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Airborne laser scanning (ALS) has recently gained increasing attention in forestry, as ALS data may facilitate the efficient assessment of forest inventory attributes and ecological indicators related to forest stand structure. This paper presents a novel workflow for individual tree detection and tree crown delineation using ALS data. The developed point-based approach included several tree allometry rules on permissible tree heights and crown dimensions to increase the likelihood of detecting the actual tree profiles. The accuracy of the method was assessed in a heterogeneous forest with a complex stand structure in Slovakia (Central Europe). ALS measurements were taken using a RIEGL Q680i scanner at 700 m of height with a point density of 20 echoes per m^{2}. The ground reference data included the measured positions and dimensions of 1332 trees in nine plots distributed across the region. We found that the number of individual trees detected by the algorithm using ALS data was systematically underestimated by 34 ± 15% relative to the reference data. The delineated crown coverage was underestimated by 2 ± 6% as well, but the latter difference was not statistically significant (p>0.05).

In recent years, airborne laser scanning (ALS), also referred to as airborne light detection and ranging (LiDAR), has become established as a novel technology for estimating forest inventory attributes (

The area-based prediction of forest attributes relies on the statistical dependency between the field-measured and ALS-derived variables (

ITD methods involve a sequence of steps that includes tree detection, feature extraction, and estimation of tree attributes (

Many approaches have been developed to detect individual trees based on ALS data. Overviews were provided by

The comparability of accuracy assessments conducted under different conditions is limited. However, it has been suggested that the extraction method from ALS data is the main factor affecting the accuracy of tree detection, while point cloud density has a lesser impact (

The aim of this paper is to present a point-based workflow for detecting individual trees and delineating their crowns based on ALS data. The proposed algorithm attempts to improve several shortcomings of the current extraction methods through the following steps:

the algorithm uses the complete information contained in ALS data in all procedures of tree detection workflow, and optimizes the computationally demanding operations by tiling and thinning techniques applied on the raw ALS data;

treetops detection and tree crowns delineation is done iteratively, and each iteration includes tests for treetop identification based on tree allometry rules, aiming to ensure that the permissible spatial and the dendrometric structure of a forest stand and a tree are not violated, and that the likelihood of falsely identified trees is reduced;

users can modify a number of parameters and customize the algorithm for matching specific stand conditions and/or meeting specific objectives.

The presented algorithm is implemented in the reFLex (remote Forest Land explorer) software, which was developed by the National Forest Centre, Slovakia. The objective was to develop an easy-to-use application to be employed in the forestry practice.

The algorithm for treetop detection and tree crown delineation includes five connected procedures which are described in detail in the following sub-chapters.

The input file is a classified point cloud containing ground and vegetation classes. The initial procedures are applied to: (i) divide the points into a 3-dimensional regular tiles (Tiling procedure); (ii) calculate the absolute height above ground for each point (Normalization procedure); and (iii) reduce the number of points in the input file by applying a minimum tree height threshold (Height restriction procedure). These operations yield a point cloud that is further used for an iterative search of treetops and tree crowns (Finding the local maxima, Geo-Dendrometric test, Delineation of tree crowns). Finally, the outputs of all procedures are exported to point and polygon vector files in the ESRI shape (shp) format.

The tiling procedure is used to divide the raw point cloud to a regular 3-dimensional tiles. This procedure is applied to efficiently use the computer memory and allow for parallel processing of points allocated to the tiles. The user-defined tile size (TS) is a variable that can significantly affect output accuracy.

The normalization of raw point cloud was applied to calculate the absolute height above ground (h_{nor}) for each point in each tile (

where h_{nor} is the normalized height of points in the tile (in m), z_{max} is the elevation of points in the tile (m a.s.l.), z_{min} is the elevation of the lowest point in the tile interpolated from the three adjacent tiles (m a.s.l.).

The height restriction procedure defines the minimal height (m) of trees to be identified, thereby all points below this threshold are discarded. This operation reduces the initial number of points and the required computation time, and defines a shortest tree to be identified in the next steps.

A moving-window analysis (_{teo}), and then subjected to a geo-dendrometric (GD) test.

