# Point Cloud Repair Method via Convex Set Theory
## 3 Results and Discussion
### Qualitative Analysis  
Figure 5 shows the subjective repair effect of our and other comparison methods on the PCN dataset. We selected four types of objects in the PCN dataset: airplane, table, chair, and car. As can be seen from the results, our method could accurately repair the missing parts in the point cloud without producing redundant 3D points in nonmissing regions. For example, in the table category, our method could focus on repairing the missing areas in the point cloud, keeping nonhole areas unchanged, and the distribution of newly filled points was more uniform than that of other methods. On the other hand, SpareNet could not focus on the missing area and only generated a complete point cloud on the basis of the trained parameter model. Therefore, redundant 3D points were generated in the nonpore area, blurring the original shape of the point cloud. The point cloud completed by the SnowflakeNet method had new missing areas on the chair point cloud because it had reconstructed the entire point-cloud model and generated new 3D points in the nonhole area. New hole areas appear when new 3D points are not evenly distributed. Our method predicts the surface shape of the missing area according to the distribution information of the points in the hole neighborhood in order to ensure that the distribution of 3D points in the nonhole area remains unchanged. PF-Net is a rough-to-fine process. To improve the resolution of the output results, the number of 3D points was increased. However, this is different from the ground truth. The SCCR method failed to completely repair the large holes on the table and the surface of the airplane because when the point distribution is too scattered, and the hole area is large, the SCCR method only generates new filling points on the basis of a small number of hole boundary points. In addition, our repair method achieved a better visual effect for the car model than that of related work. Figure 6 shows the visualization effect on the point cloud collected by Stanford and our method. We selected monsters, monkeys, and a sphere as experimental point clouds, and none of these three categories of point clouds was used as training data for SpareNet, PF-Net, and SnowflakeNet. The monster point-cloud model was from the Stanford dataset, and we collected the monkey [37] and sphere point-cloud models. The experimental results show that SpareNet, PF-Net, and SnowflakeNet repaired the results, severely distorting the original shape of the point cloud and causing the repaired point cloud to be far from the true shape. SpareNet, PF-Net, and SnowflakeNet produced bad results because they were constrained by the training data and could not complete the untrained point cloud. However, training a large amount of data consumes huge amounts of time, so their methods cannot be widely used. Compared with the SpareNet, PF-Net, and SnowflakeNet methods, our method only focused on the missing areas and was not limited by the object category. At the same time, our method could effectively repair various point clouds regardless of target category. This shows that our method has wider applicability. On the pipe surface model, due to the large hole area and the scattered point distribution, the SCCR method could not completely repair the hole. Compared with the SCCR method, our method could  
Figure 5: Subjective repair effect on PCN dataset. not only completely repair the holes in the point cloud, but also ensure that the repaired surface was consistent with the surrounding neighborhood. Figure 7 shows the subjective repair effect of our method for multiple holes in a single point cloud. The rabbit point cloud is from the Stanford dataset, and there were many holes at the bottom. To prevent the influence of adjacent holes on the repair results, our method does not repair multiple holes at the same time, but repairs them one by one. The repaired surface was assumed to be a real surface that provided geometric information for repairing adjacent holes.