# Optical and SAR Image Registration Based on the Phase Congruency Framework
## 3 Experiments
### Experiment Analysis  
In Table 3, the correct matching number (CMN) and the root mean square error (RMSE) are used to quantitatively evaluate the performances of the three algorithms. We used FSC [18] to obtain CMNs by removing the outliers from the initial correspondences and obtain CMN. RMSE is calculated as follows:  
\[RMSE=\sqrt{\frac{1}{m}\underset{i=1}{\overset{m}{\sum}}\left[\left(x_{i}^{o_{1 }}-x_{i}^{s}\right)^{2}+\left(y_{i}^{o_{1}}-y_{i}^{s}\right)^{2}\right]} \tag{19}\]  
We manually selected 20 checkpoint pairs from each set of correspondences to evaluate the matrix \(H\) based on the affine transformation model. \((x_{i}^{o},y_{i}^{o})\) and \((x_{i}^{s},y_{i}^{s})\) are the coordinates of the \(i\)th correspondence. \((x_{i}^{o_{1}},y_{i}^{o_{1}})\) represents the transformed coordinates of \((x_{i}^{o},y_{i}^{o})\) through the transformation matrix \(H\), and \(m\) denotes the number of the correspondences in optical and SAR images after FSC. Table 3 shows the quantitative analysis of the three comparison algorithms. Since the geometric information is obvious and there are almost no dense regions, it is relatively easy to register Pair A. The OS-SIFT algorithm describes the image information based on the gradient. The gradient orientations corresponding to Pair A are single, and the representativeness and uniqueness of the descriptors are poor. Therefore, the number of correspondences is few. Both the RIFT and the proposed algorithm use PC to describe the structural information, and the PC-based information of the homonymous regions is consistent between optical and SAR images. Thus, the proposed algorithm and RIFT perform better than OS-SIFT. However, RIFT only extracts corner points from the maximum and minimum moment maps, while the proposed algorithm uses the convolution of the maximum moment map and log-Gabor filter to extract keypoints, which reduces the interference of the speckle noises in SAR images. Therefore, the proposed algorithm has a larger CMN and smaller RMSE than RIFT. Pair B contains fields, roads, buildings, and mountains, where the structural information is dense and unevenly distributed. In the regions where buildings and mountains are located, OS-SIFT only obtains a few correspondences with low matching accuracy due to the obvious gradient differences and scattering in SAR images. Since the RIFT uses the PC method to capture structural information, RIFT performs better than OS-SIFT. RIFT is insensitive to radiometric differences because it is based on the PC maximum moment information. Although the number of correspondences obtained by RIFT is superior to the proposed algorithm, the proposed descriptor framework is unique and has a better discrimination ability for the farmland with single structural features. Therefore, the proposed algorithm has a more uniform correspondences distribution and a smaller RMSE than RIFT. For Pair C with a time differences, the corresponding field is divided into two by a road. The cars on the road can be clearly seen in the optical image, which are not present in the corresponding SAR image. The gradient difference between optical and SAR images is not obvious. Thus, the correspondences obtained by OS-SIFT are few, and they are \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**P-A**} & \multicolumn{2}{c}{**P-B**} & \multicolumn{2}{c}{**P-C**} & \multicolumn{2}{c}{**P-D**} \\ \cline{2-9}  & **CMN** & **RMSE** & **CMN** & **RMSE** & **CMN** & **RMSE** & **CMN** & **RMSE** \\ \hline OS-SIFT & 6 & 9.2547 & 11 & 7.6965 & 8 & 6.3563 & 22 & 5.0750 \\ RIFT & 26 & 5.7254 & 43 & 4.7385 & 32 & 4.6788 & 40 & 3.7918 \\ Proposed & 75 & 2.0676 & 36 & 4.3173 & 64 & 2.5721 & 54 & 2.1136 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: CMNs and RMSEs of several methods for test images. concentrated in the areas where the gradient differences are significant. Since the proposed descriptor is representative, the proposed algorithm is superior to RIFT in both CMN and RMSE.