-story
coniferous stands and 47% for single-layered mixed forests
with a 29% coniferous proportion. However, detecting co-dom-
inant trees in dense forests poses challenges for all considered
methods. Previous benchmarking studies (Kaartinen etal.
2012; Vauhkonen etal. 2012) have reported similar results.
A novel ITD and segmentation approach using a CHM-based
hierarchical transformation of height levels from highest to
lowest demonstrated accuracies between 83 and 86% in various
forest stands (Zhao etal. 2017). Furthermore, a sophisticated,
self-calibrating segmentation algorithm (without ITD), tested
in a Central European lowland forest, achieved accuracies of
85% in coniferous and deciduous stands and 75% in mixed for-
ests (Stereńczak etal. 2020). However, these high-performance
tools were not released under open-source licensing. There-
fore, there is a critical demand for an ITD approach that (1) is
freely accessible, (2) has the potential to surpass the LM with
VWF and can be seamlessly integrated with different segmen-
tation approaches, and (3) can be easily developed.
This study aimed to introduce a novel algorithm for ITD
developed in Central European mixed forests, utilising low-
resolution LiDAR-derived CHM. The specific objectives of
this study were as follows:
(i). Develop a straightforward yet flexible CHM-based
algorithm for treetop detection.
(ii). Create an open-source tool that seamlessly integrates
this algorithm, which is compatible with the lidR
package in the R computational environment.
(iii). Assess and validate the accuracy of the proposed
algorithm by utilizing reference data collected insitu
from one forest and derived from combined laser
scanning data from four other forests. This evaluation
includes a performance analysis comparing our algo-
rithm with the widely used treetop detection method
that employs an LM search with an optimized VWF.
GTR
The algorithm
Our proposed method, called the Growing Tree Region (GTR),
is a treetop localization algorithm based on the LiDAR-derived
CHM. The algorithm was implemented in the R programming
language and relied heavily on the C + + -based terra (Hijmans
2023) and sf (Pebesma and Bivand 2023) packages. Therefore,
the terminology used in this study was adjusted to align with
the terminology used by those packages.
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5227Modeling Earth Systems and Environment (2024) 10:5225–5240
Similar to the LM algorithm using VWF, our algorithm
conceptualizes tree crowns as mountains protruding from a
three-dimensional canopy surface (i.e., CHM). The apex of
a tree corresponds to the peak of a mountain. Height values
decrease continuously starting from the treetop, following
the slope of the mountain, which represents the tree crown.
This descent stops at the valley, which can indicate either
the boundary between the trees or the edge of the crown.
The algorithm comprises three major steps: (i) CHM cut-
ting and storage, (ii) treetop location, and (iii) reduction in
the number of treetops.
(i). CHM cutting and storage
The GTR algorithm employs a horizontal plane to vertically
slice the CHM from top to bottom into multiple horizontal ras-
ter layers, where non-no data values are labelled as 1 (Fig.1).
The files were stored in a stacked format. The vertical cutting
distance, referred to as the height increment, is set at 0.2m.
Consequently, each raster represents the CHM values (1) at a
specific height, with the height information (Z) stored in the
filename of the corresponding raster file within the stack.
During the tree-growing process, sections of growth inter-
sect, forming a new patch at a certain height. In our example,
the first new patch (i.e., intersection) occurs between heights
of 31.8m and 30m (Fig.1).
(ii). Treetop location
GTR identification is a crucial step for locating treetops.
The process is iterative and involves the selection of three
consecutive layers (from top to bottom) at each iteration
(Fig.2). During one iteration, the algorithm searches for
new intersections and identifies GTR. Treetops are extracted
by determining the centroids of the GTR calculated from
layers 2 and 3 and then filtering them based on the criterion
of overlapping with the GTR from layers 1 and 2 (Fig.2).
The three-layer concept is explained below.
