## 4 Results and Discussion
### Point Cloud Accuracy  
The results from the point clouds generated from the IMU/GPS only trajectory were first evaluated against the observed ground control targets. The method used to identify the number of points belonging to ground control allowed an average of 14 points per target to be observed. Across the 8 point clouds only 3 targets were rejected as they were observed with five or less points. All 3 of these rejected targets were only partially observed at the edge of the swath. Table 4(a) shows that the errors are generally within the expected values from the stochastic modelling outlined [PERSON] _et al._[22]. The standard deviation in both North and East measurements are similar. This suggests that they are not dominated by the effect of the beam divergence properties of the Ibeo LUX laser scanner. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Transect** & **Area (m\({}^{2}\))** & **Point Density (ppm\({}^{2}\))** & **\% 2 nd Returns** & **\% 3 rd Returns** \\ \hline
1a & \(5,931\) & \(38.7\) & \(4.09\) & \(0.35\) \\
1b & \(6,288\) & \(37.2\) & \(5.88\) & \(0.53\) \\
2a & \(5,586\) & \(62.6\) & \(3.46\) & \(0.54\) \\
2b & \(4,922\) & \(42.2\) & \(13.90\) & \(2.05\) \\
3a & \(5,459\) & \(35.9\) & \(15.01\) & \(2.02\) \\
3b & \(4,986\) & \(36.5\) & \(15.41\) & \(2.37\) \\
4a & \(6,176\) & \(40.6\) & \(2.92\) & \(0.25\) \\
4b & \(5,811\) & \(52.0\) & \(2.63\) & \(0.17\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Properties of the eight generated point clouds. Figure 7: An example point cloud produced by the SfM trajectory determination algorithm. This particular point cloud has an average point density of 40 points per m\({}^{2}\)and covers 4,877 m\({}^{2}\). The results from the IMU/GPS/SfM solution shown in Table 4(b) are close to the expected values from stochastic modelling [22]. The horizontal RMS error across all of the 130 measured ground control locations is 0.34 \(\mathrm{m}\) (expected 0.26 \(\mathrm{m}\)) and the vertical error is 0.15 \(\mathrm{m}\) (expected 0.14 \(\mathrm{m}\)). One source of error which is not included in stochastic modelling can be attributed to the use of large ground control targets and the systematic sampling properties of the laser scanner. This target size is required in order to ensure the ground control target is directly measured and to ensure that these measurements are found. The use of an average position from all identified target strikes relies on either an even point sampling across the target or a significant number of random strikes being recorded. This is potentially biased in  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Flight**} & \multirow{2}{*}{**No. Targets**} & \multicolumn{2}{c}{**East (m)**} & \multicolumn{2}{c}{**North (m)**} & \multicolumn{2}{c}{**Up (m)**} & \multicolumn{2}{c}{**RMSE (m)**} \\ \cline{3-10}  & & **Mean (m)** & \(\sigma\) (m)** &  
the along track direction by the location of scan lines across. On average 19 points were used in the calculation of each ground control target location. Another effect of the averaging technique used is that the error due to beam divergence is not fully represented in the final RMS errors. Beam divergence, which is high in Ibeo LUX laser scanner, affects predominantly the horizontal accuracy of the point cloud in the along track direction. The standard deviation in flights one (flown north-south) and two (flown east-west) suggest that some of this effect is captured. The effects of these errors are more evident when examining the high intensity returns within the point clouds, in which the footprints of each individual ground control points can measure up to 0.6 m in the across track direction. This averaging will not occur in measured trees for future surveys, therefore, careful consideration will need to be given to tree metrics measured in the horizontal direction such as canopy width. These measurements are likely to be exaggerated and may require adjustment before being applied within any further modelling.