# An Automatic Geometric Registration Method for Multi Temporal 3D Models
## 4 Experiment Results and Discussions
### Distribution and Correspondence Analysis of Spatial-Feature Points  
The number and distribution of spatial-feature points are the basic conditions for 3D model geometric registration. Firstly, the feature points were extracted from the texture images in the 3D model, and then the spatial positions of the feature points were calculated based on the triangulation of the 3D model to generate the corresponding spatial-feature points. Figure 8 shows the feature-point-extraction results of two texture images.  
The white dots in Figure 8 represent the extracted feature points, of which the feature points extracted in Figure 8a were evenly distributed and not significantly different from those of the conventional image. In Figure 8b, due to the fragmentation of texture images, many feature points were distributed in the non-textured image area. Obviously, these feature points were invalid and needed to be eliminated in the feature-matching process. According to the analysis of feature-point-extraction results in Figure 8, although 3D texture images are irregular and fragmented, a sufficient number of feature points could still be extracted. After extracting all the feature points of the lowest-level model, the spatial positions of the feature points were calculated, and the planar feature points were converted into spatial-feature points. The spatial-feature points were superimposed and displayed with the 3D grid model, as shown in Figure 9.  
Figure 8: The distribution of feature points in texture images. (**a**) A continuous texture image. (**b**) A fragmented texture image.  
Figure 7: The 3D model of the study site and the spray-painted stones.  
The green dots in the left of Figure 9 are the extracted spatial-feature points, which were uniformly distributed on the surface of the mesh model. The right side of Figure 9 shows the enlarged display of the red box. Analysis from the visual performance showed that the extracted spatial-feature points were strictly fitted to the surface of the mesh, and their planar positions and elevation interpolation results were consistent with the actual situation, and were reasonable. After obtaining the spatial-feature points, the initial similarity determination and 3D model geometric registration were performed to obtain the corresponding points in different stages, as shown in Figure 10.  
The yellow dots in Figure 10a,b represent the distribution of spatial-feature points extracted from the 3D model in two periods, respectively, which were evenly distributed but had no correspondence between spatial-feature points. Figure 10c,d shows the initial matching correspondence of the spatial-feature points for the two periods' data, from which it can be seen that it still contained a certain number of outlier points, as shown in the red-boxed area. Figure 10e,f shows the final correspondence of the spatial-feature points obtained after model registration. Compared with Figure 10c,d, the outliers existing in the initial corresponding spatial-feature points have been eliminated. After statistics, the number of spatial-feature points extracted from the data in the two periods was 100,834 and 93,751, respectively. After similarity-determination, a total of 4914 initial corresponding points were obtained. A total of 2816 final corresponding spatial points were obtained after the two periods of 3D model registration. Based on the analysis of the above results, it is possible to obtain sufficient and evenly distributed corresponding points by extracting spatial-feature points from the multi-period 3D model.