As part of the local maxima detected in the previous operation might not be indicative of true treetops, an additional test is applied to select a subset of T_{teo} that is considered to include the real treetops. We conceived a set of dendrometric criteria which define a permissible tree and stand structure in terms of tree distribution, height relationships between trees, and the relationship between tree height and crown dimensions. The values of such criteria can be derived from ground-sample data collected in the evaluated area or taken from literature on tree allometry. The T_{teo} that pass the GD test conditions are referred to as true treetops (T_{true}). The remaining T_{teo} become false treetops (T_{false}) and are processed along with the remaining points in a cloud in the next operations of the workflow. The GD test consists of the following steps:

(a) _{mean}), is created around each T_{teo} (_{teo} within the test area is evaluated. The size of the test area r_{lim} (m) is defined as (

where Th_{teo} is the tree height of the theoretical top (m), and cr_{mean} is a user-defined estimate of the ratio of mean crown radius to tree height in the investigated forest. If no additional T_{teo} occurs at a distance < r_{lim}, such T_{teo} is accepted as a real treetop and is maked T_{true} (_{teo} occur within the r_{lim}, such T_{teo} are marked as T_{test} and tested for height differences (_{teo} are convex, such T_{teo} represent two treetops. In the opposite case, the lower T_{teo} is discarded, and only the higher T_{teo} is marked as a real treetop, while the discarded T_{teo} is considered as a part of crown of the higher T_{teo}. To decide which T_{test} in the tested pairs is the real treetop, the normalized heights (h_{T.nor}) connecting the respective pair of T_{test} are evaluated (_{mean}). Then, the limit h_{lim} (m) is calculated for each lower T_{test} as (

where h_{lim} is the limit of the test (m), Th_{L.test} is the tree height of the lower tested top (m) and hd_{mean} is the estimate of the ratio of mean tree height differences to tree height in the investigated forest.

Finally, if at least one h_{T.nor} between the evaluated pair of T_{test} is below h_{lim}, both tested T_{test} are accepted as real treetops (_{test} is considered as a real treetop (

(b) _{true} is calculated for all new T_{test} (i.e., those appearing in the second and subsequent iterations of the mowing-window-based search for the local maxima - _{max }- crown width expressed as a proportion of tree height) to be customarily established for the investigated forest. Then, the limit d_{lim} (m) is calculated for each T_{true} (

where d_{lim} is the limit of the test (m), Th_{true} is the tree height of the true top (m), cw_{max} is the estimate of the ratio of maximum crown diameter to tree height in the evaluated forest. The test assumes that no treetop is allowed to occur within the distance d_{lim} around any T_{true}. The case of trees growing in the understorey is described below.

The vertical distance between trees is tested to discard false treetops situated in the crowns of other trees, and to capture the trees situated under the canopy. The test requires the user to specify the maximum crown length in the investigated forest, in terms of crown length proportion of tree height (cl_{max}). Then, the limit l_{lim} (m) is calculated for each T_{true} (

where l_{lim} is the limit of the test (m), Th_{true} is the tree height of the true top (m), cl_{max} is the estimate of the ratio of maximum crown length to tree height in the investigated forest. This test assumes that a treetop can occur under the crown of any T_{true} (

Each T_{true} is assigned to its central crown part (CCP), which is a circle of diameter equal to the tile size (TS). Then, the peripheral crown parts (PCP) of the point cloud are repeatedly assigned to the nearest CCP until they meet any point already assigned to any other CCP or until they reach the limits for assigning new crown parts (described below). A height limit ensures that all PCP which are to be assigned to the CCP are lower than T_{true} and in the height range specified by the crown length limit (l_{lim}). Distance limit ensures that PCP is situated within the permissible width range specified by the crown distance limit (d_{lim}). The information on the horizontal and vertical positions of all tested PCP is obtained from the point cloud data.

Finally, all parts of the crown (central and peripheral) assigned to the T_{true} are merged to create a single crown object, and its profile is smoothed by Bezier interpolation. We found this method to well approximate the real 2D crown projection, allowing the fast processing of a large number of tree crowns. After the crown delineation phase is completed, the crown coverage is calculated as the ratio of the forest floor covered by the delineated vertical crown projection and the whole stand area.

We tested the effect of three tile sizes (TS = 1, 2 and 3 m) on tree detection performance. A minimum tree height parameter was set with respect to the conventional forest definitions by IUFRO and FAO to 5 m. Limits for geo-dendrometric test and crown delineation were estimated based on field sample data. The ratio of mean crown radius to tree height (cr_{mean}) was set to 0.15, the ratio of mean tree height differences to tree height (hd_{mean}) was 0.1, the ratio of maximum crown width to tree height (cw_{max}) was 0.4, and the ratio of maximum crown length to a tree height (cl_{max}) was set at 0.7.

