# Automatic Matching of Multi-Source Satellite Images: A Case Study on ZY-1-02C and ETM+
## 2 Methods
### Finalizing the Matching Process by Lsv  
The different imaging timing and undulating terrain in ZY-1-02C images and DOMs of ETM+ can cause errors in image matching. Such error matches must be eliminated before the images can be used to refine the RPCs of ZY-1-02C. However, elimination is difficult when a mathematical model is used to directly describe the image relationships. In most cases, the effects of the differences can be minimized when the judging area is reduced to a relatively small area [27]. In this case, local image relationships could be accurately approximated on a small surface, as shown in Figure 3. A transformation vector that is consistent with statistical laws can be fitted with the coordinate differences between correct matches on the small surface. Figure 4 shows that the relationship between the corresponding points, which are organized by Triangulated Irregular Network (TIN), must be analogous when the judging area is limited to a small local part. The median lines of the triangles in TIN are used to build the LSV, \(\left[\text{L}_{\text{P}},\text{A}_{\text{P}},\text{w}_{\text{P}}\right]\), where \(\text{L}_{\text{P}}\) is the length of the triangle median lines, \(\text{A}_{\text{P}}\) is the angle of the triangle medians with the horizontal, and \(\text{w}_{\text{P}}\) is the parameter of the distance weights. The LSV of each triangle, where the point to be determined in the local facet center is located, can be calculated according to the corresponding point pairs in the triangle network. Reliability coefficients are obtained by the statistical results of the points to be determined in the triangle networks of the left and right images. The positions of the points with gross errors are eliminated on the basis of a given reliability coefficient threshold. In this situation, a similarity comparison is conducted for the corresponding points one at a time. The vector differences of the correct matches can be fitted well between the two images, in contrast to those of the error matches. Weighting and voting strategies were designed for connecting the surrounding points with the judging point, as shown in Equation (6). The process of determining the judging point as a gross error to be eliminated is shown in Equation (7). \[\left\{ \begin{array}{c}Q=\sum\limits_{i=1}^{n}\left(\frac{\left[L_{p},A_{p} \right]_{i}}{\left[L_{p},A_{p}\right]_{i}}*w_{p}\right)\\ w_{p}=\left|D_{p\_h}^{t}-D_{p\_h}^{r}\right|\end{array} \right. \tag{6}\]  
where \(\left[L_{p},A_{p}\right]_{i}\) is the vector of the left images, \(\left[L_{p},A_{p}\right]_{r}\) is the vector of the right images, \(w_{p}\) is the absolute value of the length difference of the vertical segment through the judging point, and \(Q\) is the judging value. \[\left\{ \begin{array}{c}Q\geq\ Q_{T},\ correct\ matches\\ Q<\ Q_{T},\ error\ matches\end{array} \right. \tag{7}\]  
where \(Q_{T}\) is the threshold for determining if the point is a gross error. This threshold is usually set as three times the root-mean-square error (RMSE) of \(Q\). Figure 4: Model of local image and local statistic vectors (LSV). Based on the preceding analysis, error matches could be eliminated effectively by the statistics with LSV. The proposed error elimination method is as follows: (1) A TIN, based on the divide-and-conquer approach, was constructed using the coordinates of the matching points, and the points in the TIN were judged individually in the following steps. (2) Several nearest neighboring points around the current judging point were collected based on the TIN structure. All these points, which were collected as candidate points, were selected according to the distance from the judging point. Extremely long distances of more than 300 pixels were disregarded. (3) The LSV of the left and right images were calculated in a small local area, which was based on the selected matching points in Step 2. Through Equation (5), the statistics were initiated. The judging of the current point was estimated using Equation (6) until every point pair had been judged.