# Surface Reconstruction Planning with High-Quality Satellite Stereo Pairs Searching
## 6 Discussion  
### Quality Comparison Using Real Images  
Though Figure 7 depicts the comparison based on the estimated quality values, the realistic reconstruction quality can also be evaluated because a subset of stereo pairs have the original images observed by the World-View3 satellite as described in Section 5.1. By  
Figure 7: Result comparison with estimated reconstruction quality value. DSM errors as estimated by a regression model for different optimization objectives (task quantity \(Q_{1}\), reconstruction quality \(Q_{2}\), timeliness \(Q_{3}\), and the combinations) are compared.  
selecting these real images from the planned results of the scenarios as shown in Figure 7, the performance of the proposed quality-driven planning method is further evaluated.  
Figure 8 demonstrates the quality statistics of real 3D reconstructions using the planned stereo pairs, averaged from the same 10 planning scenarios in Figure 7 for the whole year. The quality results of the top 10 and 30 image pairs selected by the planning algorithm are presented in Figure 8 for different optimization objectives. The trend shown in Figure 8 is consistent with that in Figure 7, which validates the effectiveness of the proposed method. For instance, among the top 10 image pairs, the reconstruction error is lowest when planning based on quality objectives. This indicates that quality-driven planning effectively identifies image pairs that yield higher reconstruction accuracy for future imaging implementation. By relaxing the selection of real image pairs to the top 30, the advantage of the quality-driven planning is still obvious though the mean error slightly increases for \(Q_{2}\) (4.00 vs. 3.98). Moreover, by combining quality with other objectives, the overall quality can be significantly boosted (\(Q_{1,2}\) vs. \(Q_{1}\)), further demonstrating the effectiveness of the proposed method.  
In Figure 9, we present typical 3D reconstruction results for three objectives: task quantity ((a1)-(a3) for \(Q_{1}\)), reconstruction quality ((b1)-(b3) for \(Q_{2}\)), and timeliness ((c1)-(c3) for \(Q_{3}\)). The results are selected around the average level of DSM error in Figure 8, which is 4.0 for \(Q_{2}\), 5.2 for \(Q_{1}\), and 4.2 for \(Q_{3}\) to reflect the average visual quality of DSMs. The heat values in Figure 9 indicate the elevation in each DSM. It is not hard to notice that the 3D surfaces for \(Q_{2}\) (middle row) are much smoother than the others. Meanwhile, when optimizing for \(Q_{2}\), surface details such as building structures can be accurately constructed, which is consistent with the lowest DSM error values illustrated in Figure 8. Though using \(Q_{3}\) (bottom row) as an objective achieves better quality than \(Q_{1}\), it still falls short compared to \(Q_{2}\) in terms of both DSM error and visual appearance.  
Figure 8: Result comparison with realistic reconstruction quality values. DSM errors as measured based on ground truth for different optimization objectives (task quantity \(Q_{1}\), reconstruction quality \(Q_{2}\), timeliness \(Q_{3}\), and the combinations) are compared.