# An Automatic Geometric Registration Method for Multi Temporal 3D Models
## 4 Experiment Results and Discussions
### Geometric-Registration-Accuracy Analysis of Spatial-Feature Points  
A total of three methods are used to generate 3D models for evaluating the relative geometric positioning accuracy of multi-temporal 3D models. The first method is to generate 3D models based on low-precision UAV airborne POS data. The second method uses post-processed kinematic (PPK) technology to obtain high-precision position at the time of image acquisition, and uses a GPS-support method to complete 3D reconstruction to obtain 3D models. The third method uses the 3D-model alignment method proposed in this paper, and performs vertex updates on the 3D model to be aligned based on the model-alignment parameters. The spatial-feature points of the above three types of 3D models were extracted, respectively, and the corresponding points of the final spatial features were obtained. The positions of the spatial-feature points in the base 3D model were subtracted from the positions of those in the 3D model to be aligned to obtain any residual positioning errors, and the results are shown in Figure 11.  
Figure 9: The distribution of feature points in the mesh model. DX, DY, and DZ in Figure 11 represent the position residual errors in X, Y, and \(Z\) directions, respectively. The residual error distribution in Figure 11a shows that the positioning accuracy of conventional UAV-borne POS was low, and there were obvious systematic errors among the generated multi-temporal 3D models. When high-precision PPK data was used to generate 3D models, the positioning accuracy of its multi-period 3D models was greatly improved. The relative positioning accuracy of the two temporal 3D models was less than 0.2 m, as shown in Figure 11b. However, the average values in the Y and \(Z\) directions were not zero, indicating that a small amount of systematic positioning error still existed in these two directions. The residual errors of the corresponding points of the 3D model after using the geometric alignment of this paper were all close to 0 m, showing a random distribution in Figure 11c. The residual-error accuracy of spatial-feature points obtained by the three methods was calculated, and the results are shown in Table 2.  
Figure 10: The corresponding distribution of spatial-feature points, the yellow dots in the figure are the spatial-feature points. (**a**) The initial spatial-feature points extracted. (**c**) The initial correspondence of spatial-feature points, with incorrect correspondence in the red box. (**e**) The fine correspondence of spatial-feature points after registration. (**b,d,f**) corresponds to (**a,c,e**) and are the results of the second-cycle data. In Table 2, AVG represents the average error of corresponding points of spatial features, which reflects the systematic error of relative positioning accuracy of multi-temporal 3D models. STD represents the standard deviation, which reflects the internal aggregation of corresponding points of spatial features. Based on the results in Table 2, it can be seen that the overall average error of the 3D model generated from conventional UAV airborne POS data was 2.91 m. The accuracy was low and cannot be directly used for change detection in multi-temporal 3D models. The overall average error of the multi-temporal 3D models generated based on PPK data was better than 0.18 m, but there were still a few systematic errors in the Y and Z directions, which were consistent with the results in Figure 11b. The \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **AVG X (m)** & **AVG Y (m)** & **AVG Z (m)** & **STD X (m)** & **STD Y (m)** & **STD Z (m)** \\ \hline POS & 1.21 & \(-\)2.21 & \(-\)1.46 & 0.12 & 0.12 & 0.13 \\ PPK & 0.01 & 0.08 & \(-\)0.16 & 0.09 & 0.11 & 0.09 \\ REG & 5.37 \(\times\) 10\({}^{-5}\) & \(-\)2.38 \(\times\) 10\({}^{-5}\) & 7.10 \(\times\) 10\({}^{-7}\) & 0.05 & 0.06 & 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the positioning accuracy of corresponding points for different 3D models.