First, the first emerging tree region (FETR) is determined
by subtracting layer1 from layer2 (FETR21), and the opera-
tion of layer3—layer2 results in FETR32 (Fig.3). Subse-
quently, GTR21 and GTR32 were computed. GTR21 was
calculated by utilizing layer2 and FETR21 under the follow-
ing conditions (Eq.1, Fig.3):
Fig. 1 Circular example of a CHM with a pixel size of 0.5∙0.5m,
displayed in decreasing order between 31.8m (maximum height) and
6m. The decrement interval is 2 m. In the top row on the left, the
initial example CHM is depicted, with green representing value 1 and
grey indicating no data. The locations of the two example patches are
highlighted by filled red circles with transparency
(1)
layer2patchi
⊇
FETR21patchn&Ncelllayer2patchi≠NcellFETR21patchn
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5228 Modeling Earth Systems and Environment (2024) 10:5225–5240
where i in
layer2patchi
denotes the i-th patch of layer2, ⊇ rep-
resents an improper superset and n in
FETR21patchn
denotes
the n-th patch of FETR21 (Fig.3). Hence, this double-condi-
tion can be expressed as follows: if the i-th patch of layer2 is
a superset of the n-th patch of FETR21 whose pixels belong
to layer2 AND the pixel number of the i-th patch of layer2 is
not equal to the pixel number of the n-th patch of FETR21.
The output GTR21 (and GTR32) is a binarized raster with
Fig. 2 Example patches (Fig.1) provide an overview of the three-layer concept. Green denotes value 1, whereas grey represents no data
Fig. 3 The three-layer concept (Fig.2), which is at the core of the
GTR algorithm, is visualized and mathematically explained. In the
first three columns, green represents value 1, whereas grey indicates
no data. The distinct colours in the fourth column and shades of grey
in the sixth column represent the patch IDs. The red circle around the
bottom-right raster highlights the ITD output (red unfilled dots) of the
algorithm
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5229Modeling Earth Systems and Environment (2024) 10:5225–5240
GTR and non-GTR values. Next, individual regions (i.e.,
patches) of both GTR21 and GTR32 were identified. Finally,
the treetops were located using the following formula (Eq.2,
Fig.3):
where
TREETOPSlayer2
indicates that the identified treetops
in a given iteration are associated with the height value of
layer2; ∈ represents the element-of symbol; centroids of
GTR21 overlapping GTR32 are considered as the treetops.
(iii). Reduction in the number of treetops
Because the treetops are stored in a self-updating process
after each iteration (Fig.4a), it is necessary to reduce the
number of treetops. Our solution is a highly flexible three-
parameter distance-based treetop reduction method. Tech-
nically, it identifies all neighbours within a defined radius
(first parameter), referred to as the distance, and retains the
highest value (Fig.4a and b). The other two parameters,
min_H (minimum height) and max_H (maximum height),
facilitate convenient threshold settings. This process enables
the identification of lower trees in multilayered forests, as
long as these trees are not under the canopy (Fig.4b).
TREETOPS
From the user’s perspective, the GTR algorithm is bun-
dled into an R package called TREETOPS, which provides
two main functions (Fig.4c): get_TREETOPS() and final-
ize_TREETOPS(). The get_TREETOPS() function executes
the entire ITD process, including the CHM cutting, storage,
and treetop location. The finalize_TREETOPS() function
applies the distance-based treetop-reduction method. Both
(2)
TREETOPSlayer
2
=CentroidsGTR
21
∈GTR32
functions are user friendly and require a maximum of four
parameters. To set the threshold, the user must set the min_H
and max_H (height-defining) parameters within the final-
ize_TREETOPS() function (Fig.4c). The outputs of both
functions are simple sf objects.
Testing materials andmethods
Study sites
The research encompassed three distinct study areas: the
Hardtwald forest in Karlsruhe, the Bretten municipal forest
(both situated in the federal state of Baden-Württemberg,
Germany), and the Nagyerdő forest in Debrecen (located
in the federal state of Hajdú-Bihar, Hungary) (Fig.5). Ter-
rain characteristics varied across the study sites. The two
Karlsruhe sites (KA09 and KA10) and the Nagyerdő forest
were situated on flat terrain, whereas the two Bretten sites
(BR01 and BR05) were characterized by a hilly landscape.
