# Boundary-Inner Disentanglement Enhanced Learning for Point Cloud Semantic Segmentation
## 4 Experimental Results and Discussion
### Ablation Analysis  
**Effectiveness of BIDEL.** The proposed BIDEL can maximize the feature similarity between boundary points and its neighboring points on the boundary (\(C_{i}^{1}\) and \(C_{i}^{3}\)), thus preserving the boundary and boosting segmentation accuracy. However, CBL [12] encourages the learned representations of boundary points more similar to their neighboring points within the same category (\(C_{i}^{1}\) and \(C_{i}^{2}\)) in decoding layers. Therefore, several different boundary loss functions are discussed in this section to prove the effectiveness of BIDEL.  
For the first loss function setting, the learned representations of boundary point \(\chi_{i}\) are encouraged to be more similar to its neighboring collections \(C_{i}^{1}\) (boundary points within the same category), which can be represented as \(L_{A}\):  
\[L_{A}=-\frac{1}{|B_{l}|}\sum_{\chi_{i}\in B_{l}}log\left(P_{i}^{1}\right). \tag{8}\]  
For the second loss function setting, the learned representations of boundary point \(\chi_{i}\) are encouraged to be more similar to its neighboring collections \(C_{i}^{1}\) and \(C_{i}^{2}\) (points within the same category), which can be represented as \(L_{B}\):  
\[L_{B}=-\frac{1}{|B_{l}|}\sum_{\chi_{i}\in B_{l}}log\left(P_{i}^{1}+P_{i}^{2} \right). \tag{9}\]  
As shown in Table 5, when setting \(L_{A}\) as the boundary loss function, the mIoU reached 64.5%, showing a 1.8% increase compared to the baseline. \(L_{BIDEL}\) achieved the best result of 64.8%. Points in collection \(C_{i}^{3}\) only accounted for a small proportion of all neighboring points, which limited the effect of BIDEL and resulted in a slight improvement in accuracy. However, \(L_{B}\) unfortunately diminished the accuracy. Compared to \(L_{A}\), \(L_{B}\) also encouraged entanglement between the boundary point and its neighboring collections \(C_{i}^{2}\) (inner points within the same category). This shows that a high engagement of inner points in LAO can  
Figure 7: Visualization results on Toronto-3D dataset [48], highlighting mislabeling. The images from top to bottom are the input point cloud and the ground truth. Yellow rectangles show regions where objects were labeled wrongly in the ground truth. (**a**) Subscene-1; (**b**) Subscene-2; (**c**) Subscene-3.  
weaken the boundary information, thus reducing overall performance. Such observations successfully verify the effectiveness of BIDEL.  
Figure 8: Qualitative results on Toronto-3D L002 dataset. The images from top to bottom are (**a**) the input point cloud overlaid with the boundaries (red points) generated from the ground truth, (**b**) the ground truth, (**c**) the baseline (RandLA-Net), (**d**) the baseline + BIDEL, and (**e**) the improved areas (blue regions were misclassified by the baseline but identified accurately by BIDEL).  
**Hyperparameter optimization.** Three values of \(\lambda\) were evaluated to select the best loss weight for \(L_{BIDEL}\). The experiments were conducted on S3 DIS Area 5, and the results are reported in Table 6. It can be seen that \(\lambda=1\) was the best choice.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Boundary Loss** & **mIoU (\%)** & **OA (\%)** & **mACC (\%)** \\ \hline \(L_{A}\) & 64.5 & 87.5 & 72.5 \\ \(L_{B}\) & 62.2 & 86.7 & 71.7 \\ \(L_{BIDEL}\) & **64.8** & **87.8** & **72.9** \\ \hline \end{tabular}
\end{table}
Table 5: The quantitative results of different boundary loss functions for semantic segmentation. Bold font denotes the best performance.  
Figure 9: Visualization results on the challenging Semantic3D reduced-8 dataset [49]. The images from left to right are (**a**) the input point cloud, (**b**) the baseline (RandLA-Net), and (**c**) the baseline + BIDEL. Objects in red rectangles were misclassified by the baseline but identified accurately by BIDEL. Note that, although the ground truth of the test set was not publicly provided, the class of objects in the red rectangles could be easily recognized by human eyes with the support of RGB attributes.