# 3-D Point Cloud Registration Using Convolutional Neural Networks
## 6 Experiments
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c c c c} \hline \hline
**Test Sample** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline Points (n, m) & (116, 1015) & (0116, 900) & (1116, 1052) & (1116, 1012) & (1116, 1001) & (1116, 909) & (1116, 1025  
In order to draw thorough comparisons and reinforce an efficient improvement on reducing the computation time but maintaining the high precision when estimating the pose of a 3-D data point cloud of the proposed algorithm, average values in terms of the MSE and computation time of all tested samples for 5 objects are figured out and visualized into two bar charts as shown in Figures 10 and 11. In fact, it is obvious that FGR method witnesses the strongest fluctuation as well as the highest error of MSE values that lead to the worst performance in terms of the precision of this method. Particularly, the average MSE value of 5 tested objects of this approach is approximately two times as high as the average MSE value of the proposed and RANSAC+ICP approach as illustrated in the last column group in Figure 10. In addition, the lowest discrepancy among the average MSE values of 5 tested objects at roughly 1.130 mm, followed by a larger disparity at approximately 1.840 mm according to RANSAC+ICP approach, draws that our CNNs-based algorithm achieves the robust performance for a variety of objects. Moreover, the proposed approach matches the comparable precision with a slightly smaller average MSE value at around 0.108 mm in comparison with RANSAC+ICP algorithm as given in the column group \"Average\" in Figure 10. As regards the computation time, the presented algorithm significantly outperforms with approximately 15 times and 2 times as fast as RANSAC+ICP and FGR method, respectively, as shown in the last column group in Figure 11.  
To conclude these comparisons, registration results of these three algorithms with specific samples are visualized in Figures 12-16 for Bunny, Horse, Dragon, Buddha and Armadillo data, respectively. It is noticeable that data point clouds transformed by the proposed and RANSAC+ICP algorithm are closer to the model point clouds than FGR approach. Additionally, as shown in Figures 12b-16b, the registration result in the precise stage (blue point cloud) is better than the result in the rough stage (green point cloud) because the 2-D CNN model covers a smaller uncertainty from \(-15^{\circ}\) to \(15^{\circ}\) than the 3-D CNN model with the full range of uncertainty from \(-180^{\circ}\) to \(180^{\circ}\). Therefore, based on 3-D point clouds of an object captured by a 3-D camera, the pose of the object can be precisely estimated in fixed time that is sufficient for the application of real-time closed-loop object picking and assembly systems because of two redeeming features such as the high accuracy and fast estimation. Figure 11: The comparison about average computation time of 20 tested samples. Figure 12: The registration results of Bunny data for test sample 6: (**a**) The initial state; (**b**) 3-D CNNs then 2-D CNNs, (**c**) RANSAC then ICP, (**d**) Fast Global Registration. Figure 13: The registration results of Horse data for test sample 2: (**a**) The initial state; (**b**) 3-D CNNs then 2-D CNNs, (**c**) RANSAC then ICP, (**d**) Fast Global Registration.