# Remote Sensing Multimodal Image Matching Based on Structure Feature and Learnable Matching Network
## 4 Experiment
### Results and Analysis  
The matching results of the tests (i.e., \(T_{1-4}\)) are shown in Figure 9. Notably, the CMRs of the investigated algorithms increase with the size of the templates. This is because a larger template aids in avoiding repetitive patterns in the base images. Overall, the PCA-LMN achieved the best matching performance in the tests. The average CMR of PCA-LMN was 91.69%, which is 10.63% higher than that of the CFOG (the best traditional method in this test). It is assumed that this is because the PCA-LMN benefits from the PCA orientation enhancement and LMN. The PCA-enhanced orientation can accurately capture the structural features, even in the presence of significant noise distortions. This makes PCA-LMN more reliable in matching multimodal images with noise distortion, such as the optical SAR matching pairs in Figure 10c. In addition, LMN can be trained to adapt to the gradient reversal caused by the radiometric difference among remotely sensed multimodal images. The measurement function trained from LMN can be more sophisticated and accurate than the remapping function employed by the CFOG and HOPC. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test** & **Variance of Gaussian Noise** & **Size of Base Image** & **Size of Template** \\ \hline \(T_{1}\) & Without noise & \(512\times 512\) & \(64\times 64\) \\ \(T_{2}\) & Without noise & \(512\times 512\) & \(96\times 96\) \\ \(T_{3}\) & Without noise & \(512\times 512\) & \(128\times 128\) \\ \(T_  
The performance of DHE is not ideal in the tests, the average CMR of DHE is 3.44% lower than that of the CFOG and 14.07% lower than PCA-LMN. We believe the reason for these results is that the testing dataset is too small to train the deep feature extraction network of DHM, while the pre-trained dataset is not including multi-modal image pairs, which is very different from the testing dataset. A clear contribution of the PCA can be observed by comparing the PCA-LMN and LGO-LMN. The average CMR of PCA-LMN is 6.38% higher than the average CMR of LGO-LMN in \(T_{1-4}\), as shown in Figure 9. This is because the proposed PCA-enhanced method is more stable and can accurately capture the structure direction of remotely sensed multimodal images when compared with the log-Gabor orientation method, as described  
Figure 10: (**a-c**) Matching results of investigated algorithms on multimodal images. The first column shows true positions on the base image; columns 2–7 show matching positions of investigated algorithms on the sensed image; red and green numbers indicate erroneous and correct matching results, respectively. Figure 9: Matching results of test T1–T4. in parts 1 and 2 of Section 3. A clear contribution of the LMN can be observed by comparing the PCA-LMN and PCA-SAD. The average CMR of PCA-LMN is 22.50% higher than that of the PCA-SAD in \(T_{1-4}\), as shown in Figure 9. This indicates that gradient reversal is a significant problem in matching remotely sensed images, as emphasized by numerous other works in this field of research [9; 10; 35]. Clearly, the matching performance considerably can be improved by resolving the gradient reversal problem with the proposed LMN. In tests \(T_{5-16}\), Gaussian noise is added to the test images to evaluate the noise adaptability of the investigated algorithms; Figure 11 shows the matching results. Notably, the CMRs of the algorithms decrease as the noise level increases. The CMRs of the structure feature-based algorithms (i.e., HOPC, CFOG, and PCA-LMN) decrease faster than the three algorithms directly based on the image grayscale (MTM, and MI). This indicates that the structure feature-based methods are more sensitive to noise distortion than the methods directly based on the image grayscale. This trend is assumed to occur because structural features can be easily distorted by image noise. For example, the log-Gabor orientation used in the HOPC, and the gradient orientation employed by the CFOG, are considerably sensitive to noise distortion.