The research was conducted in the Forest Enterprise of the Technical University in Zvolen, central Slovakia (48° 37′ N, 19° 04′ E -

The ALS data used to test the applicability of the presented workflow were acquired in April 2012 using a RIEGL Q680i scanner. The average flying altitude was 700 m. The instrument operated at pulse rate frequency of 320 kHz, with a 122 Hz scan frequency and scan angle of ± 50 degree. The obtained laser data covered the whole study area and had an average density of laser hits of 20 points per m^{2}. From each emitted pulse, a maximum of seven returns were recorded. The point ratios were 56% for the first echo, 21% for the second, 13% for the third, and 10% for other echoes.

The ground data were obtained by a terrestrial survey in a part of the study area. The survey was carried out in nine reference plots (RP) covering a total area of 3.3 ha (

Most tree species occurring in the region were represented in the RPs. The species composition was dominated by Norway spruce (

The crown canopy closure in the RP was between 78% and 100%. Almost 70% of the measured trees were situated in the main crown level (co-dominant trees, constituting the main canopy), 20% belonged to the upper level (dominant trees higher than the main canopy level) and 10% to the lower level (intermediate and suppressed trees lower than the main canopy).

A total of 1322 trees with diameter ≥ 7 cm were measured for position, species, height and diameter. The crown coverage in each RP was estimated as the proportion of forest floor covered by the estimated vertical projection of tree crowns.

An accuracy assessment was carried out by comparing the ground reference data (TER_{j}) with outputs derived from the ALS data using the method described above (ALS_{j}). The accuracy of both individual trees detection and crown coverage delineation was evaluated for three tile sizes - 1×1 m (TS1), 2×2 m (TS2) and 3×3 m (TS3).

Differences were calculated between ALS_{j} and TER_{j} and the mean difference (

where _{i} is the individual difference, RMSE is the root mean square error, _{i} and hat{_{i} are the ground-reference and ALS-derived attributes, respectively for the

The following detection rates were used to assess the ratio of detected individual trees and the reference trees: (i) the extraction rate (ER), as the total rate of detected trees (ALS) in respect to the number of reference trees in RP (TER -

(ii) the matching rate (MR), i.e., the total rate of matched trees (

where TP indicates the true positives; (iii) the commission rate (CR),

where FP indicate the false positives; and (iv) the omission rate,

where FN indicates the number of false negatives.

The analysis of ground survey data revealed a number of treetops larger than that detected by the ALS-based assessment. Especially in densely forested areas, the detected local maxima do not always represent the exact tree positions, thus the matching rate was low. Trees that were standing alone, coniferous and clearly separated trees in loosely stocked areas were correctly detected in most instances.

First, we evaluated the extraction and matching rates for the three forest types represented in the reference plots (coniferous, deciduous and mixed forest) and for three tile sizes (TS = 1, 2 and 3 m -

The evaluation of differences in the number of individual trees detected by the proposed method and the number of reference trees on the ground suggested an overestimation using the tile size TS1 and an underestimation using tile size TS2 and TS3. The use of TS2 resulted in the highest accuracy, yielding an underestimation of -34 ± 15%, with a RMSE% of ± 41%. The mean or median paired test confirmed that the differences between number of field-measured and detected trees for each tile size were statistical significant (p<0.05),

We investigated the effect of the selected stand (in terms of tree species composition, number of tree species, mean height, mean diameter, and crown coverage), and site characteristics (slope) on the quality of the ALS-based tree detection (

The crown coverage values obtained using the three alternative tile sizes (TS1, TS2 and TS3) are shown in

The proposed algorithm underestimated the crown coverage by -11 ± 6% with tile size TS1 and overestimated the crown coverage by 8 ± 6% with tile size TS3. The RMSE% was ± 12% for TS1 and ± 10% for TS3. As it was the case for the number of trees, the TS2 setting provided the best estimate of crown coverage, resulting in a slight underestimation (-2 ± 6%). The RMSE% indicated that the crown cover was estimated with an accuracy of ± 7%. Our analyses confirmed that different tile sizes significantly affect the accuracy of crown coverage delineation as well. At the same time, we found that only the TS2 setting provided the output that matched well with the ground measurements, however, this difference was not statistically significant (

In this study we explored the performance of a newly-developed point cloud-based algorithm for the detection of treetops and the delineation of tree crowns in a temperate mixed forest in Slovakia. We were particularly interested in evaluating the benefits of integrating customizable tree allometry information in the model for the detection of individual tree.