The studied managed German forests consist primarily
of the following tree species: Norway spruce (Picea abies),
Scots Pine (Pinus sylvestris), Douglas fir (Pseudotsuga
menziesii), common oak (Quercus robur), red oak (Quercus
rubra), sessile oak (Quercus petraea), European beech
(Fagus sylvatica) and European hornbeam (Carpinus betu-
lus). Scots pine, red oak, and European beech were dominant
in KA09 and KA10. A more diverse tree species composi-
tion, including spruce, Douglas fir, European beech, oaks,
and European hornbeam, characterises BR01 and BR02. The
mixed species composition, dense canopy cover, and mul-
tiple layers describe the four forests. Detailed information
on plot characteristics was obtained from a previous study
(Weiser etal. 2022).
Fig. 4 Example CHM (0.5∙0.5m pixel size) with treetops (a); exam-
ple CHM with treetops after applying the distance-based treetop filter
(b); (c) the two main functions, get_TREETOPS() and finalize_TREE-
TOPS() from the R package TREETOPS, and the implementation of
threshold settings using the min_H and max_H parameters
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5230 Modeling Earth Systems and Environment (2024) 10:5225–5240
Our selected Nagyerdő forest plot accommodates native
trees like common oak, silver poplar (Populus alba), and
stands of cultivated Austrian pine (Pinus nigra), Scots pine,
common hackberry (Celtis occidentalis), red oak, and east-
ern American black walnut (Juglans nigra). The forest site
is characterized by a very dense, mostly single-layer canopy
structure and a composition dominated by deciduous tree
species.
LiDAR data
LiDAR acquisition for German forests was conducted using
a RIEGL VQ-780i sensor (RIEGL Laser Measurements Sys-
tems, 2019). The flight was conducted on July 5, 2019. For
Nagyerdő, the LiDAR data was acquired on May 22, 2020,
using the RIEGL VQ780ii system. For a detailed descrip-
tion of the German LiDAR acquisition, refer to Weiser etal.
(2022). LiDAR data characteristics for all study areas are
summarized in Table1. Note that the Nagyerdő point cloud
has a mean point density of 10 pts/
m2
, which is considered
low-resolution.
Reference data
Tree stem positions andtree heights
Reference tree stem positions in the German forests were
determined using DTMs derived from ALS point clouds,
complemented with data from terrestrial laser scanning
(TLS) or unmanned laser scanning (ULS) point clouds
(Weiser etal. 2022). Tree heights were extracted from
ALS data because of the reported non-visibility of treetops
caused by dense canopy conditions (Weiser etal. 2022). In
Nagyerdő, 60 reference stem coordinates were collected
using the Stonex S9i RTK GNSS system (https:// www.
stonex. it/ proje ct/ s9i- gnss- recei ver/) to ensure accuracy under
the canopy. For trees with problematic coordinates caused
by a low received signal owing to dense canopy filtering,
15 repeated measurements were conducted, and the coordi-
nates were calculated by averaging the results. Tree heights
were measured using the Haglöf EC II D-R electronic tool
(https:// haglo fswed en. com/ proje ct/ ec- ii-d-r) employing the
reference height mark control method. Each tree was marked
Fig. 5 Locations of the four German forest plots (left) in the federal state of Baden-Württemberg and the Hungarian Nagyerdő forest site (right)
in the federal state of Hajdú-Bihar
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5231Modeling Earth Systems and Environment (2024) 10:5225–5240
at 2m using a tape measure, and during measurement, the
EC II D-R was aligned to ensure that it displayed 2m when
aimed at the mark. This accuracy control process resulted in
the determination of the 60 reference tree heights.
Filtering trees based onCHM‑derived heights
Nagyerdő forest was selected as the target site, whereas the
four German forests served as test sites. Therefore, Nagyerdő
forest will undergo individual tree segmentation in a subse-
quent study, guided by the treetops identified by the CHM-
based treetop detector presented in this study. Additionally,
the LiDAR data acquired over Nagyerdő has consider-
ably lower resolution compared to the German aerial laser
scanned data (Table1). We aimed to develop a raster-based
ITD method using low-resolution LiDAR data. It should also
be noted that the resolution of the raw LiDAR data did not
affect the information quality obtained from the rasterized
topological surface of the canopy. However, acquiring low-
resolution ALS data is significantly less expensive.
