## 4 Experiment
### Verification Example  
To verify the effectiveness of the proposed model, we constructed the experimental environment presented in Figure 8. The 3 DM vision system is responsible for obtaining the three-dimensional coordinates of control points by encoding points in real time, while the binocular vision measurement system is responsible for obtaining the shape data of the solid model.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Network** & **Train Loss** & **Test Loss** & **Train RMSE (mm)** & **Test RMSE (mm)** \\ \hline CNN-GRU & \(1.03\times 10^{-4}\) & \(5.60\times 10^{-8}\) & \(1.99\times 10^{-4}\) & \(2.31\times 10^{-4}\) \\ CNN-GRU-CBAM & \(1.07\times 10^{-4}\) & \(5.56\times 10^{-8}\) & \(2.02\times 10^{-4}\) & \(2.30\times 10^{-4}\) \\ CNN-LSTM-SA & \(9.32\times 10^{-5}\) & \(5.14\times 10^{-8}\) & \(1.80\times 10^{-4}\) & \(2.24\times 10^{-4}\) \\
**CNN-GRU-SA** & \(\mathbf{6.31\times 10^{-5}}\) & \(\mathbf{2.94\times 10^{-8}}\) & \(\mathbf{1.02\times 10^{-4}}\) & \(\mathbf{1.64\times 10^{-4}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Network comparison results.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Net Frame** & **Max (mm)** & **Min (mm)** & **Mean (mm)** & **Std (mm)** \\ \hline CNN-GRU & \(4.90\times 10^{-1}\) & \(6.42\times 10^{-3}\) & \(6.22\times 10^{-2}\) & \(4.99\times 10^{-2}\) \\ CNN-GRU-CBAM & \(3.80\times 10^{-1}\) & \(\mathbf{3.56\times 10^{-3}}\) & \(5.99\times 10^{-2}\) & \(4.75\times 10^{-2}\) \\ CNN-LSTM-SA & \(2.52\times 10^{-1}\) & \(4.80\times 10^{-3}\) & \(6.60\times 10^{-2}\) & \(4.39\times 10^{-2}\) \\
**CNN-GRU-SA** & \(\mathbf{2.33\times 10^{-1}}\) & \(\mathbf{3.79\times 10^{-3}}\) & \(\mathbf{5.70\times 10^{-2}}\) & \(\mathbf{3.89\times 10^{-2}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Deviation statistics results.  
Figure 8: Real experimental environment.  
Figure 7: (**a**) Control point before change; (**b**) surface before change; (**c**) control point after change; (**d**) surface after change; (**e**) deduction results of CNN-LSTM-SA; (**f**) deduction results of CNN-GRU; (**g**) deduction results of CNN-GRU-CBM; (**h**) deduction results of CNN-GRU-SA.  
Based on the coordinates of the control points, we obtained the deduction results presented in Figure 9 using the proposed model. The gray point cloud represents the appearance data obtained by the binocular vision system. The red point cloud represents the deformation results derived by the proposed model. Significant deviations are observed in three regions, i.e., A1, B1, and C1 because the A2, B2, and C2 regions are encoding point locations, which do not contain point cloud information. Therefore, only the closest points could be used for calculating deviations. Additionally, owing to the poor quality of the point cloud in the edge region of the scanning results, for the deduction results in region D, the deviation could only be calculated by finding relevant points nearby. However, most of the results are consistent with the actual situation. According to our statistical analysis, the average deviation was 0.57544 mm.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Encoding Point Number**} & \multicolumn{3}{c}{\(t_{0}\)} & \multicolumn{3}{c}{\(t\)} \\ \cline{2-7}  & **x (mm)** & **y (mm)** & **z (mm)** & **x (mm)** & **y (mm)** & **z (mm)** \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 6: Control point coordinates.  
Figure 9: Actual deduction results. (A-C) Deviation caused by encoding points; (D) Missing scanning data in the edge area.