## 3 Experiments and Results
### Experimental Results
#### 3.3.1 Experiment 1 Using the Wenchuan Dataset  
In the experiment using the first image pair, the proposed method obtained 52 matched tie points, which is slightly more than that of the Patch-SIFT method (\(N_{\alpha p}=45\)) but significantly more than that of the SIFT method (\(N_{\alpha p}=21\)). The proposed method yielded very similar performances when using the quadratic and cubic polynomial models. Using the cubic polynomial model, the proposed method yielded an \(RMSE_{T}\) value of 1.40 pixels, which is significantly lower than those of the Patch-SIFT (\(RMSE_{T}=2.01\) pixels) and SIFT (\(RMSE_{T}=9.18\) pixels) methods. Although the SIFT method provided the lowest \(RMSE_{T}\) value (0.81 pixels), the \(RMSE_{T}\) value of 9.18 pixels is extremely high. Using the cubic polynomial model, the running time of the proposed method was 2.20 s, which is only 6.47% \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{4}{c}{**Parameters Setting**} & \multirow{2}{*}{**Specification of Parameters**} \\ \cline{2-2} \cline{4-5}  & **1** & **2** & **3** \\ \hline \(\mathbf{n}\) & \(10\times 10\) & \(10\times 10\) & \(7\times 7\) & The number of image patches \\ \hline \(\mathrm{N_{max}}\) & 1500 & 1500 & 1500 & The maximum number of corner points for each image patch \\ \hline \(\mathrm{N_{iter}}\) & 10 & 10 & 10 & The number of iterations for eliminating mismatched tie points \\ \hline \(\mathrm{T_{R}}\)/pixel & 5 & 3 & 5 & The residual threshold for eliminating mismatched tie points \\ \hline \(\mathrm{T_{L}}\)/pixel & 100 & 100 & 30 & The distance threshold for removing high-density tie points \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter settings for the three sets of experimental data. of the SIFT (33.98 s) method and 44.27% of the Patch-SIFT (4.97 s) method. Similarly, the proposed method using the quadratic polynomial model gave a lower \(RMSE_{T}\) value and a shorter running time than the other two methods. Figure 11 shows the spatial distribution of matched tie points (dots in red) of the first image pair. It can be seen that the distribution of matched tie points obtained by the proposed method, as shown in Figure 11a, is the most even. As can be seen from Figure 11c, the 21 matched tie points obtained by the SIFT method are unevenly distributed, which contributes to the extremely high validation error it yielded. In contrast, the proposed method can still extract correct tie points in the areas with large topographic relief, such as the top-left corner of images shown in Figure 11.  
The registration results of the Wenchuan dataset using the cubic polynormal model are shown in Figure 12. It can be seen that only the registered image obtained using the proposed method (Figure 12b) can effectively rectify the geometric position deviations of the objects on the original \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Image Pair** & **Method** & \(N_{cp}\) **(pair)** & \(N_{d}\) & \(T\) **(s)** & \(RMSE_{M}\) **(pixel)** & \(RMSE_{T}\) **(pixel)** \\ \hline \multirow{6}{*}{1} & \multirow{2}{*}{The proposed method} & \multirow{2}{*}{52} & 3 & 2.20 & 1.65 & 1.40 \\ \cline{3-6}  & & & 2 & 1.95 & 1.79 & 1.95 \\ \cline{3-6}  & & & 3 & 4.97 & 1.94 & 2.01 \\ \cline{3-6}  & & & 2 & 4.91 & 2.07 & 2.27 \\ \cline{3-6}  & & & 3 & 33.98 & 0.81 & 9.18 \\ \cline{3-6}  & & & 2 & 33.89 & 1.24 & 9.27 \\ \hline \multirow{6}{*}{2} & \multirow{2}{*}{The proposed method} & \multirow{2}{*}{29} & 3 & 1.56 & 1.81 & 1.75 \\ \cline{3-6}  & & & 2 & 1.48 & 1.93 & 1.95 \\ \cline{3-6}  & & & 2 & 3.23 & 2.39 & 2.76 \\ \cline{2-6}  & & SIFT & 4 & 1 & 4.55 & 2.69 & 5.10 \\ \hline \multirow{6}{*}{3} & \multirow{2}{*}{The proposed method} & \multirow{2}{*}{118} & 3 & 2.05 & 1.37 & 1.24 \\ \cline{3-6}  & & & 2 & 1.93 & 1.39 & 1.30 \\ \cline{3-6}  & & & 3 & 6.36 & 1.27 & 1.88 \\ \cline{3-6}  & & & 2 & 6.31 & 1.32 & 1.92 \\ \cline{3-6}  & & & 3 & 27.85 & 0.72 & 2.48 \\ \cline{3-6}  & & & 2 & 27.88 & 0.76 & 2.51 \\ \hline \hline \end{tabular}
\end{table}