1 Introduction

There is an increasing need for accurate forest inventories to assist forest managers and decision makers in the planning of forest resources. However, forest inventory is a highly expensive and time-consuming task. Detailed information collected at the tree level, such as height and diameter are needed for stand parameters estimation.

Airborne LiDAR (Light Detection and Ranging) technologies now provide means to retrieve 3-D information at high sampling frequency and spatial accuracy. The actual accuracies of the approach are in the order of 15-20 cm vertically and 20-30 cm horizontally (Suarez et al. 2004). Such high accuracies can be achieved, thanks to recent developments in airborne Global Positioning System (GPS) and Inertial Measurement Unit (IMU).

LiDAR airborne overflow the Tree canopy model and Digital Terrain Model. Stems are located at the position of the tree top. Example taken from plot 8.

The actual accuracy of the LiDAR sensors makes possible the construction of Tree Canopy Models (TCM) at resolutions of 70 cm or less (Leckie et al. 2003). Using TCM, it is then possible to delineate individual crown. Several algorithms have been developed to automatise the delineation process and to help in predicting other forest parameters such as height, basal area, volume and biomass.

The aims of this study were therefore twofold: (i) to evaluate how well individual tree crowns can be delineated using the algorithms developed by Gougeon (1995), Popescu et al. (2003) and Weinacker (2004) and (ii) to investigate the usefulness of LiDAR-derived crown diameter in addition to other LiDAR-measured parameters, such as tree height and number of trees, to estimate inventory forest variables such as top height, basal area and volume in a Sitka spruce Scottish plantation.

2 Material

2.1 Study Area

The study area is located in the Aberfoyle Forest District, Scotland. This area is located in the Trossachs National Park approximately 30 km north of Glasgow.

2.2 Laser Data

The airborne laser data was acquired at the end of the growing season on the 16th of September 2002. The total area surveyed by the scanner was 17.5 km² at a cost of 5 pounds per ha.

*Parameter*	*Performance*
Sensor	Optech ALTM2033
Laser pulse frequency	33000 Hz
Flying altitude	1000 m
Beam divergence	10 cm
Scanning angle	20 degrees
Sampling intensity	3-4 returns per m2
Position accuracy	X,Y < 40 cm
Elevation accuracy	Z < 9- 15 cm

2.3 Field Data

Nine 50x50 m plot were surveyed to measure DBH and the position for every tree in X and Y. Within small 10x10 plots tree height and crown diameter were also measured.

The dominant species in all plots was Sitka spruce (Picea sitchensis). Other species present in the stands were Larchs (Larix x Kaempferi) and Birch (Betula sp.) in proportions lower than 5%.

3 Methodology

3.1 Calculation of the tree canopy model (TCM)

The delineation algorithms work on gridded data that represent the height of the canopy in every pixel. The grid dimension chosen was 0.5 x 0.5 m. With grids of spatial resolution below 0.7 m, it is possible to represent the dimensional shape of individual tree crowns thereby facilitating the segmentation process (Leckie et al. 2003).

3.1.1 Tree Canopy Model for use with the algorithms by Popescu and Gougeon

The DTM from Lidar data is made by interpolating the second returns that hit the underlying ground terrain. The filtering method used is an iterative selection of points within kernel of variable sizes that have the lowest height value. The kernel size is increased until all non ground points are removed (Suarez et al. 2004). Second returns, after the filtering process, were interpolated into a regular grid of 0.5 x 0.5 m, using the kriging interpolator without anisotropy.

The second step is the creation of the Digital Surface model (DSM) that represents the surface of the top of the canopy. The first returns of the LiDAR data have been interpolated in a regular grid of 0.5 x 0.5 m using the kriging interpolator without anisotropy.

The final Tree Canopy Model (TCM) was calculated by subtracting the DTM from the DSM.

Before using the algorithm by Gougeon, the TCM was filtered with a 3x3 average filter as in the previous work by Leckie et al. (2003). This was achieved in order to smooth the TCM and to eliminate an important proportion of the noise in this highly variable surface. The TCM has not been filtered before using the algorithm by Popescu as the filtering process is already integrated into the delineation algorithm.

TCM=DSM-DTM

3.1.2 Tree Canopy Model for use with the algorithm by Weinacker

The TCM to use with the algorithm by Weinacker has been produced from algorithms already implemented in Treesvis. The basic method to calculate both the DTM and DSM is called Active Surface Fitting. The lowest and highest values are assigned on a per pixel basis to calculate the DTM and the DSM respectively. In order to calculate the DSM, we chose the option that keeps most of the highest points within the raw data. Additionally, the surface has not been located at each laser point in first return raw data. It is the suggested option for future delineation process by authors. Initial default parameters for flat areas in plots 2 and 4 were selected while those for rough and irregular terrain were selected for the rest of the plots. Finally, the TCM was calculated by subtracting the DSM from the DTM.

