Spatial Biases in LiDAR-Based Tree Delineation

Abstract
In recent years, airborne LiDAR instruments have become increasingly popular in forest applications. However, due to sensor characteristics as well as feature extraction algorithms, we hypothesise that spatial tree pattern in remotely sensed forest inventories differ depending on the method used. These potential biases in the location and distribution of trees are particularly relevant for data fusion of optical and LiDAR data, for comparing forest inventories as well as for the interpretation of horizontal forest structures. Our results confirm that (1) location errors are greater, the higher a tree is and that (2) automatically detected trees exhibit a more evenly spaced tree distribution compared to manually detected trees. The observed spatial biases are highly relevant for remote sensing applications in forestry and forest ecology. Firstly, there is a caveat with data merging of optical and LiDAR data for forest inventories. Secondly, quantifications of the structural characteristics of forest stands strongly depend on the applied image analysis method.

1 Introduction
In recent years environmental monitoring and forest management can build on a rapidly increasing amount of high resolution remote sensing data. Particularly airborne LiDAR instruments have become very popular in forest applications. Unlike other remote sensing techniques, LiDAR provides a 3D model of the forest canopy and thus provides valuable, additional information to optical imagery (HILL & THOMSON 2005; SUAREZ et al. 2005; VIAU et al. 2005; LEVICK & ROGERS 2006). In the environmental sciences LiDAR data is used to derive the vegetation structure and species composition, two major components of the forest habitat quality (HILL & THOMSON 2005). Given a high sampling density of several points per square meter, the canopy model allows for the automatic delineation of individual tree crowns (SECORD & ZAKHOR 2007). This process automation has a great significance for building and maintaining forest inventories as well as for monitoring and management purposes (KOUKOULAS & BLACKBURN 2005; SUAREZ et al. 2005). Several authors suggest fusing optical images with LiDAR data for automatic tree detection based on an object based image analysis approach (KOUKOULAS & BLACKBURN 2005; SUAREZ et al. 2005; LEVICK & ROGERS 2006). However, systematic location errors may be introduced by the use of automatic tree detection based on LiDAR data compared to manual delineation based on optical data due to the scanning angle or the delineation algorithm (GOODWIN et al. 2006). The detected tree location is shifted towards the platform, because the crown side towards the scanner reflects more pulses than the opposite crown side (PYYSALO 2006). Contrary to LiDAR, in aerial photos the tree tops tend to "lean back", i.e. to appear further away from the platform as the actual trunk is located on the ground. Furthermore, automatic tree delineation algorithms that detect local maxima within a defined search range inhibit the placement of the nearest tree closer than the search range. This algorithm is thus likely to produce a relatively regular placement of tree points in dense forests. These potential biases in the location and distribution of trees are particularly relevant for data fusion of optical and LiDAR data, for comparing forest inventories as well as for the interpretation of horizontal forest structures. In this study we investigate to which extent spatial forest pattern differ between an automatic, LiDAR based delineation method compared to manual tree detection based on optical data of the same area. We hypothesis that (1) location errors are greater, the higher a tree is due to the scanning angles of the remote sensing instruments and (2) automatically detected trees exhibit a more evenly spaced tree distribution compared to manually detected trees, caused by the finding local maxima algorithm.

2 Methods
The investigated forest lies at about 1500m a.s.l. in the Eastern Central Alps. The study area has an extent of 110m by 120m and is characterised by a diversely structured forest with mature stands, young growth and open patches. Two remote sensing images build the basis for the tree delineation. Firstly a true colour image with a ground resolution of 25cm from 2003 and secondly LiDAR data that was converted to elevation and surface rasters with a 1m resolution in the same area, captured in 2006. Both images are georeferenced and provided by the government of Tyrol.

In the manual tree detection, each tree that can be identified in the orthophoto is marked with a point at its top. For the automatic delineation a find local maxima algorithm is used to extract the tree tops of individual trees from the LiDAR data. The two resulting point data sets are compared in terms of systematic differences in the quantity, location and distribution of trees.

To compare the spatial distribution between the manually and the automatically detected trees, the spatial distribution of both tree data sets is computed with the Ripley's L function (RIPLEY 1976). This function computes the spatial distribution of a point data set against complete spatial randomness at multiple distances. Regularly spaced points have positive values, whereas negative values indicate clustered data. The Ripley's L function is computed for each of the data sets between one and thirty meters with one meter increments. The resulting distribution curve is compared to the 95% confidence envelope generated from 99 stochastically simulated distribution patterns.

The magnitude of the hypothesised location error is evaluated by correlating the nearest neighbour distances of the automatically to the manually delineated tree locations with the respective tree heights. However, the nearest neighbour point pairs of the two data sets do not necessarily refer to the same tree and can thus not generally be interpreted as location error. Therefore, the neighbouring point pairs are analysed for their angular distribution. Given the hypothesis is true that the location error is due to the scanning angle of the LiDAR and the optical instrument respectively, a main offset direction can be expected. Those tree pairs, which are located within the identified angular band, are likely to refer to the same tree. Hence, nearest neighbour distances of point pairs in the main offset direction mainly represent the location error.

3 Results
Manual tree extraction from the aerial photo results in a different tree point pattern compared to the automatic tree delineation from LiDAR data (Figure 1). Whereas the manual image interpreter detected 239 trees in the study area, the automatic tree delineation algorithm resulted in 255 trees.

Figure 1 Extracted tree points: automatic delineation, based on LiDAR data (dark points) and manually extracted trees, based on the aerial photo (light points).

