## 4 Experiment
### Ablation Study and Analysis
**Comparison with Different Input Point Size in AE and Segmentation Network:** To optimize the hyper-parameters, we further investigated the effect of the different input point-cloud size (number of sampled points in each block) on the semantic segmentation results of the 3D buildings' point cloud. For this purpose, we set up four sets of experiments, conducted in codeword dimensions at 512 and 1024, respectively:  
1. Trained on 2048 points with (\(x\), \(y\), \(z\)) coordinates when training the AE and segmentation network;
2. Trained on 2048 points with (\(x\), \(y\), \(z\)) coordinates when training the AE, and segmentation network training with 4096 points;
3. Trained on 4096 points with (\(x\), \(y\), \(z\)) coordinates when training the AE, and segmentation network training with 2048 points; and
4. Trained on 4096 points with (\(x\), \(y\), \(z\)) coordinates when training the AE and segmentation network. Table 7 shows the effect on the segmentation result of \"Scene_A\" with different input point size (2048 or 4096) in the AE and segmentation network training stages. This table is quite revealing in several ways: \begin{table}
\begin{tabular}{c c c} \hline
**Codeword\_Dims** & **Seg\_n\_Points** & **OA\_Scene\_A** \\ \hline
512 & 2048 & 0.747 \\
1024 & 2048 & 0.722 \\
512 & 4096 & 0.773 \\
1024 & 4096 & 0.694 \\ \hline \end{tabular}
\end{table} 
Table 6: Ablation analysis of the varying codeword dimensions (512 and 1024) for codewords learned from AE. “Codeword_dims” was set as 512-dimensional codeword and 1024-dimensional codeword, respectively. Input point size in the AE training stage was fixed at 2048. \begin{table}
\begin{tabular}{c c c c c} \hline
**Reconstruction\_Loss** & **Codeword\_Dims** & **AE\_n\_Points** & **Seg\_n\_Points 1** & **OA\_Scene\_A** \\ \hline CD & 512 & 2048 & 4096 & 0.773 \\ CD\_M & 512 & 2048 & 4096 & 0.71 \\ CD & 1024 & 2048 & 2048 & 0.722 \\ CD\_M & 1024 & 2048 & 2048 & 0.71 \\ \hline \end{tabular} \({}^{\dagger}\) Note: The reason why we chose to set the different “Seg_n_points” in the second controlled experiment (4096 in the first controlled experiment and 2048 in the second controlled experiment) is that if “Codeword_dims” is set to 1024 and 4096 points used in the segmentation network training stage, the AE training time would take too long, and the improvement of performance would not be significant or even decrease.  
\end{table} 
Table 5: Ablation analysis of using various reconstruction losses, tested on the “Scene_A” of ArCH dataset in different settings. Acronyms “CD” and “CD_M” denote that we used Chamfer distance or modified Chamfer distance as our reconstruction loss in our training process. “Codeword_dims” denotes the dimension of the codeword. “Seg_n_points” represents the input point size in the segmentation network training phase. “AE_n_points” denotes input point size in the AE training stage. Comparing rows 1 and 5, rows 2 and 6, rows 3 and 7, and rows 4 and 8, we found that whether 2048 or 4096 points are used as input in the segmentation network with the codeword dimension 512 or 1024, using 2048 points as input in the AE performs much better than if 4096 points are used;
* When analyzing the effect of the input point size in the segmentation network, different results are found: when the dimension of the codeword is 1024, point-cloud size of 2048 in the segmentation network provides better results than 4096; however, when the dimension of the codeword is 512, the segmentation network with a point-cloud size of 4096 outperforms or draws the case of the point cloud with 2048 points; and
* The best overall accuracy (0.773) was achieved when the input point-cloud size was 2048 and 4096 in the AE and segmentation steps, respectively, and was 2.6% better than the second performing network, which had a point-cloud size of 2048 in both steps. However, considering that the training time of the network will be much longer when the input point-cloud size is 4096, in this paper, the experiments were mostly based on input point clouds of size 2048 in both steps.