## 5 Evaluation of Keypoint Matching
### Result and Discussion
Although the number of corresponding points in the \"Urban\" dataset for HOPC was more than that of the proposed method, only the proposed method achieved more accuracy and several corresponding points. Table 3 shows the inlier (correct matches) rates, in which our proposed method achieved a high inlier rate. For Pix2 pix, Pix2 pix + EE, and the proposed method, some outliers were already removed based on the scale value and the gradient direction of each keypoint [36]. This was the reason why the three methods achieved higher inlier rates than DLSC, HOPC, and CFOG. Figure 11 shows the results of the optical image generation and the subsequent feature-point matching. A sufficient number of correspondences were estimated, and it was confirmed that Pix2 pix was effective for SAR-to-optical image translation. Although false correspondences remained, they could be removed using a robust estimation method, such as RANSAC [43]. As Figures 9 and 10 show, the Pix2 pix + EE results indeed gave sharper images than those of Pix2 pix and Proposed. However, the quantitative evaluation result showed better results than the others. The reason was that Pix2 pix + EE enhanced not only effect image features but also artifacts. After all, the Pix2 pix + EE results seemed sharper, but did not yield as good results. Considering the \"Urban\" dataset in Figure 11 more closely, the center part of the generated optical image failed to translate in both methods. Even if fewer corresponding points were found in some parts of the images, it was possible to correctly calculate the total correspondences in a case where partial correspondence was correctly achieved in other areas since SIFT or other keypoint detection/description methods could calculate local features. Through this experiment, we confirmed that precise feature matching between the optical and generated optical images was possible. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **DLSC** & **HOPC** & **CFOG** & **Pix2 pix** & **Pix2 pix + EE** & **Proposed** \\ \hline \multirow{2}{*}{Urban} & \multirow{2}{*}{0.437} & 0.703 & 0.575 & 0.900 & 0.900  \\ \cline{2-6}  & & (60.8\%) & (31.6\%) & (105.9\%) & (105.9\%) & **(108.9\%)** \\ \multirow{2}{*}{Farm} & \multirow{2}{*}{0.588} & 0.615 & 0.606 & 0.805 & 0.815 & **0.896** \\  & & (4.6\%) & (3.1\%) & (36.9\%) & (38.6\%) & **(52.4\%)** \\ \multirow{2}{*}{Hill} & \multirow{2}{*}{0.155} & 0.396 & 0.200 & 0.809 & 0.808 & **0.880** \\  & & (155.5\%) & (29.0\%) & (421.9\%) & (421.3\%) & **(467.7\%)** \\ \hline \end{tabular}
\end{table} 
Table 3: Mean inlier (correct matches) rates. A practical example of SAR-to-optical registration is shown in Figures 12 and 13. A SAR image was projected onto an optical image that had a rotation and translation formation. The projection was estimated by finding the corresponding points between the optical and generated optical images. We confirmed that high-precision image registration was achieved, even on the assumption of planarity, since this dataset covered an area that was not very wide. Alternatively, we could estimate a 3D projection of the corresponding keypoint if necessary [22]. Figure 11: Results of keypoint matching. Yellow points connected by yellow lines mean corresponding points, and blue points mean other keypoints. No local feature correspondences were found in a collapsed area, but many corresponding points could be found in the remaining area. Figure 12: Example of SAR and optical image registration assuming planarity. To overlay a SAR image on the target optical image (**a**), after finding the local feature correspondences between the optical and generated optical images, the original SAR image was projected onto the optical image using an estimated homography transform (**b**). Half of the area was transparent, similar to a checkerboard pattern (**c**), and ground truth, which was registered by accurate DEM (**d**). Figure 13: (**a,b**) are Close-up of a part of Figures c and d in Figure 12. Yellow lines were drawn along the roads to demonstrate the registration accuracy.