# MPCR-Net: Multiple Partial Point Clouds Registration Network Using a Global Template
## 4 Experiments
### Experiments Based on Untrained Models
#### 4.2.2 Correspondence Point Estimation  
We used deep learning-based algorithms such as MPCR-Net, PRNet, and RPM-Net, which have correspondence point estimation and point cloud local registration functions, to carry out the correspondence point estimation experiments.  
In the experiment, each global template point cloud contained 1024 data points and was sampled from each original point cloud model in the ModelNet40 dataset through the voxel grid downsampling [44; 45; 46] algorithm. The process of creating a partial point cloud was as follows:  
1. Using the FPS algorithm, the initial partial point cloud was sampled from the global template point cloud according to a sampling ratio of 0.05 to 0.95; the sampling ratio refers to the ratio of the data volume of the initial partial point cloud to the global template point cloud.
2. The initial local point cloud was rotated by 20\({}^{\circ}\) around the three Cartesian coordinate axes with the coordinate origin as the center and translated 0.5 units along the three coordinate axes to obtain the local point cloud.  
Taking the chair model in the ModelNet40 dataset as an example, its creation process of the global template point cloud, the initial partial point cloud, and the partial point cloud is shown in Figure 7, where the correspondence point estimation experiment was carried out under the condition that the proportion of correspondence points was 0.5. The green part is a global template point cloud that contained 1024 data points, the orange part is the initial partial point cloud that contained 512 data points sampled from the template point cloud at a sampling ratio of 0.5, and the blue part is the partial point cloud obtained after the initial partial point cloud was rotated and translated.  
Taking the chair model as an example, when the proportion of correspondence points was 0.5, the accuracy of estimation of MPCR-Net, PRNet, and RPM-Net algorithms are shown in Figure 8, where green parts are the global template point clouds, and purple parts are the correspondence points estimated by three algorithms, respectively.  
The distribution of these estimated correspondence points and the initial partial point cloud (Figure 8c) in the global template point cloud were compared. The closer two distributions are, the more correspondence points are correctly estimated, and the higher the estimation accuracy \(p\) of the correspondence point estimation.  
Under the condition that the proportion of correspondence points was 0.05 to 0.95, estimation experiments were performed on all models in the test set. Then, the average estimation accuracy of the correspondence point of the three algorithms was calculated.  
As shown in Figure 9, the average estimation accuracy of the corresponding points of the three algorithms increased as the proportion of correspondence points increased. However, as the proportion of correspondence points decreased, the accuracy gap between PRNet, RPM-Net, and MPCR-Net gradually widened. When the proportion of correspondence points was 0.95, the estimation accuracies of the correspondence points of the PRNet and RPM-Net were 26.0% and 8.0% lower than that of MPCR-Net, respectively, and when the proportion of correspondence points was 0.05, the estimation accuracies of correspondence points of PRNet and RPM-Net were 86.9% and 91.2% lower than that of MPCR-Net, respectively. This indicates that compared to the PRNet and RPM-Net algorithms, the MPCR-Net algorithm proposed in this paper can effectively improve the estimation accuracy of the correspondence point, especially when the proportion of correspondence points is low.  
Figure 8: Accuracy of correspondence point estimation: (**a**) TPCC-Net, \(p=0.90\); (**b**) PRNet, \(p=0.51\); (**c**) RPM-Net, \(p=0.25\).  
Figure 7: The creation process of a global template point cloud, initial partial point cloud, and partial point cloud: (**a**) Chair model in ModelNet40; (**b**) Global template point cloud; (**c**) Initial partial point cloud; (**d**) Partial point cloud.