# MPCR-Net: Multiple Partial Point Clouds Registration Network Using a Global Template
## 4 Experiments
### Experiments Based on Untrained Models
#### 4.2.3 Point Cloud Registration  
To explore the influence of the proportion of correspondence points on the accuracy of point cloud registration, we used the MPCR-Net, PRNet, and RPM-Net algorithms to perform point cloud registration experiments.  
The point cloud registration results of three algorithms on the chair model in the ModelNet40 dataset when the proportion of correspondence points is 0.5 are shown in Figure 10. The green parts are the template point cloud, and the red parts are the positions of the partial point cloud after registration by the three algorithms. \(R\) and \(t\) represent the calculation error of the rotation angle and the translation distance of each algorithm, respectively; the smaller the values of \(\Delta R\) and \(\Delta t\) are, the higher is the accuracy of point cloud registration.  
Under the condition that the proportion of correspondence points was 0.05 to 0.95, the registration experiment was performed on all models in the test set, and the average registration errors of the three algorithms were calculated. Figure 11a, b show the average calculation error of the rotation angle, and the average calculation error of the translation distance, respectively. The average calculation error of the rotation angle of the MPCR-Net is 23.8-72.8% smaller than that of the PRNet and 27.1-77.6% smaller than that of the RPM-Net. The average calculation error of the translation distance of the MPCR-Net is 27.0-90.9% smaller than that of the PRNet and 30.2-94.3% smaller than that of the RPM-Net. This indicates that the registration accuracy of the MPCR-Net is higher than that of the other two algorithms, especially when the proportion of correspondence points is low.  
Figure 9: Average estimation accuracy of correspondence points with different proportions of correspondence points.  
Figure 11 shows that average calculation errors of the rotation angle and the translation distance are negatively correlated with the proportion of correspondence points, indicating that the point cloud registration accuracy decreases as the proportion of correspondence points decreases. This is because the coordinate information of the correspondence points directly participates in the calculation of the rigid body transformation matrix in the point cloud registration. Since the average estimation accuracy of the correspondence points of PRNet and RPM-Net is significantly lower than that of MPCR-Net, the average registration accuracy is also lower than that of MPCR-Net.  
When the proportion of correspondence points changes from 0.95 to 0.05, the average calculation errors of the rotation angle of the MPCR-Net increase by 13.6\({}^{\circ}\), whereas the calculation errors of PRNet and RPM-Net increase by 29.7\({}^{\circ}\) and 31.6\({}^{\circ}\), respectively. Simultaneously, the average calculation error of the translation distance also changes similarly. This indicates that, compared to the PRNet and RPM-Net algorithms, the MPCR-Net algorithm is more robust to changes in the number of correspondence points. When the correspondence point is low, the MPCR-Net algorithm can still maintain a high registration accuracy and effectively register two point clouds with a large difference in the amount of data.