Because German forests consist of multiple layers and
raster-based ITD is not capable of capturing the treetops
of suppressed or under-canopy trees (Eysn etal. 2015),
CHM-derived forest height distributions were visualized to
understand the similarities and differences between the tar-
get and the four test sites (Fig.6). The differences between
the two highest peaks of these distributions were calculated
to define the CHM-based layering of the respective forests.
While Nagyerdő presented a height difference of 1.93m,
suggesting a single-layer forest, the German sites revealed
height differences ranging from 3.42m to 12.17m with mul-
tiple peaks (Fig.6). Overall, the tree heights in the Nagyerdő
forest were considerably lower. Moreover, the distributional
line segments of BR01 and BR05 showed similarities over
their 20-m ranges in the Nagyerdő height profile (Fig.6).
This phenomenon suggests that the CHM-induced one-to-
one comparability between the trees of BR01 and BR05 and
the trees of Nagyerdő is only meaningful for trees, especially
of the BR01 and BR05 forests, which are higher than 20m.
Therefore, the reference trees of the four German forests
were filtered, and only trees higher than 20m were consid-
ered in this study.
Number ofreference trees andtree species distributions
After height filtering, the number of reference trees in the
five study sites: BR01, BR05,KA09, KA10, and Nagyerdő,
became 153, 173,106, 32 (Fig.7a), and 60 (Fig.7b), respec-
tively. Concerning the area of the four test forests, BR01
accommodated 2.02ha and BR05 1.89ha, while KA09 and
KA10 were left with 1.80ha and 1.22ha (Fig.7c). Our tar-
get forest, Nagyerdő was the only 1ha square area because
it was earmarked for future research. The encircling cuts
from the respective CHMsof the four test forests ensured
that their area boundaries were close to the test reference
trees, minimising their areas. Smaller areas facilitated faster
ITD processing.
The selection of these German forests for testing was
also motivated by the similarity between their tree species
composition and that of Nagyerdő forest. From an ALS per-
spective, the ratio of coniferous to deciduous trees was of
primary interest (Eysn etal. 2015; Stereńczak etal. 2020;
Zhao etal. 2017). Therefore, the ratios of the reference tree
species and coniferous-to-deciduous ratios of each site were
plotted and visually compared (Fig.8). The reference trees
of BR01 and KA10 showed high similarity, those of BR05
showed low similarity, and those of the KS09 forest were
dissimilar to the Nagyerdő reference trees (Fig.8c).
LiDAR data preprocessing
Three preprocessing steps were conducted using the lidR
package (Roussel etal. 2020) in the R computational envi-
ronment (R Core Team 2022). First, the raw LiDAR point
cloud was classified into ground and surface points using
cloth simulation filtering (Zhang etal. 2016). Next, the
CHM was derived directly from the classified above-ground
and ground points using a pit-free algorithm (Khosravipour
etal. 2014). However, the resulting CHMs of the BR01,
BR05, and KA10 test sites exhibited two, one, and three
pits, respectively (Fig.7a). These pits did not influence the
Table 1 Characteristics of
LiDAR data used for study sites Characteristics KA09, KA10, BR01 and BR05 Nagyerdő
ALS sensor RIEGL VQ-780i RIEGL VQ-780ii
Flying altitude AGL 650m 1077m
Off-nadir scan angle ± 30° ± 30°
Laser beam divergence 0.25 mrad 0.18 mrad
Pulse repetition frequency 1000kHz 2000kHz
Flight line distance 175m 240m
Flight line overlap 76% 20%
Point density > 40 pts/
m2
(max: 103 pts/
m2
) > 2 pts/
m2
(mean: 10 pts/
m2
)
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5232 Modeling Earth Systems and Environment (2024) 10:5225–5240
ITD and were therefore not subjected to further processing.
Finally, Gaussian filtering with a window size of 3 × 3 pixels
was applied for image smoothing and noise removal.
