## 3 Experimental Results and Analysis
### Robustness to Illumination, Color and Brightness  
In order to compare the robustness of different image registration algorithms to illumination, color, and brightness, the test set in the experiments is augmented, and the used image augmentation method is the same as that of the training set. After image augmentation, the registration accuracy and failure rate of each algorithm are compared. We only randomly augmented some of the images in the test set, but not all of them. The higher the number of augmented images is, the higher the image augmentation degree of the test set is, and the test set has more diversity in illumination, color and brightness. The image augmentation degree can be represented by the probability of an image being augmented in the test set. The test set used in this experiment contains 5000 pairs of test images. Each algorithm runs 10 times repeatedly, during which the image augmentation is randomly implemented at a pre-specified image augmentation degree, and the average result of the 10 runs is taken as the final result of this algorithm with respect to the pre-specified image augmentation degree. Therefore, the image augmentation degree also represents the degree that the test set is affected by image augmentation. The accuracy and failure rate of image registration can be used to measure the robustness of different image registration algorithms. Since the maximum perturbation values of each grid point in the sample image in the horizontal and vertical directions are \(\rho_{x}\) and \(\rho_{y}\) respectively, when the accuracy of image registration of a pair of images is greater than \(\sqrt{\rho^{2}{}_{x}+\rho^{2}{}_{y}}\), the pair can be considered as a registration failure, and the failure rate of image registration on the test set can further be calculated. Considering that the RMSE values of test samples failed to be registered may be too large, and these extreme data may affect the RMSE values of the whole test set greatly, therefore, the RMSE of the whole test set is defined as  
\[RMSE_{i}^{\prime}=\min(RMSE_{i},\sqrt{\rho^{2}{}_{x}+\rho^{2}{}_{y}}) \tag{20}\] \[RMSE=\frac{1}{k}\sum\limits_{i=1}^{K}RMSE_{i}^{\prime}\]  
where \(RMSE_{i}\) represents the RMSE value of the \(i\)th pair of images, and \(K\) denotes the total number of image pairs in the test set. Figures 2-5 show the failure rate and RMSE achieved by different algorithms under different image augmentation degrees. The abscissa is the image augmentation degree of the test set, which changes from 0.0 to 1.0 with a step size of 0.1; the ordinate represents the registration failure rate or RMSE. Figure 2 shows the robustness comparison of seven image registration algorithms, in which the CNN model used by [PERSON]'s and [PERSON]'s algorithms is VGG, while the model used by the proposed algorithm is Xception. As can be seen from Figure 2, the robustness of the traditional image registration algorithms to illumination, color, and brightness is very poor, and the robustness of the learning-based algorithms, especially the supervised learning-based algorithm, is better than that of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm Type** & **Algorithm** & **Running Time of GPU (s)** & **Running Time of CPU (s)** \\ \hline Pixel based & ECC & - & 226 \\ \hline \multirow{4}{*}{Feature based} & SIFT & - & 99 \\  & ORB & - & 65 \\  & APAP & - & 456 \\ \hline \multirow{4}{*}{Learning based} & [PERSON] + VGG & 36.2 & 123 \\  & [PERSON] + Googlenet & 26.9 & 57.3 \\  & [PERSON] + Xception & 46.2 & 208 \\ \cline{1-1}  & [PERSON] + VGG & 36.2 & 123 \\ \cline{1-1}  & [PERSON] + Googlenet & 26.9 & 57.3 \\ \cline{1-1}  & [PERSON] + Xception & 46.2 & 208 \\ \cline{1-1}  & Proposed + VGG & 47.2 & 138 \\ \cline{1-1}  & Proposed + Googlenet & 39.7 & 61 \\ \cline{1-1}  & Proposed + Xception & 59.6 & 213 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Running time comparison of different image registration algorithms. the traditional ones.