## 4 Experiments
### Comparison Experiments
#### 4.2.2 Quantitative Experiments  
The number of correct matching points (NCM), F1-measure value and root mean square error (RMSE) of matching points were introduced as the quantitative measurements for five matching networks: Contextdesc, R2D2, D2-Net, ASLFeat and PM-Net. The threshold \(\varepsilon\) of NCM and RMSE in this paper was chosen as 3 pixels. The experimental results are shown in Tables 1-3 and Figure 12. The experimental results with best performance are marked in bold Precision in the above equation is the ratio of correct matches to the total number of matches, and is used to calculate the ability of matching method to exclude false matching points. Recall is the ratio of correct matches to the number of corresponding keypoints [48], which evaluates the accuracy of returning correct matching points.
3. The root mean square error of matching points reflects the accuracy of points derived by the matching algorithm and RMSE is calculated as: \[RMSE=\frac{1}{\text{NCM}}\sum_{i=1}^{\text{NCM}}\parallel H(x_{i},y_{i})-(\dot{ x},\dot{y})\parallel\] (9) To calculate RMSE, 20 checkpoints for each set of test images are selected manually, and then we can calculate the image geometric affine transformation parameters \(H\) and theoretical coordinates \((\dot{x},\dot{y})\).  
By comparing and analyzing the experimental results, it can be seen that PM-Net can give a certain number of correct matching points for all the experimental image pairs, and the RMSEs are within three pixels. In contrast, Contextdesc, which is designed specifically for multimodal images, only completes matching in image pairs A and B with rich texture information and fails in the other four pairs. This is because Contextdesc does not include the detection of keypoints, but rather extracts the regional and geometric information of images to enhance the feature description of matching network. Therefore, it performs the worst experimental results for optical and SAR images with large differences. R2D2 considers the repeatability of keypoints and improves the reliability of matching, so it is slightly improved compared with Contextdesc. ASLFeat can extract richer keypoints in the dense feature extraction process, and it uses the inherent characteristics of network hierarchy to store spatial resolution and local details for achieving more accurate keypoints localization. As for image pairs E and F with weak texture, the overall performances of ASLFeat are better than Contextdesc. However, for pairs C and D with noise and huge image differences, ASLFeat matching fails.  
For the experimental image pairs of A and B, D2-Net outperforms PM-Net in terms of F1-measure values in Table 2. Because D2-Net uses a 'Describe-and-Detect' strategy, i.e., it  
Figure 12: Quantitative experimental results.  
extracts descriptors and keypoints simultaneously, D2-Net generates feature maps from the original image and then performs feature detection on low-level feature maps. Therefore, for the two image pairs A and B with strong texture, D2-Net can extract richer information from the original images, resulting in slightly better F1-measure values than PM-Net.  
As can be seen from Tables 1-3, PM-Net obtains the greatest number of correct matching points on six pairs of test images, and it is also clear from the qualitative experiments that the points are more evenly distributed. With F1-measure comparisons, PM-Net obtains better results overall. This shows that PM-Net is able to extract robust matching points from optical and SAR images. Apart from this, RMSE of the matching points of PM-Net are all less than three pixels. PM-Net learns the similarity function of optical and SAR image patch pairs to matching labels through the end-to-end network structure. It can complete the matching task without descriptors, which is more adaptable for optical and SAR image matching. Therefore, PM-Net is able to obtain better matching accuracy for optical and SAR image pairs with noisy interference and large feature differences.