LM withVWF versustheGTR
To ensure logical comparability between the two methods,
we proposed an equation based on our target study site to
adjust the window size of the VWF depending on the tree
height embedded in the CHM. This function was defined as
follows (Eq.3, Fig.9):
where y represents the window size for the VWF and the
distance parameter of finalize_TREETOPS() and x represents
the height values stored by the CHM. A sensible minimum
height threshold of 5m was chosen, below which no trees
could be found in the single-layered Nagyerdő forest. The
delinearised green curve became linear at 20m (Fig.9,
x-axis), indicating that the window size was fixed at 5m for
(3)
y
=5.7 ⋅(−
(
e
−0.08
⋅
(x−5)
−1
)
+
1
the B01, B05, KA09, and KA10 test forests. Throughout
this study, the LM with VWF was optimised and computed
using the lidR package.
The GTR distances (i.e., the window sizes of VWF)
were calculated for the following thresholds: 5.00 to
9.99m, 10.00 to 20.00m, and above 20.01m, using the
following formulae (Eq.4–6, Fig.9):
where
VWSheight
>
andVWSheight=
denote the variable win-
dow size greater than and equal to a given height (y-axis
in Fig.9), respectively. The distance for treetop reduc-
tion for treetops taller than 20m corresponds to 4m,
whereas for treetops between 10 and 20m, it is 2.93m.
For treetops smaller than 10m, this distance was negli-
gible (Fig.9).
(4)
4=VWSheight
>20
−1
(5)
2.93 =(VWSheight=
10
+(VWSheight=
20
−VWSheight=
10
)∕2)−1
(6)
0.94 =(VWSheight=
5
+(VWSheight=
10
−VWSheight=
5
)∕2)−1
Fig. 6 CHM-derived height
distribution of the target forest
(shown in green). The inset
graphs show the vertical height
profiles of the BR01, BR05,
KA09, and KA10 test forests
(depicted in red). In the insets,
the horizontal dashed lines
indicate the highest two peaks
at each site, with the differences
expressed using the symbol
Δm
.
The grey horizontal lines in the
inset graphs represent the 20-m
comparability threshold
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5233Modeling Earth Systems and Environment (2024) 10:5225–5240
Accuracy assessment ofindividual treetop detection
A verification method developed by Eysn etal. (2015) has
established itself in studies focussing on Central European
alpine and lowland forests (Eysn etal. 2015; Stereńczak
etal. 2020). The key algorithm of this approach is called
the Matching Algorithm (MA), which links treetop detection
results to reference data. During the matching process, the
MA produces various qualitative and quantitative statistical
parameters (Eysn etal. 2015).A modified version of MA
was applied to assess the accuracy of the ITD results. This
had to be altered because our particular interest lay in a com-
parative analysis between the LM with VWF and the GTR
on a one-to-one basis. More importantly, the German and the
Nagyerdő reference trees did not provide reference informa-
tion for every tree standing within the study area boundaries.
Thus, the number of trees extracted using the two methods
was not reliably linked to the number of reference trees.
This phenomenon technically hindered obtaining the correct
extraction and commission rates. To address this issue, both
the extraction and commission rates were mathematically
adjusted using Eq.7:
where the
NMTest
parameter is the Modified Number of
Extracted trees described below.
The following validation parameters were output by the
MA:
NTest → Number of Extracted trees,
NRef → Number of Reference trees,
RRef → Rate of Reference trees ~
NRef ∕(NRef +NTes t )
,
NMTest → Modified
NTes t
~
if RRef
<
0.3
−
→
NMTest
=
NTes t
⋅
(
1−R
Ref )
−N
Ref
else-→ NMTest
NTes t
,
(7)
adjustment
=log10
(
N
MTest)
⋅
20
Fig. 7 Study sites and reference tree coordinates of the four German forests (a) and of Nagyerdő forest (b). Site-specific reference tree character-
istics in tabular form (c). The mean height were derived from the respective CHMs
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
5234 Modeling Earth Systems and Environment (2024) 10:5225–5240
NMatch → Number of Matched trees,
NCom → Number of Extracted trees that could
not be matched ~
NMTest −NMatch
,
NOm → Number of Reference trees that could
not be matched ~
NRef −NMatch
,
NMTest/NRef → Modified Extraction rate,
NCom/NMTest-adjustment → Modified Commission rate,
Extracted trees that could not be
matched.
HTest → Extracted Height of Matched Test
trees,
HRef → Height of Reference trees,
DHor → Horizontal distance between
Matched Test and Reference
trees,
NMatch/NRef → Matching rate,
Nom/NRef → Omission rate, Reference trees
that could not be matched.
