## 3 Results and Discussion
**(b)** 2D distribution of the combined Hue and Saturation cues. The 2D feature space is made of 100x100 bins; each bin represents the rate of this cue set appearance in the training set. Figure 13: 2D distribution of the combined range and the intensity cornerness cues. The 2D feature space is made of 100 \(\times\) 100 bins; each bin represents the rate of this cue set appearance in the training set. Analyzing the \(k\)-NN algorithm performance (discussion on the parameter selection appears in the following), the classification results are shown in Figure 17. As can be seen, most segments were correctly classified. On the pixel level the confusion matrix is:  
\[C= \begin{bmatrix}0.2246&0.0101\\ 0.0061&0.7592\end{bmatrix} \]  
leading to an accuracy of 0.9838. Figure 17 bottom shows examples for type I and type II error entities. Testing the effect of adding the \(u\)-\(v\) color cues shows improvement, with the pixel level confusion matrix reaching:  
\[C= \begin{bmatrix}0.2250&0.0050\\ 0.0057&0.7642\end{bmatrix} \]  
leading to an accuracy of 0.9892. As can be observed from the matrix, the false negative (type II errors) value has been cut in half. The classification results as applied on the dataset are presented in Figure 18.  
Figure 16: Distribution of the segment-averaged range-cornerness and intensity-cornerness values following the whitening transform. Green/red, tree/non-tree related segments, respectively, according to the ground-truth. The circle size is proportional to the segment size. Figure 15: Distribution of the segment-averaged range-cornerness and intensity-cornerness values. Green/red, tree/non-tree related segments, respectively, according to the ground-truth. The circle size is proportional to the segment size. Applying the graph-cut refinement phase is demonstrated on a single tree (Figure 19(a)), and its outcome is shown in Figure 19(b,c), which show the 'before' and 'after' refinement states. Figure 19(d) shows the points that have changed their labeling. Figure 19(e,f) shows type I and type II errors before and after the refinement phase respectively, in which the number of misclassified points is greatly reduced. Small branches that were first unsegmented have now been added to the tree structure. The  
Figure 17: Classification results using range and intensity cornerness cues. Green: true positive, Cyan: true negative, Magenta: false positive, Red: false negative. Figure 18: Classification results using range cornerness, intensity cornerness, and \(u\)-\(v\) cues. Green: true positive, Cyan: true negative, Magenta: false positive, Red: false negative. only regions that were mis-classified following the refinement are at the bottom of the trunk where the connectivity to both ground and tree can be mixed. The application of the graph-cut on scan 23 further improves the confusion matrix to:  
\[C= \begin{bmatrix}0.2254&0.0049\\ 0.0053&0.7643\end{bmatrix} \]  
leading to an accuracy of 0.9897. **Figure 19.** Demonstration of the graph-cut application: (**a**) Image of the studied tree. (**b**) The classified tree segment before applying the graph-cut refinement phase. (**c**) The classified tree segment following the graph-cut application. (**d**) Differences following the application of the refinement phase: in green added points, in red deleted points. (**e**) Difference between the ground truth and the classified tree segment, before the graph-cut application: in red type-I error (false alarm) and in green type-II error (miss). (**f**) Difference between the ground truth and the classified tree segment, following the graph-cut application: in red type-I error (false alarm) and in green type-II error (miss). Broadening the analysis, the algorithm is applied to eighteen scans that were acquired in urban and an open park environments. The classification phase is analyzed first. For the experiment, tree objects in these scans were manually marked and all related points were assigned as the ground-truth. The 24 scans generated \(\sim\)16,000 segments total (\(\sim\)660 segments per scan).