## 3 Results and Discussion
### Validation
#### 3.1.2 Segmentation of Leaves  
The results (Figure 7a,b) showed that our algorithm could segment the leaves with an average accuracy of 95% (ranging from 90% to 98%) for the sampled leaves from the mochi tree and an average accuracy of 90% (ranging from 87% to 94%) for the Japanese camellia. The average classification accuracy for the mochi tree was higher than that for the Japanese camellia. Between the two sampled species, the segmentation accuracy for the top region of the tree was relatively low, and the angular resolution that was degraded over the scanning distance was considered to have a slight influence on the accuracy, but this was not confirmed in the study. Furthermore, the size of the octree space of each terminal node (Oi) may have been the cause of the results. The computational efficiency was considered to be the most affected here. The size of the octree space determined the number of \(k\)-values that needed to be specified. When the octree space was large, a larger \(k\)-value was required to run \(k\)-means, resulting in a longer calculation time. On the one hand, some of the leaves that surrounded the space boundary might have been split into small pieces of incomplete leaves. This might also be a factor affecting the accuracy of classification. Fortunately, our method gradually increases the value of \(k\) and can make the value of \(k\) eventually larger than the number of clusters in the space. Since the \(k\)-value was, finally, greater than the number of clusters in the space, the accuracy of the classification was not affected.  
A higher leaf curvature was observed in the Japanese camellia than in the mochi tree, which was caused by the overlapping of leaves. Leaf PCDs of overlapped leaves consist of continuous and close points within the surrounding leaf edges, which makes the group centroid move to a position located in the middle of the leaf gap (Figure 4a, _C_). As the centroid of the grouped cluster is located in the space within the leaves, the distance \(r\) (the distance farthest from the centroid, as mentioned earlier, should be specified to be at least less than half of the leaf gap distance to avoid two leaves being classified into the same class (r \(\leq\) L/2). In this case, as the group centroid is positioned in the middle of L, with L assumed at 2 cm, \(r\)\(\leq\) 1 cm should be satisfied. Due to the mostly uneven distribution of the PCDs, the group centroid is not located in the middle, but is closer to the leaves, so the condition is satisfied even when the leaf gap is less than 2 cm. However, if the leaf gaps are smaller than 2 cm, for example, 1 cm, and the group centroid is positioned in the middle, the condition must be set at  
Figure 6: The classification for removing non-photosynthetic material in the case of Japanese camellia: (a) a* value in L*a*b* color space; (b) classified results (red: leaves; blue: wood); (c) original sampled tree; (d) sampled tree with wood removed.  
\(r\leqq 0.5\) cm to prevent false segmentation. The lower the value of the required \(r\) distance, the larger the \(k\)-value to operate the \(k\)-means is. Even assuming that a larger \(k\) is possible in suppressing the limit, the decreased computational efficiency and the noise effect on the leaf angle estimation of a small group of clusters cannot be ignored (for example, in our case, using the general commercial computers, it took 2-5 min to complete the calculation using a sampled tree formed by about 2 million PCDs). In addition, after the verification of accuracy, the segmentation error was considered to be small enough to affect the estimation of LAD. Therefore, we compromised here by approximating more accurate results while maintaining higher computational efficiency without increasing the \(k\)-value.