3.2 Delineation process

3.2.1 The algorithm by Popescu et al. (2003)

This algorithm assumes that there exists a relationship between crown size and tree height. The method requires (a) maximum and minimum crown diameter as initial parameters and (b) an empirical relationship between tree height and crown diameter.

Once the location of the trees is set, the TCM is sampled at the positions of the treetop to calculate the height of each tree.

Thereafter, the algorithm calculates crown diameter for each tree. Firstly a 3 x 3 median filter is applied over the TCM in order to avoid noise in the top of the canopy. In order to calculate crown diameter, two perpendicular profiles are extracted from the TCM and then, a fourth-degree polynomial equation is fitted to each profile. The algorithm finds the local minimum of the fitted functions. The edges of the crown profiles are local minimums where the first derivative equals zero and the second derivative is positive. The crown diameter is calculated as the distance between the two edges of the crown profile. The final crown diameter is calculated as the average of the crown diameters of the two perpendicular profiles. More details of can be found in Popescu et al. (2003).

3.2.2 **Weinacker et al. (2004) algorithm**

This algorithm was designed to delineate single trees. The algorithm starts by finding treetops using a local maximum filter in the DSM. This filter finds the local maxima as the pixel with highest value compared to its surrounding pixels (Weinacker et al. 2004).

Once the tree tops are located, a pouring algorithm, starting from the tree top, is detecting the tree borders in the DSM. This algorithm works in similar way to the inverted watershed algorithm (Soille 1999). After the application of this algorithm, some segments have sizes or shapes that are improbable to represent a tree. In order to merge this improbable tree segment with other segments, rules on defining the area and the shape of the segmented crown and the proximity with the nearest tree top are applied. The final edge of the crowns is determined with Friedlaender (2002) idea. A complete description of the algorithm can be found in Weinacker et al. (2004a).

3.2.3 Gougeon (1995) algorithm.

This algorithm was developed for high spatial resolution aerial images, but it can also be used with LiDAR data to delineate individual tree crowns (Leckie et al. 2003).

The algorithm is divided in two parts: firstly, the following-valley approach starts by finding the local minima in the TCM. A pixel is considered as local minima if all its surrounding pixels have higher values. Starting in the local minima, the algorithm follows the valley pixels which are found between pixels with higher value. The algorithm continues to find valley pixels until the crown is delimited by valley pixels. Secondly, a complete delineation is done with the application of the second-rule approach. A complete description of the algorithm can be found in Gougeon (1995).

As initial parameter of the algorithm running over LiDAR data, all TCM pixels lower than 4 meters were filtered out as no crown. This threshold has been chosen after the analysis of the field data stored in the Forestry Commission database. The database shows that 98 % of trees with similar age and within 50 km of the study area have the lower part of the crown above 4 m.

3.3 Linking of LiDAR delineated trees and field measured trees for validation

Good delineated crowns are considered as those with a single tree top. Sometimes delineation algorithms are not able to delineate properly a crown. The methodology applied in the linking process was applied in previous works by Persson et al. (2002, 2003). In order to evaluate the results, each detected tree was automatically linked to the corresponding field tree. In the linking process only good delineated crowns are linked with field trees.

3.4 Forest attributes estimation

Forest parameters have been divided in individual tree and stand level. Individual tree parameters considered were tree height (H), crown diameter and stem diameter at breast height (DBH). The stand forest parameters considered were top height (Ho), basal area (BA) and volume (V).

In order to calculate the error in the estimation of individual tree parameters, the values from each segmented tree were compared with the field measured tree after the linking process.

At stand level, all trees segmented with at least one tree top, linked or unlinked with a field measured tree, were used in the estimation of number of delineated trees and stand forest parameters such as top height, basal area and volume. Unlinked trees were included because they were also delineated by the algorithms. Linking delineated and field measured trees has as the only aim, the validation of individual parameters.

4 Results

4.1 Number of delineated trees

The algorithm by Popescu delineated 948 tree crowns (89.3%), the algorithm by Weinacker delineated 1368 (128.8%) and the algorithm by Gougeon delineated 827 trees (77.9%). The algorithm by Weinacker splits some crowns in several segments. As a result the number of crowns detected is higher than the number of field measured trees. The algorithm by Popescu also achieved detection rates higher that 100% in plots 2 and 7, which have the lowest tree density.

The number of delineated trees linked with field measured trees was higher when the algorithm by Weinacker (807 trees, 76.0%) was applied than when that by Popescu (763 trees, 71.8%) and Gougeon (639 trees, 60.2%) were applied. When only the linked trees were analysed, all the algorithms delineated the trees with large diameters better, achieving percentages of delineation of 87.2%, 89.4% and 78.7% in trees larger than 45 cm by the algorithms by Popescu, Weinacker and Gougeon respectively.

