## 2 Methodology
### Image Partitioning Strategy Based on Geographic Information Constraints  
For large high-resolution remote sensing images, the extraction and matching of feature points usually have high computational complexity, which requires considerable memory and is time-consuming. In addition, it yields a low accuracy of registration when enough feature points are extracted from only some of the regions of the image. To solve this problem, an image partitioning strategy based on geographic information constraints was adopted to divide remote sensing images  
Figure 2: Tie points obtained using the original multispectral image (**a**) and the enhanced image obtained using the 2% linear stretch method (**b**). into several image patches. For each image patch, the corresponding reference image can be obtained according to the projected coordinates of the image patch. The extraction and matching of feature points were applied to each image patch pair. With respect to the geometric information of RS images, the mapping relationship [33] between the image coordinates and geographic coordinates can be expressed using Equation (2). \[\left[ \begin{array}{c}X_{i}\\ Y_{i}\end{array} \right]=\left[ \begin{array}{c}X_{0}\\ Y_{0}\end{array} \right]+\left[ \begin{array}{cc}G_{1}&G_{2}\\ G_{4}&G_{5}\end{array} \right]\left[ \begin{array}{c}I_{i}\\ J_{i}\end{array} \right], \tag{2}\]  
where \((I_{i},J_{i})\) are the image coordinates of the \(i\)th pixel, and \((X_{i},Y_{i})\) are the corresponding projected coordinates of \((I_{i},J_{i})\); \((X_{0},Y_{0})\) are the projected coordinates of the top left corner in the original whole scene input image, and \(G_{1}\), \(G_{2}\), \(G_{4}\), and \(G_{5}\), are the parameters of the transformation model. Figure 3 shows a schematic of the image partitioning strategy. The image partition of the input RS image and the corresponding reference image can be conducted using the following steps:  
First, the input image is divided into \(n\times n\) patches, each of which has a size of \(M\times N\) pixels. Each patch is numbered, and the coordinates of the four corners of the patch are recorded. For example, the corners of patch \(F_{2N}\) are recorded as \(A_{1}\), \(A_{2}\), \(A_{3}\), and \(A_{4}\). The image coordinates of corners \(A_{1}\) and \(A_{3}\) are then calculated and recorded as \((I_{1},J_{1})\) and \((I_{3},J_{3})\), respectively. Second, the image coordinates are transformed using Equation (2) into the projected coordinates according to the geometric information of the input image. Specifically, \((X_{0},Y_{0})\) are the projected coordinates of the top left corner in the original whole scene input image; \((I_{i},J_{i})\), \(i=1\) or \(3\) are the image coordinates of corners \(A_{1}\) and \(A_{3}\) of the image patch \(F_{2N}\); \((X_{i},Y_{i})\), \(i=1\) or \(3\) are the projected coordinates of \(A_{1}\) and \(A_{3}\); \(G_{1}\) is the pixel size of the input image; \(G_{5}\) is the negative value of pixel size of the input image; and the values of \(G_{2}\) and \(G_{4}\) are equal to \(0\). Third, according to the projected coordinates \((X_{i},Y_{i})\) of an input image patch, the pre-earthquake satellite image covering this patch is found through the pre-earthquake high-resolution image database. If there is more than one image covering the patch, the reference image is the one whose spatial resolution is closest to the input image. Additionally, the extension of the corresponding reference patch can be determined according to \((X_{i},Y_{i})\). The image coordinates \(((I_{1}^{{}^{\prime}},J_{1}),(I_{3}^{{}^{\prime}},J_{3}^{{}^{\prime}}))\), which correspond to the two corners \((B_{1}\) and \(B_{3})\) of the reference image patch shown in Figure 3c, are calculated using Equation (2). Finally, the image coordinates of the other two corners \((B_{2}\) and \(B_{4})\) of the reference image patch can be obtained according to those of corners \(B_{1}\) and \(B_{3}\).