Using the values of
HTes t
and
HRef
, the mean absolute
error (MAE) was determined for height difference verifica-
tion between Matched Test and Reference trees by using
Eq.8:
where i indicates the i-th value regarding Reference and
Test heights and the modulus is denoted by the | | symbol.
Furthermore, the MA output parameters described above
were used to define the following root mean square (RMS)
parameters:
(8)
MAE
height[m]=(1∕NRef )⋅
∑|
|
|
HRef i−HTes t i
|
|
|
Fig. 8 Reference tree species distributions (%) of the four German forests (a) and of the Nagyerdő forest (b). Panel (c) shows the ratios of conif-
erous to broadleaf tree species in the respective forest plots
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5235Modeling Earth Systems and Environment (2024) 10:5225–5240
RMSMatch → Root Mean Square of Matching rates,
RMSExtr → Root Mean Square of Extraction rates,
RMSCom → Root Mean Square of Commission rates,
RMSOm → Root Mean Square of Omission rates.
Results
ITD results atsite permethod
The highest matching rate was found in the KA10 forest,
where both methods showed 81% matching. Interestingly,
the lowest rate (55%) was produced by LM with VWF in
the BR01 forest (Fig.10a). Regarding our target forest, the
GTR method (80%) slightly outperformed the LM with
VWF (77%). Overall, a minor performance advantage was
observed in favour of the GTR method.
Regarding the accuracy of height matching, the GTR
method displayed Mean Absolute Error (MAE) values
between 0.73 and 2.04m, while the LM with VWF evi-
denced MAE values between 1.01 and 2.50m (Fig.10a).
Across all forest sites, the GTR achieved slightly better
MAE results.Spatially, it is noteworthy that the two types
of matched trees (those located by the LM with VWF and
the GTR methods matching a particular reference tree) were
situated within a distance of less than 4m from each other
in every case where both methods matched the same refer-
ence tree (Fig.10b).
Concerningcommission errors, no differences were
observed between the LM with VWF and the GTR meth-
ods at the KA09 site (Fig.11). While the LM with VWF
obtained a 2% lower value in KA10, the three remaining
forests—BR01, BR05, and Nagyerdő—witnessed the GTR
having 2%, 1%, and 2% lower rates, respectively (Fig.11).
The highest omission rate of 45% was found with the
LM using VWF in BR01, whereas the lowest rate (19%)
was observed with both algorithms in the KA10 forest
(Fig.11). For BR01, BR05, KA09, and Nagyerdő, the
GTR method showed lower omission error rates by 5, 6,
5, and 3%, respectively.
ITD results permethod
Quantitatively, both ITD approaches yielded high RMS
values: 74% by the GTR and 71% by the LM with VWF.
The RMS differences concerning the modified commission
Fig. 9 Calibrated variable win-
dow size for the Nagyerdő forest
(depicted by the green line)
and the adjusted GTR distances
(represented by the red line)
in relation to height (x-axis).
The main equation is displayed
in green, while equations and
values of distances are written
in red;
VWSheight
>
or =
signifies
a variable window size greater
than or equal to a given height
(y-axis)
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5236 Modeling Earth Systems and Environment (2024) 10:5225–5240
and omission rates were 1% and 4%, respectively, provid-
ing an edge to the GTR (Fig.12). The modified extraction
rates were high for both methods: 140% for GTR and 134%
for LM with VWF (Fig.12).
Discussion
The GTR method described in this study is a simple CHM-
based treetop detection algorithm that was developed for
Central European forests. It was provided in a ready-to-use
Fig. 10 Matching rates concerning forest sites and the dual methods
(a; diamonds indicate MAE values, grey numbers on bars represent
the number of reference trees for each forest site, white numbers show
the matching error rates for each forest depending on the methods:
GTR, Growing Tree Region, and VWF, Variable Window Filtering).
The spatial locations of the 60 reference (REF) trees, GTR-extracted
treetops, and Local Maxima with VWF-extracted treetops of the
Nagyerdő forest are shown in (b)
Fig. 11 Modified commission
and omission error rates for the
studied forest sites with regard
to the two methods (GTR:
Growing Tree Region; VWF:
Variable Window Filtering)
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5237Modeling Earth Systems and Environment (2024) 10:5225–5240
form for both forest managers and the research community.
