## 4 Discussions  
The experimental results demonstrate the advantages of the proposed method over the SIFT and Patch-SIFT methods in terms of accuracy, running time, and the number and distribution of matched tie points for the three sets of pre- and post-earthquake images. All three image pairs covered mountainous areas affected by disasters (such as landslides and river expansion, triggered by severe earthquakes). Topographic relief in the images increased the difficulty of image registration. However, in this case, the proposed method still achieved better registration results.  
Both the quadratic (\(N_{\mathrm{d}}=2\)) and cubic (\(N_{\mathrm{d}}=3\)) polynomial models were used in the experiments to generate registered images. The proposed method yielded very similar performances when using the two models. Using the quadratic polynomial model (\(N_{\mathrm{d}}=2\)), the proposed method also provided shorter running times and lower \(RMSE_{T}\) values than the Patch-SIFT and SIFT methods using the same model. The proposed method using the cubic polynomial model yielded slightly longer running times and lower \(RMSE_{T}\) values than the proposed method using the quadratic polynomial model. Consequently, we think that both the quadratic and cubic polynomial models can be selected for the images used in the experiments.  
The proposed method can be also used for satellite images (such as GF-1 and GF-2 images) covering plains, according to the results of the other experiments. For example, a GF-1 multispectral image covering Chengdu City, Sichuan province, China, was also tested. The image was recorded  
Figure 16: Registered images for the Jüuzhaigou dataset. (**a**) The original image; (**b**) the registered image of the proposed method; (**c**) the registered image of the Patch-SIFT method; and (**d**) the registered image of the SIFT method.  
on March 9, 2018 and had a relatively large size (\(5354\times 5354\) pixels) and a spatial resolution of 8 m. A total of 175 matched tie points were extracted by the proposed method, with an \(RMSE_{T}\) of 0.38 pixels. The Patch-SIFT method obtained 116 matched tie points with an \(RMSE_{T}\) of 0.55 pixels, whereas the SIFT method provided 80 tie points with an \(RMSE_{T}\) of 0.66 pixels. The proposed method obtained the registered image within 17.17 s, which is only 26.5% of the SIFT (64.77 s) and 36.7% of the Patch-SIFT (46.76 s). The experimental results also show that the registration results of the proposed method are better than those of the other two methods. This demonstrates that the proposed method also works for RS images covering urban areas and shows advantages in running time on larger RS images.  
The GE images were used in this work to construct the pre-earthquake image database and then used as the reference for the co-registration of post-earthquake RS images. If higher quality high-resolution satellite remote sensing images were available in the study area, the images could be used as the reference for image registration. In this case, the proposed method is also applicable and is expected to yield better performance than the other two methods.  
In general, the proposed method can provide geometrically accurate images for disaster information extraction, and is helpful for the assessment of disasters, such as collapsed buildings, damaged roads, and landslides. The proposed method also has potential applications. For instance, the registered images obtained by the proposed method can be integrated with big data, such as the Floating Car Data [41], which is used to observe historical traffic patterns, traffic facilities, and services, to the phenomenon after the earthquakes.