3.1 Spatial distribution
The manually detected trees are more regularly spaced than a complete random distribution would suggest in the distance band between 0 to 5m, whereas points that are further apart than 8m are clustered (Figure 2a). Automatic tree detection results in a peak of uniformity at the minimum possible tree distance due to the search radius used in find local maxima algorithm for automatic tree detection. Figure 2b shows the distribution function for a search radius of 2m, which results in a strong uniformity at this distance. The peak of uniformity at near distances is a characteristic pattern that gets even more accentuated for larger search range distances (Figure 2c). In contrast to the manually detected trees, the distribution for automatically detected trees lies within the 95% confidence interval of random distribution for distances over 8m.

Figure 2 the Ripley's L function for tree point data against the 95% confidence envelope generated from 99 stochastically simulated distribution patterns. Positive values indicate even distribution, clustered data has negative values (a) manually detected trees (b) automatic tree detection, search radius 2m (c) automatic tree detection, search radius 3m.

3.2 Location error
As hypothesised, the location errors show a clear correlation with the tree height, where small trees have a smaller location error than tall trees. The tallest trees in the study area (35m) exhibit a deviation of their location between the two data sets of more than five meters. As expected there is no correlation between automatically delineated tree heights and the distance to the nearest trees in the manually extracted point data set. However, the histogram in Figure 3b shows a clear peak of bearings between nearest neighbour pairs ranging from 60° to 80°. This distribution indicates a skewed angular distribution due to a systematic location error into one direction. This pattern can be revealed when only nearest neighbour distances in the identified range of angles are selected in the scatter plot of nearest neighbour distances against tree heights. After the removal of outliers that do not refer to the same tree and thus do not represent the location error, a linear correlation results at the 99% significance level with a correlation coefficient of 0.81 (Figure 3c).

Figure 3 Automatic detected tree points and their nearest neighbours (NN) in the manually extracted data set. (a) tree heights in dependence to the NN distance (b) angular distribution of NN tree pairs (c) tree heights in dependence to the NN distance in the main offset direction, representing mainly the location error.

4 Discussion

4.3 Location errors in LiDAR-based forest inventories
Forest inventories that are based on remote sensing data can have a significant spatial bias, depending on the applied method. The hypothesised differences between automatic algorithms on LiDAR data and manual interpretation of spectral data were confirmed for both, the tree location and the tree distribution. The location error depends on the tree height, with a maximum of 6m for 30m high trees. This result is in accordance to the findings of Hyvonen and Anttila (2006), who found displacements of objects varying from 0 to 7m, where the accuracy declined with the distance to the nadir.

This observed spatial bias between the described airborne forest monitoring methods raises a number of important issues, when it comes to applications in forestry. First of all, there is a caveat with data merging of optical and LiDAR data for forest inventories. SUAREZ (2005) report a good match of the horizontal tree location and found encouraging results for tree counting and stand characteristics. However, the deviation between the two data sets for high objects get more relevant the more off nadir the objects are observed. This issue has to be accounted for, before merging LiDAR with aerial imagery.

4.4 Tree distribution errors and its implication for forest ecology
A more subtle difference between the two compared forest data sets is the spatial distribution of trees. Both tree inventories exhibit a regular distribution pattern over near distances. This can be explained by competition among neighbouring trees (STOYAN & PENTTINEN 2000). However, the automatic delineation results in a significantly stronger regularity at one particular distance. This pattern is related to the search range distance of the "find local maxima" algorithm, applied for the automatic tree extraction. The Ripley distribution functions shows that larger search ranges, result in a wider spacing between the detected trees, which results in an artefact of accentuated uniform distribution at this distance. Small search ranges would minimise this problem. However, Nelson et al. (2005) show that the algorithm is likely to detect multiple tops in one tree for small search ranges, and thus overestimates the number of trees.

Taking account for the bias in tree distribution indices depending on the applied method is particularly relevant for the assessment of structural forest characteristics. STOYAN & PENTTINEN (2000) point out that structural features describe the naturalness as well as the evolutionary state of forest stands, as spatial patterns emerge from ecological processes. KINT (2005) advocates that in sustainable forest management structural features should be considered as well as species composition. Natural distribution of trees is random, whereas forest plantations are regular due to planting and thinning. In our study we demonstrate that automatic tree delineation based on the local maxima algorithm tends to result in a comparatively regular tree distribution pattern. This bias leads to an underestimation of the ecological forest quality, as rich structural diversity is often linked with higher biodiversity, stronger resilience against disturbance and a higher habitat quality (KINT et al. 2004).

5 Conclusion
Spatial forest pattern differ between an automatic, LiDAR based tree delineation method compared to manual tree detection based on optical data of the same area. The hypothesis was confirmed that (1) location errors are greater, the higher a tree is due to the scanning angles of the remote sensing instruments and (2) automatically detected trees exhibit a more evenly spaced tree distribution compared to manually detected trees.

As hypothesised, the location errors show a clear correlation with the tree height, where small trees have a smaller location error than tall trees. Accordingly, also differences in terms of the distribution of trees were confirmed. At near distances the automatic delineation resulted in an artefact of strong regularity at the local maxima search distance. Furthermore, the automatic delineation resulted in a random distribution of trees at the stand scale, whereas manual tree extraction revealed a clustered pattern of tree locations.

The observed spatial bias is important for remote sensing applications in forestry and forest ecology. Firstly, there is a caveat with data merging of optical and LiDAR data for forest inventories. Secondly, quantifications of the structural characteristics of forest stands strongly depend on the applied image analysis method.

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