Its open access availability, an issue that other researchers
often overlook (Stereńczak etal. 2020; Zhao etal. 2017),
makes it indisputably useful. We offer a flexible user-friendly
tool that outperforms the widely used LM with VWF, and
can be adjusted to various forest ecosystems depending on
their vertical structure. The five tested Central European for-
ests were mixed and partly dominated by deciduous trees.
According to previous studies, similar forest communities
make ITD highly demanding (Eysn etal. 2015; Vauhkonen
etal. 2012). Based on prior knowledge (Eysn etal. 2015;
Stereńczak etal. 2020), we selected possibly visible trees
from the low-resolution ALS perspective using the canopy
layer of multi-story forests. Moreover, our approach to accu-
racy assessment is derived from a method established in
ITD performance evaluation, focusing on Central European
alpine and lowland forests (as described in SectionAccuracy
assessmentof individual treetop detection). This enabled our
findings to be directly linked to those presented by Eysn
etal. (2015). A segmentation-centered study that conducted
ITD before delineation in mixed and deciduous forests, simi-
lar to the ones in this research, also provided comparable
results to our findings (Zhao etal. 2017).
An important aspect of the comparative analysis between
the GTR and the LM with VWF is that the VWF was cali-
brated specifically for the Nagyerdő forest (SectionLM
with VWF versus the GTR ). Notably, the GTR was math-
ematically adjusted for logical comparison with the LM with
VWF, which means that the threshold-setting capability
(SectionThe algorithm, (iii) Number of treetop reduction)
of the GTR tool was not fully utilized.
Eysn etal. (2015) analysed the performance of eight
different ITD methods and reported RMS matching rates
between 66 to 82% for trees above 20m. One of the best-
performing methods, considering extraction, commission,
and omission error rates, was the LM with VWF, which
achieved 72%. Although their research areas were located
in the Alpine region, our results (74% revealed by GTR and
71% by the VWF) aligned with theirs. This phenomenon
suggests, unlike statements from other studies (González-
Ferreiro etal. 2013; Khosravipour etal. 2014), that domi-
nant and co-dominant treetops can be equivalently well
extracted independently of the topographic characteristics
of the forest. In general, the declared overall performance
was comparable. While the article published by Eysn etal.
(2015) described 47% as the best matching rate, our study
reported 52% for both methods. These correspondences
underline the plausibility of our proposed method for com-
mission and extraction adjustments.
At the Nagyerdő site, the GTR matching rate was 80%.
Similar ITD results with percentages between 80 and 87
were reported in temperate, less dense boreal deciduous
forests (Zhao etal. 2017). This analogy can be explained by
the fact that both algorithms applied a theoretically similar
top-down CHM-cutting approach.Although GTR outper-
formed the calibrated LM with VWF, the obtained RMS
differences in matching, modified commission, and omission
rates are marginal. While the VWF has been used through-
out this study in its calibrated form based on Nagyerdő for-
est, the GTR was adjusted to conduct a logically founded
comparative analysis. Thus, it can be stated that the GTR is
a competitive alternative to the LM with VWF, and it should
also be optimized by using its threshold-setting feature with-
out limitations. However, a calibrated VWF can match the
robustness of the non-optimized GTR method in lowland
mixed and deciduous forests.
