## 5 Evaluation of Keypoint Matching
### Result and Discussion  
The generated optical images were properly translated when Pix2 pix or the proposed method--which used GANs in their structure--were applied. The average, standard deviation and median values of the peak signal-to-noise ratio (PSNR) of 300 test images for Pix2 pix were 22.70, 3.08, and 22.50 dB, respectively, whereas those of the proposed method were 23.01, 3.14, and 22.87 dB, respectively. PSNR is calculated as  
\[PSNR(I_{1},\ I_{2})=10\times log_{10}\frac{MAX(I_{1})^{2}}{MSE(I_{1},\ I_{2})}\, \tag{9}\]  
where \(MAX(I_{1})\) is the possible maximum value of image \(I_{1}\), and \(MSE(I_{1},\ I_{2})\) is the mean squared error between \(I_{1}\) and \(I_{2}\). \(MAX(I_{1})\) needs to equal \(MAX(I_{2})\). Figure 9 shows the results of the SAR-to-optical image translation. It shows the input, output, and ground truth sets with the best PSNR values. Afterward, we evaluated the probability of these images for keypoint matching. Figure 10 shows an example of improvement by the proposed method. The proposed method improved the local blur and low reproducibility that were problems in the conventional cGANs. Figure 9: Results of SAR-to-optical image translation. Tables 1 and 2 summarize the results of the quantitative evaluation experiments. Table 1 shows the accuracy of the corresponding point detection. In the test dataset for each \"Urban\", \"Farm\", and \"Hill\" area, the proposed method had high precision with an average accuracy of 0.538 pixels, 0.569 pixels, and 0.577 pixels, respectively. The result \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **DLSC** & **HOPC** & **CFOG** & **Pix2 pix** & **Pix2 pix + EE** & **Proposed** \\ \hline Urban & 0.965 & 0.863 & 0.838 & 0.564  & 0.566 & **0.538**1  \\  & 0.847 & 0.700 & 0.675 & 0.676 & **0.569** \\  & 0.070 & (0.74) & (0.20) & (0.20) & (0.20) \\ Hill & 1.128 & 1.052 & 1.114 & 0.668 & 0.667 & **0.577** \\  & 0.070 & (1.22) & (40.8) & (40.9) & (48.9) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean average (pixels) of the \(\overline{d}\) in Equation (4). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **DLSC** & **HOPC** & **CFOG** & **Pix2 pix** & **Pix2 pix + EE** & **Proposed** \\ \hline Urban & 49.8 & **80.7**1  & 63.0 & 67.6 & 63.5 & 78.5  \\  & & **(62.0\%)** & (26.5\%) & (35.7\%) & (27.5\%) & (57.6\%) \\  & & 65.9 & 62.1 & 57.4 & 57.2 & **101.1** \\  & & (5.4\%) & (\(-0.6\%\)) & (\(-8.2\%\)) & (\(-8.5\%\)) & **(61.8\%)** \\  & & 45.2 & 22.6 & 57.5 & 56.4 & **85.0** \\  & & (162.8\%) & (31.4\%) & (234.3\%) & (227.9\%) & **(394.2\%)** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean number of corresponding points (correct matches). The improvement score was larger in the “Farm” and “Hill” datasets. Figure 10: Improvement examples of image translation with our proposed method. of the proposed method was more accurate than those of DLSC, HOPC, CFOG, Pix2 pix, and Pix2 pix + EE; the absolute accuracy was the highest in the \"Urban\" area. However, the improved accuracy of the \"Farm\" and \"Hill\" was higher than \"Urban\". This was because several objects had strong local features with sharp edges and corners, such as artificial structures, in urban areas. On the other hand, the local features of the \"Farm\" and \"Hill\" areas are weaker than those of the \"Urban\" area. When edge enhancement was applied to the prediction result of Pix2 pix in the Pix2 pix + EE method, the accuracy was not as high as that of the proposed method, probably because the enhancement was equally applied to the artifacts generated in the prediction result. Hence, it was difficult to selectively enhance the effective local features. Table 2 shows the number of detected corresponding points (correct matches). In the test dataset for each of the \"Urban\", \"Farm\", and \"Hill\" areas, the average scores of the proposed method were 78.5, 101.0, and 85.0 points, respectively. As the results in Table 1 indicate, the improvement score was larger in the \"Farm\" and \"Hill\" datasets.