Although the accuracy of the proposed method did not exceed that reported by other researches (

Our findings indicated that the application of the developed algorithm using optimal settings can correctly capture approximately 65% of all trees in the study area. According to previous studies (

There are several factors which could have affected the accuracy of tree detection in our assessment, and which should be considered when interpreting our findings. First, the RPs selected for the assessment included a broad range of site condition (including different tree species mixtures, stand density and relief slopes). This allowed the evaluation of the effect of site variables on tree detection accuracy. However, the selected RPs reflected a more complicated stand structure than commonly occurs in the study region, and this could have affected our results. Second, the geo-dendrometric criteria included into the tree position test decreased the number of detected trees, thus increasing the underestimation rate. On the other hand, such criteria reduced the false positive detections, thus preserving the permissible tree and stand structure and generating more realistic stands.

Although the accuracy of the proposed method suggests a limited applicability, the analysis of detected and undetected trees can provide a different perspective. The majority of undetected trees in the RPs had small size which poorly affects the assessment of the total stocking volume. Indeed, our previous research suggested that 32% of the undetected trees in the RPs contained only 11% of the growing stock (

Our results showed that the tile size had significant effect on the detection performance. We expect that testing the effect of a broader range of non-integer tile sizes could greatly improve the accuracy of the method, providing also a better adaptation to different stand structures and scanning densities (

The scanning density could affect tree detection performances as well.

Additional improvement in the accuracy of tree detection can be attained by statistical correction of the results. In this study, a significant underestimation in the number of tree detected was observed and a bias correction could be applied. However, such correction should be applied with caution, particularly when the sample size is small, as it was the case of the current study.

Unlike the proposed method, most studies used a canopy height model (CHM) as input for tree detection algorithms (

Most of the commonly used algorithms for tree detection from ALS-derived data consider all the local maxima detected as actual trees (

A distinctive feature of the developed algorithm is the crown delineation procedure. While other authors used mostly the CHM-based crown delineation (

The tree detection accuracy attained in this study (65%) is approximately in the middle of the range of tree detection accuracy (40-93%) reported by

ALS-based mapping of forest structure is an innovative component of forest inventory efforts, and has potential to significantly reduce the laborious field works and related costs.

We proposed a new method which integrate tree allometry criteria for detecting individual trees and delineating their crowns using ALS data. The method was validated using 1332 trees from 9 reference plots with heterogeneous stand structures. A significant underestimation rate in the accuracy of tree detection was obtained, while the accuracy of estimates of crown coverage was high and consistent with similar studies. Based on our findings we conclude that ALS-based forest inventory can provide reliable information only in particular stand conditions, specifically in commercial forests with simple structure, while their use in heterogeneous, vertically differentiated forests still remain limited.

The implementation of the proposed algorithm in the freely-available and easy-to-use reFLex software is intended to support a broader use of ALS data and promote new researches aimed at improving the presented tree detection methods.

This research was supported by the Slovak Research and Development Agency, in the framework of the projects “Innovations in the forest inventories based on progressive technologies of remote sensing” (APVV-15-0393) and “Innovative methods of close-to-nature forests management” (APVV-0439-12).

(a) Test for height difference between trees: a testing area (r_{lim}) is created around each theoretical treetop (T_{teo}, grey trees) with radius equal to the ratio of mean crown radius to tree height in the investigated forest (cr_{mean}, 0.15 or 0.3 of tree height in the example); (b) If only one T_{teo} is found in the r_{lim}, it is marked as real treetop (T_{true}, green tree); (c) otherwise, all co-occurring T_{teo} are marked as testing tops (T_{test}, brown trees).

Test for height difference between trees (second part). (a) The normalized heights h_{T.nor} (black points) between the pairs of T_{test }are calculated using the point cloud data. Then, the height difference limit h_{lim} is calculated for the lower T_{test} in each pair of T_{test} (light brown tree). The limit depends on the ratio of mean tree height differences to tree height in the stand (hd_{mean}, 0.15 and 0.3 in the example); (b) If any h_{T.nor} is lower than the h_{lim}, the T_{test} is marked as real treetop (T_{true}, green trees); (c) otherwise, T_{test} is marked as false treetop (T_{false}, dark brown tree).

Tests of horizontal and vertical distance between trees are performed simultaneously to remove the theoretical treetops in locations where treetops are not expected to exist. (a) A horizontal limit d_{lim} is calculated for each treetop T_{true }to represent a maximum permissible crown width in the stand (cw_{max}, 0.4 of tree height in the presented example). A vertical limit l_{lim} is calculated to define a maximum permissible tree length (cl_{max}, 0.5 and 0.8 of tree height in the presented example); (b, c) Then, all tested treetops (T_{test}) are classified as either new real treetops (T_{true}) or false treetops (T_{false}).