Three further issues need to be addressed. First, consid-
ering the CHM as a topographic surface makes it difficult
for the GTR to detect suppressed trees and trees with flatly-
shaped crowns because such objects lack the necessary pro-
trusions emerging from the CHM. This issue becomes rel-
evant if treetop distances in the same height class (as defined
by threshold setting) of the studied forest vary, and the out-
put of the finalize_TREETOPS() function would be errone-
ous. Second, the lack of abundant reference trees covering
the target (Nagyerdő forest) study area led us to develop a
strategy for modified commission and extraction rates, which
were used to evaluate the performance of both algorithms
on the test sites (BR01, BR05, KA09, and KA10). While
plausible, this strategy is a prone-to-error replacement for
commission and extraction rates obtained using forest inven-
tory data covering the entire study area. Third, the GTR was
Fig. 12 Overall performance of the compared ITD methods: Root
Mean Square (RMS) of matching, modified extraction, modified com-
mission, and omission error rates for the two methods (GTR: Grow-
ing Tree Region; VWF: Variable Window Filtering) were computed
across all study sites
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5238 Modeling Earth Systems and Environment (2024) 10:5225–5240
tested in temperate Central European mixed- and deciduous-
dominated forests; thus, the robustness of the algorithm in
other forested ecosystems is unknown. It is reasonable to
assume that the algorithm would perform better in a conifer-
ous environment, as the ITD in coniferous forests has been
reported to achieve higher accuracy. The robustness of the
GTR method should be evaluated in the future using other
types of LiDAR forest data combined with area-covering
forest inventory data from different forested ecosystems.
Conclusions
We introduced a novel and robust method for detecting tree-
tops, termed the Growing Tree Region (GTR) algorithm,
which leverages canopy height models (CHM) derived from
low-resolution LiDAR data. Our algorithm surpasses the
widely employed local maxima (LM) search technique with
calibrated variable window filtering (VWF) in deciduous-
dominated forests in Central Europe. To enhance the user-
friendly implementation of our algorithm, we developed an
R package named TREETOPS that seamlessly integrates
into the lidR package specialised for LiDAR applications
in forestry.
In contrast to the automated search of LM with VWF,
TREETOPS provides users with a three-parameter-con-
trolled threshold-setting option to effectively detect lower
treetops in multilayered forests. While this study did not
specifically address the performance of the threshold setting,
it is likely influenced by the limitations of the CHM, par-
ticularly in the detection of trees beneath the canopy layer.
TREETOPS has the capability to accurately detect younger
(lower) trees that are visible from an airborne laser scanning
(ALS) perspective and are not concealed by the canopy. This
suggests that TREETOPS may outperform LM with VWF in
detecting treetops of younger trees in multilayered forests,
although comprehensive testing is essential to validate this
assertion.
It is strongly recommended that future studies focus
on evaluating the effectiveness of the GTR method across
diverse forest types worldwide. Given the tool's open acces-
sibility, exploring the combination of GTR with various seg-
mentation techniques within the lidR programming frame-
work is also encouraged. Additionally, a viable two-stage
procedure for tree detection in multi-layered forests could
involve i) CHM-based treetop detection and ii) tree crown
delineation utilizing the original point cloud in conjunction
with the treetops identified by TREETOPS.
Acknowledging the low-resolution of LiDAR data, there
is an ongoing effort to develop point-cloud-based tree
segmentation. This development relies on the assignment of
laser points to detected treetops generated by TREETOPS.
This approach aims to enhance the accuracy of tree segmen-
tation despite data limitations (i.e., low-resolution LiDAR),
emphasizing the potential of TREETOPS in contributing to
comprehensive forest analysis methodologies.
Acknowledgements The authors were supported by the NKFI
K138079 and the KKP 144068 projects during manuscript prepara-
tion. We are grateful to Envirosense Hungary Ltd. for providing the
LiDAR data used in this study.
Author contributions Gergő Diószegi conceived the ideas, conceptual-
ized, preprocessed data, conducted programming and visualising, wrote
original draft and finalized draft; Vanda Éva Molnár and Loránd Attila
Nagy collected reference data; Péter Enyedi provided LiDAR data;
Péter Török reviewed, edited original draft and finalized draft; Szilárd
Szabó led writing, reviewed and edited original draft and finalized
draft. All authors contributed to the research and gave final approval
for publication.
Funding Open access funding provided by University of Debrecen.
Data availability TREETOPS package is available at https:// git hub.
com/ DijoG/ TREET OPS, and can be installed by executing the follow-
ing line:
devtools::install_github(“DijoG/TREETOPS”).
Declarations
Conflict of interest The authors declare that they have no known com-
peting financial interests or personal relationships that could have ap-
peared to influence the work reported in this paper.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article are
included in the article’s Creative Commons licence, unless indicated
otherwise in a credit line to the material. If material is not included in
the article’s Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will
need to obtain permission directly from the copyright holder. To view a
copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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