## 4 Experimental Results and Discussion
### Performance Analysis on Multi-Date Satellite Images  
We selected 4 sites to test the performance of the proposed method on multi-date satellite images, where Site 1 is the same as the site in Section 4.2. The input images of Site 2, Site 3, and Site 4 are shown in Figure 8, and the corresponding ground truth DSMs are shown in the first column of Figure 9. Site 1 is a mixed area of low-to-medium buildings and roads, with an altitude range of 18-35 m. Site 2 is a medium-high building area with an altitude range of 18-42 m, and we still use the red color to indicate the high altitude. Site 3 is a low-rise building area with an altitude range of 18-35 m, and it can be seen that most of the buildings in this area are blue (blue color indicates low altitude). Site 4 is the park area, where there is some water surface, so the ground truth DSM has significant holes in the water surface area. Figure 8: The input satellite images of Site 2, Site 3, and Site 4. According to the analysis in Section 4.2, we selected 10 image pairs with the acquisition interval of less than 15 days, the sun angle difference of less than 20\({}^{\circ}\), and the intersection angle of 3\({}^{\circ}\)-15\({}^{\circ}\) to generate DSMs, and then the 10 DSMs are aligned and fused. We chose the multi-date S2P method [20] and the traditional BA method [32] to compare with the proposed method. The multi-date S2P method is one of the best methods for automatic DSM generation of multi-date satellite images [21; 25]. Different from the S2P method, which only deals with a single satellite image pair, the multi-date S2P method uses the experience-based image pair selection strategy to select the multi-date satellite images and registers and fuses the 3D point clouds after generating multiple independent point clouds. The final generated DSMs are shown in Figure 9. The details of the DSMs are shown in Figure 10. It can be seen from Figures 9 and 10 that the details of the DSM generated by the multi-date S2P method in Site 1 are poor, and the DSMs generated by the proposed method and the traditional BA method have better visual quality. For Site 2, the DSM generated by the multi-date S2P method has a great number of 3D points with large errors (about 8 m) at the edge of the high buildings. The altitude estimation of the DSM generated by the traditional BA method in the high building area is obviously lower this area is orange instead of red, and the error of this area is about 4 m. The visual quality of the DSM generated by the proposed method is significantly better than that of the other two methods, but there is also a problem that the edge of the building is not clear, which is due to the difference of the shadows and vegetation around the building in the image pair composed of satellite images on different dates. This issue shall be considered in the future study. As shown in the third row of Figure 9, the visual quality of the DSMs generated by the multi-date S2P method and the proposed method in the Site 3 area is good, but the overall altitude of the DSM generated by the traditional BA method is 3.2 m higher (the DSM in Figure 9 is mint green instead of blue) than the ground true DSM, which may be due to the fact that the objective function of the traditional BA method falls into a local optimal value when solving the optimization problem, and the local optimal value is still large. For  
Figure 9: The ground truth DSM and the generated DSMs of the multi-date S2P method [20], the traditional BA method [32], and the proposed method. the Site 4 area, the altitude error of the DSM generated by the multi-date S2P method in the high building area is large (the overall altitude value here is about 1.5 m higher than the ground truth DSM), and the building edge of the DSM generated by the traditional BA method is not as clear as that of the DSM generated by the proposed method. In summary, the proposed method achieves good visual quality in the four sites.