				Linked trees grouped by diameter classes (cm)
Plot	N Trees	Linked Trees	%	5-15	15-25	25-35	35-45	>45
1	145	85	58.6%	37.5%	38.2%	67.4%	66.7%	66.7%
2	86	56	65.1%	18.2%	40.0%	71.8%	85.0%	83.3%
4	110	86	78.2%	Null	42.9%	78.9%	90.6%	85.7%
6	126	87	69.0%	0.0%	58.1%	73.9%	85.7%	Null
7	95	76	80.0%	Null	60.0%	73.3%	91.4%	100.0%
8	103	67	65.0%	0.0%	66.7%	45.7%	71.4%	100.0%
9	130	91	70.0%	33.3%	51.6%	71.8%	90.9%	100.0%
10	137	111	81.0%	0.0%	65.0%	82.0%	96.0%	100.0%
12	130	104	80.0%	0.0%	68.1%	87.9%	100.0%	100.0%
Total	1062	763	71.8%	18.2%	55.2%	74.7%	83.2%	87.2%

Linked trees from the algorithm by Popescu. There is a NULL value when any field tree is into this class. There is a 0% when there are field trees into this class; however any of them were delineated. For instance, in plot 4, there are no field rees with diameter between 5 and 15 cm.

Tree crown delineation from the algorithm by Popescu in LiDAR data (example taken from plot 2). Delineation is represented in the left side over the TCM and in the right side over the optical image. The green lines represent the edges of the crown obtained with the algorithm by Popescu. The yellow dots represent the treetops. The yellow rectangle represents the limit of the sample plot.

				Linked trees grouped by diameter classes (cm)
Plot	N Trees	Linked Trees	%	5-15	15-25	25-35	35-45	>45
1	145	81	55.9%	37.5%	41.2%	56.5%	66.7%	66.7%
2	86	61	70.9%	27.3%	60.0%	74.4%	85.0%	100.0%
4	110	95	86.4%	Null	57.1%	87.7%	93.8%	100.0%
6	126	104	82.5%	40.0%	77.4%	84.1%	95.2%	Null
7	95	78	82.1%	Null	60.0%	80.0%	88.6%	100.0%
8	103	65	63.1%	0.0%	50.0%	37.1%	77.6%	91.7%
9	130	108	83.1%	66.7%	74.2%	81.7%	100.0%	100.0%
10	137	111	81.0%	50.0%	65.0%	83.1%	88.0%	100.0%
12	130	104	80.0%	66.7%	70.2%	84.8%	92.3%	100.0%
Total	1062	807	76.0%	39.4%	64.0%	77.4%	84.7%	89.4%

Linked trees from the Algorithm by Weinacker.

Tree crown delineation from the algorithm by Weinacker in LiDAR data (example taken from plot 2).

				Linked trees grouped by diameter classes (cm)
Plot	N Trees	Linked Trees	%	5-15	15-25	25-35	35-45	>45
1	145	68	46.9%	25.0%	32.4%	58.7%	48.9%	50.0%
2	86	53	61.6%	18.2%	30.0%	66.7%	85.0%	83.3%
4	110	71	64.5%	Null	28.6%	61.4%	81.3%	85.7%
6	126	79	62.7%	0.0%	41.9%	69.6%	85.7%	Null
7	95	65	68.4%	Null	50.0%	64.4%	77.1%	80.0%
8	103	61	59.2%	0.0%	33.3%	62.9%	53.1%	91.7%
9	130	88	67.7%	0.0%	58.1%	67.6%	86.4%	100.0%
10	137	79	57.7%	50.0%	35.0%	58.4%	72.0%	100.0%
12	130	75	57.7%	33.3%	48.9%	59.1%	84.6%	100.0%
Total	1062	639	60.2%	18.2%	42.4%	63.1%	70.2%	78.7%

Linked trees from the algorithm by Gougeon.

Tree crown delineation from the algorithm by Gougeon in LiDAR data (example taken from plot 2).

Percentage of linked trees in each plot. The algorithm by Weinacker was the most suitable in all plots, except in plot 1and plot8 where worked better the algorithm by Popescu.

	Average Distance (m)	Standard Deviation (m)	Maximum Distance (m)
Popescu	1.03	0.52	3.01
Weinacker	1.07	0.58	4.44
Gougeon	1.04	0.51	3.20

Average, standard deviation and maximum distance between positions of detected and field measured tree.

Position of delineated trees with respect to the field measurement trees. Radial axis shows the coordinate directions. Centre of the graph represent the position of field measured tree. Intersection between lines and axis means percentage of delineated trees that are located in this direction respect the field tree.

