## 4 Experiments and Results
### Results on Bound57
Figure 10: Visual comparison of outlier-removing. PCDNF [61], PointFilter [62], DMRde-noise [24], Score de-noise [26], and PD-LTS [50] are utilized as deep-learning based methods. For the geometry-based methods, we adaptively set the input parameters using average point distances, and apply them on the outlier-removed point clouds. We extract the boundaries using the ground truth labels afterwards, and then compare them with the ground truth boundaries. For DMRde-noise and Score de-noise, we directly input the raw inputs on the trained networks on the Bound57 dataset. The PointCleanNet provides two pre-trained networks: an outlier-removing one and a de-noising one. We choose them all so that the overall processing flow is similar to the proposed PcBD, and the boundaries of the output de-noised cloud can be extracted using the ground truth boundary labels. For PD-LTS, we directly extract the boundaries on the output point clouds of the outlier-removal stage, as they have already been de-noised. For PCDNF and PointFilter, we found that the original boundary points were moved a lot after processing, so we gave these methods another opportunity to directly de-noise the boundary point clouds extracted from the proposed dataset. The results are shown in Table 3.  
Judging from the results in Table 3, the PCDNF achieved greater accuracy; however, it is based on the extracted projection boundary ground truths. Even so, PCDNF is less  
Figure 11: Visual comparison of boundary detecting. We only show the inputs with outliers. The outlier points will be removed for the comparing methods. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Methods/Results** & **Avg.** & **Bathtub** & **Camera** & **Earphone** & **Flowerpot** & **Motorbike** & **Pillow** & **Rifle** & **Train** \\ \hline DMRde-noise [24] & 61.99 & 81.24 & 55.51 & 54.01 & 81.91 & 33.96 & 63.26 & 25.12 & 37.30 \\ PointCleanNet [22] & 59.90 & 66.98 & 57.65 & 43.59 & 73.29 & 31.21 & 75.18 & 23.54 & 46.42 \\ PD-LTS-Heavy [50] & 16.03 & 18.86 & 15.90 & 13.21 & 17.75 & 11.86 & 22.59 & 8.21 & 12.53 \\ Score de-noise [26] & 14.85 & 17.39 & 14.10 & 11.75 & 17.35 & 10.67 & 19.18 & 6.89 & 11.45 \\ PD-LTS-Light [50] & 13.33 & 15.56 & 12.89 & 12.32 & 15.56 & 10.53 & 15.94 & 7.13 & 10.55 \\ Bilateral Filter [10] & 12.03 & 14.48 & 11.46 & 9.42 & 13.95 & 8.99 & 14.90 & 5.76 & 8.60 \\ AdaMLS [60] & 11.01 & 11.43 & 9.97 & 7.70 & 14.11 & 7.71 & 10.87 & 5.23 & 8.39 \\ SparseReg [58] & 11.85 & 13.59 & 11.31 & 10.36 & 12.76 & 9.67 & 12.09 & 8.27 & 9.97 \\ Iter-norm-filter [56] & 10.97 & 13.06 & 10.30 & 9.50 & 13.05 & 8.24 & 12.27 & 5.63 & 8.04 \\ PointFilter [62] * & 10.86 & 12.78 & 10.33 & 8.96 & 12.24 & 8.73 & 12.41 & 6.85 & 8.19 \\ W-Multi-Proj [57] & 10.29 & 12.86 & 9.04 & 10.00 & 12.32 & 8.36 & 12.90 & 5.57 & 7.72 \\ MLS [59] & 10.21 & 12.51 & 9.86 & 8.62 & 12.34 & 8.68 & 11.33 & 5.41 & 7.98 \\ PCDNF [61] * & 9.28 & 11.08 & 8.55 & 7.59 & 10.87 & 7.43 & 10.69 & 5.08 & 6.71 \\
**PcBD (Ours)** & **9.92** & **8.29** & **7.04** & **19.60** & **13.24** & **8.75** & **9.68** & **4.37** & **8.05** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Boundary-smoothing results on Bound57 under Chamfer-L1 distance (\(\times 10^{3}\), in millimeters). accurate than PcBD in over half of the categories in the dataset (32 of 57 categories). Comparatively, PointFilter has the same advantages but does not perform better than PcBD. The DMRNoise is now proved unsuitable for training on the proposed dataset for it performed poorly on both outlier-removing and de-noising. The pretrained model of PointCleanNet and PD-LTS also did not perform well. This is easy to explain because the dataset they originally used generated noise at a certain level, and the noise level was also needed to be an input when de-noising. Among the geometry-based methods, the MLS has the best de-noising effect on projected boundaries. Note that PcBD outperforms many traditional de-noising methods even though it was not explicitly trained on per-point displacement loss.