# Mean Shift Segmentation Assessment for Individual Forest Tree Delineation from Airborne Lidar Data
## 5 Discussion  
The mean shift algorithm was tested on three different airborne lidar datasets. The settings generating the best results varied slightly across the data. Nevertheless, certain recommendations can be made based on the tests. The Pollock model as the kernel produced the best results for all three datasets. This proves the assumption that a kernel that ensembles the crown shape will facilitate crown segmentation. Although there is one more parameter to be tuned, i.e., the crown shape, it only needs to be tested once on a subset of data, even if the data are of mixed species. For example, for the benchmark data, the same crown shape (m = 2) was set for both plots in the same forest. The Cylinder kernel also produced good results for all the tested data, similar to those demonstrated in previous studies [(26; 28)]. There are two kernel bandwidth parameters to be tested (a and b), and they can be reduced to one if the ratio (b/a) is pre-defined [(24)]. The spherical kernel was the simplest, but yielded the worst results apart from the benchmark plot B2. Given the fact that the Cylinder kernel is not much more complex, a first attempt \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Plot** & **Class** & **FGI** & **IGN** & **SLU1** & **SLU2** & **UZH** & **MS** \\ \hline \multirow{6}{*}{B1} & All & 0.8491 & 0.4941 & 0.6911 & 0.6911 & 0.7784 & **0.875** \\  & Dominant & 0.96 & 0.65 & 0.93 & 0.93 & 0.96 & **1** \\  & Codominant & 0.88 & 0.55 & 0.66 & 0.66 & 0.88 & **0.889** \\  & Intermediate & 0.66 & 0.16 & 0.25 & 0.25 & 0.33 & **0.75** \\  & Suppressed & **0.33** & 0 & 0 & 0 & **0.33** & 0 \\ \hline \multirow{6}{*}{B2} & All & **0.8864** & 0.4596 & 0.6936 & 0.7171 & 0.8027 & 0.8142 \\  & Dominant & **1** & 0.7 & 0.92 & 0.93 & 0.98 & 0.9091 \\ \cline{1-1}  & Codominant & **0.88** & 0.42 & 0.73 & 0.73 & 0.83 & 0.7667 \\ \cline{1-1}  & Intermediate & **0.91** & 0.06 & 0.42 & 0.5 & 0.63 & 0.5714 \\ \cline{1-1}  & Suppressed & 0.43 & 0 & 0 & 0.07 & 0.22 & **0.7857** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Mean shift (MS) tree detection results of the benchmark plots compared to methods in [(22)]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Settings** & **MS\_fix** & **MS\_adaptive** & **Mk+WS** & **RegGrow** \\ \hline Random & 10.15 & 23.31 & 0.016 & 0.97 \\ Each point & 80.13 & 160.62 & **-** & **-** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Computing times in seconds (s) of mean shift when the kernel is fixed (MS_fix) or adaptive (MS_adaptive) for random seed points or each point, compared to watershed and region growing. to directly use the Cylinder would be recommended. The Pollock kernel would be preferred for better results with slightly more parameter tuning. Adapting the kernel to the crown size is considered to be a valid improvement of mean shift. However, whether or not to make the kernel continuously adaptive, for instance to the tree height, is dependent on the data as demonstrated by the results. Considering that the continuous adaptiveness will cost twice the computing time, and not necessarily generate better outcome, a fixed kernel is recommended. This adaptiveness is based on the assumption that taller trees have larger crown sizes, which may not be true for mixed species forests. One possible improvement is to adapt the kernel to the individual tree crown size rather than the height. There have been attempts to extract information of the crown size from either allometric approximations [26] or crown detection [42]. In both cases, the kernel was adapted to the targeted crown sizes generated from extra steps. The weighting in the vertical direction is proved to be beneficial in some cases but not always. Higher points in the kernel have higher weights, which helps the kernel to move upwards, so that the shift can be converged at the top of the tree. In this paper the weight is normalized to [0, 1], so the highest point has weight 1, and the lowest has weight 0. Other types of weighting strategy can be designed, such as the one in [28].