## 4 Experiments and Results
### Other Experiments  
In this section, we added three experiments to test the PcBD method: first, we use PcBD to extract and smooth the projection boundaries of real-world scans from wind tunnel tests. We selected two different parachutes to simulate flexible deformable objects that may be encountered in practical applications. The output results are shown in Figure 14. The first target is a circular parachute. PcBD successfully predicted the shape of its projected boundary, and the network successfully identified boundary points at sparse edges and ignored a hole caused by reflection errors in the point cloud. The second target is a star-shaped parachute with front traction ropes. The edges are sparser in the point cloud, just as we generated in Bound57. PcBD also outputs its projected point cloud and identifies sparse boundaries while removing necessary outliers. The parachute point clouds we collected were relatively dense, so we set the input point to 16,384, which also proved that PcBD's pre-trained model has the ability to process point clouds of different sizes.  
Figure 12: Visual comparison of boundary-detecting. We only show the inputs with outliers. The outlier points will be removed for the comparing methods, and the projection boundaries of the comparisons are extracted using ground truth boundary labels. * Results on the extracted ground truth boundaries.  
Figure 13: A comparison between the PcBD processing flow and a classic processing flow which applies multiple methods.  
We then tested the PcBD model trained on Bound57 on an existing real-world scan dataset, WHU-TLS [63]. This experiment further tested the following capabilities of the model: generalization of targets, directions of projection, and the adaptability to the number of input points. As shown in Figure 15, we selected two scenes in the dataset: pedestrians and a vehicle (a), and trees (b). The pedestrians and trees are selected as deformable targets, and the vehicle as a rigid target to test the generalization of the model to different targets. In the experiment, we selected different directions as projection vectors to test the directional generalization projection boundary extraction capability of PcBD, and sampled different numbers of input point clouds to test the adaptability of the model to the number of input points. As in the figure, the PcBD model can fulfill the tasks of target outlier removal, projection boundary detection and smoothing at different input point numbers, and has good adaptability to both rigid and deformable objects. When changing the projection direction, PcBD can still output accurate and valid smoothed boundaries. However, when the projection direction leads to an exposition of too many incomplete target structures (such as the car in the third picture in Figure 15a), the error of the detected boundary will increase. This is because PcBD relies on complete two-dimensional and three-dimensional structures for predicting the projection boundary. For targets such as trees, the original point cloud is relatively scattered in the first place, but PcBD can still make reasonable boundary predictions and remove potential outliers, which has proved the rationality of our proposed processing flow.  
At last, we tested PcBD's ability to extract three-dimensional boundaries. For an input solid point cloud, we rotate it at different angles, sample the point clouds to 16,384 points, process them with PcBD, and then splice the projection boundaries of the target in all postures. We designed the process of rotating the input point cloud to ensure that the three-dimensional point cloud boundaries in all directions can be completely extracted. The result is shown in Figure 16. The PcBD network outputs fine three-dimensional point cloud boundaries and has great potential. We believe that through certain fine-tuning, the network we propose can have the ability to complete this task better.  
Figure 14: The output of PcBD on real-world parachute scans.