The study area. Elevation and position of the surveyed reference plots (RP1-RP9) are indicated by red circles on the maps.

Detection rates of extracted (orange colour) and matched (blue colour) individual trees for the reference plots (RP1-9) and for different tile sizes (TS1, TS2, TS3).

Regression between selected stand or site characteristics (^{2}) and F-test of statistical significance of the regression model (p-value) are displayed above each graph.

Description of measured stand data in the reference plots (RP).

Code | Area(ha) | Number of tree species | Conifers(%) | Mean height(m) | Mean diameter(cm) | Volume(m^{3} ha^{-1}) |
Slope(%) |
---|---|---|---|---|---|---|---|

RP1 | 0.50 | 6 | 8 | 26.67 | 32.55 | 429.16 | 25 |

RP2 | 0.30 | 6 | 43 | 27.27 | 34.73 | 611.49 | 33 |

RP3 | 0.25 | 7 | 61 | 26.64 | 37.75 | 446.25 | 5 |

RP4 | 0.25 | 5 | 73 | 32.72 | 43.57 | 622.12 | 6 |

RP5 | 0.25 | 3 | 1 | 26.91 | 26.68 | 584.45 | 37 |

RP6 | 0.25 | 3 | 80 | 27.31 | 44.31 | 617.80 | 22 |

RP7 | 0.25 | 5 | 50 | 23.70 | 36.60 | 508.44 | 22 |

RP8 | 1.00 | 6 | 75 | 28.59 | 43.37 | 507.18 | 25 |

RP9 | 0.25 | 1 | 0 | 29.20 | 35.98 | 456.33 | 22 |

Total | 3.30 | 11 | - | - | - | 4783.22 | - |

Average | 0.37 | 5 | 43 | 27.67 | 37.28 | 531.47 | 22 |

Differences and paired test between number of reference trees (TER_{n}) and detected trees (ALS_{n}) for different tile size (TS1-3). (e%): relative mean error; (se%): relative standard deviation of mean error; (RMSE%): relative root mean square error; (*): null hypothesis is rejected (p<0.05). Sample size: m=9.

Compared variables | e% | se% | RMSE% | Normality Test | Paired Test | ||
---|---|---|---|---|---|---|---|

W | p-value | t or Z | p-value | ||||

TER_{n} _{n}_TS1 |
100 | 52 | 118 | 0.802 | 0.022* | 2.666 | 0.008* |

TER_{n} _{n}_TS2 |
-34 | 15 | 41 | 0.931 | 0.486 | 4.299 | 0.003* |

TER_{n} _{n}_TS3 |
-59 | 11 | 68 | 0.837 | 0.053 | 5.315 | 0.001* |

Reference crown coverage (TER_{c}) and delineated crown coverage (ALS_{c}) for the reference plots (RP1-9) and for different tile size (TS1-3).

Variables | RP1 | RP2 | RP3 | RP4 | RP5 | RP6 | RP7 | RP8 | RP9 | Average | St. dev. |
---|---|---|---|---|---|---|---|---|---|---|---|

TER_{c} (%) |
87 | 89 | 87 | 88 | 100 | 85 | 89 | 85 | 78 | 88 | 6 |

ALS_{c}_TS1 (%) |
73 | 75 | 78 | 82 | 85 | 76 | 81 | 73 | 80 | 78 | 4 |

ALS_{c}_TS2 (%) |
85 | 83 | 88 | 90 | 84 | 86 | 92 | 85 | 75 | 85 | 5 |

ALS_{c}_TS3 (%) |
94 | 91 | 96 | 98 | 97 | 94 | 96 | 93 | 93 | 95 | 2 |

Differences and paired test between reference crown coverage (TER_{c}) and delineated crown coverage (ALS_{c}) for different tile size (TS1-3). (e%): relative mean error; (se%): relative standard deviation of mean error; (RMSE%): relative root mean square error; (*): null hypothesis is rejected (p<0.05). Sample size: m=9.

Compared variables | e% | se% | RMSE% | Normality Test | Paired Test | ||
---|---|---|---|---|---|---|---|

W | p-value | t or Z | p-value | ||||

TER_{c} _{c}_TS1 |
-11 | 6 | 12 | 0.887 | 0.187 | 5.347 | 0.001* |

TER_{c} _{c}_TS2 |
-2 | 6 | 7 | 0.811 | 0.027* | 0.770 | 0.441 |

TER_{c} _{c}_TS3 |
8 | 6 | 10 | 0.906 | 0.290 | -4.213 | 0.003* |