4.2 Estimation of Tree Height

	Observations	Average Height (m)	RMSE (m)	RMSE (%)	BIAS (m)
Popescu	79	23.82	1.93	8.12%	-1.18
Weinacker	80	23.91	2.40	10.05%	-1.45
Gougeon	61	24.19	2.29	9.46%	-1.59

LiDAR individual Tree Height estimation results.

4.3 Estimation of Crown Diameter

	Observations	Average Crown diameter (m)	RMSE (m)	RMSE (%)	BIAS (m)
Popescu	97	5.64	2.51	44.52%	-2.27
Weinacker	101	5.64	2.51	44.51%	-2.11
Gougeon	78	5.72	1.81	31.70%	-1.51

LiDAR crown diameter estimations results.

4.4 Estimation of Stem diameter

	Observations	Average DBH (m)	RMSE (m)	RMSE (%)	BIAS (m)
Popescu	763	32.08	8.68	27.07%	-5.61
Weinacker	807	31.65	8.93	28.22%	-5.03
Gougeon	639	32.39	7.05	21.78%	-3.75

LiDAR DBH estimation results.

4.5 Estimation of Top Height

	Observations	RMSE (m)	RMSE (%)	BIAS (m)
Popescu	9	0.94	3.75%	-0.72
Weinacker	9	1.48	5.92%	-1.36
Gougeon	9	1.67	6.66%	-1.59

Top height estimation from the algorithms by Popescu, Weinacker and Gougeon.

4.6 Estimation of Basal Area

	Observations	RMSE (m2/ha)	RMSE (%)	BIAS (m2/ha)
Popescu	9	15.92	42.59%	-15.64
Weinacker	9	9.10	24.33%	-8.46
Gougeon	9	13.96	37.08%	-13.32

Basal Area estimation by the algorithms by Popescu, Weinacker and Gougeon.

4.7 Estimation of Volume

	Observations	RMSE (m3/ha)	RMSE (%)	BIAS (m3/ha)
Popescu	9	180.16	44.31%	-174.42
Weinacker	9	119.71	29.45%	-108.42
Gougeon	9	169.96	41.81%	-160.24

Volume estimation by all the algorithms.

5 Discussion

Generally, all the three algorithms worked well at the prediction of parameters at stand level. At tree level, only individual tree heights seem to produce the most acceptable results. If compared with field methods such as those produced by electronic hypsometers like Suunto, which varies from 0.4 to 0.8 m, LiDAR methods provides an effective alternative in terms of cost, time and accuracy.

The algorithm by Weinacker splits tree crowns in several segments, which leads to a considerable overestimation of the number of trees in the plots. However, this does not reflect on the estimations of BA and volume, which seem to be the best. On the contrary, Gougeon seems to provide the best method for delineating tree crowns, which considerably improves the estimation of diameters at tree level. Popescu produced the best tree height estimations at both stand and tree level. However, canopy delineations seem to be worst than the other models, which influences estimations of diameters, BA and volume.

Poor results in crown diameter estimations can be explained, in part, due to a systematic underestimation in crown diameter, because delineation algorithms which work over the TCM, measures non-overlapping crown diameters. Thereafter, poor results in DBH will be affected by crown diameter estimation. Top height estimation is even better (RMSE=0.94 m) than individual tree height because it was calculated with the thickest trees and they are the best delineated.

6 Conclusions

The aims of the paper are to show how individual crown can be delineated by all the algorithms and the usefulness of LiDAR measured parameters to estimate inventory forest variables.

Results illustrates that methodologies of tree crown delineation in LiDAR could be used to delineate individual tree crowns. The algorithm by Popescu was able to delineate 89.3% of the trees. Detection rates were higher in large DBH trees. Individual Tree height can be estimated with these methodologies very accurately. The algorithm by Popescu achieved a RMSE of 1.93 m (8.12%). These results can be considered as very good if it is taken into account that electronic field measurements achieve accuracies of 0.4-0.8 m (Lindgren 1984). Poor results in estimation of crown diameter and DBH at single tree level were achieved. Best results were achieved by the algorithm by Gougeon with an error of 1.81m (31.7%) and 7.05 cm (21.78%) in Crown diameter and DBH respectively. There accuracies are far from similar works done previously and from accuracies achieved in field inventory. At stand level, great results are achieved in top height estimation. The algorithm by Popescu achieved a RMSE of 0.94 m (3.75). The results achieved are similar to field inventories. Poor current results in basal area and volume estimation were achieved. The best method to estimate these variables was the algorithm by Weinacker, which achieved a RMSE (%) of 24.3% and 29.4% for basal area and volume respectively.

There are possibilities to improve stand level variables estimation due to the fact that a strong relationship between LiDAR estimated and field measured variables exist (top height, basal area and volume). A solid fitted equation must be developed to predict these variables more accurately. More research has to be done in this sense.

7 References

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Last modified 25-08-2006