## 3 Infrared and Visible Image Fusion
### Fusion Rules for High-Frequency Subbands
In this paper, the employed semantic segmentation model focuses on classifying images into two categories: cracks and background. The fusion results of the images can be objectively evaluated by employing a confusion matrix. To assess the algorithm's performance, precision (_Pre_), recall (_Re_), and specificity (_Spe_) are evaluated using the following Equations (14)-(16). \[Pre=\frac{TP}{TP+FP} \tag{14}\]

\[Re=\frac{TP}{TP+FN} \tag{15}\]

\[Spe=\frac{TN}{TN+FP} \tag{16}\]

where \(TP\) denotes the number of pixels correctly predicted as cracks, \(TN\) denotes the number of pixels correctly predicted as background, \(FP\) denotes the number of pixels incorrectly predicted as cracks, and \(FN\) denotes the number of pixels incorrectly predicted as background. The figure shows the labeling results of \(TP\), \(TN\), \(FP\), and \(FN\) after segmentation using R2U-Net. Among the three secondary evaluation indices mentioned above, the recall reflects the leakage rate of the model, and the specificity and precision reflect the misdetection rate of the model. The accuracy rate is not used as an evaluation index because of the uneven number of samples of cracks and backgrounds. The algorithm evaluation in this study involves the use of 10 sets of samples, with the ground truth being manually labeled using visible images. The results of the semantic segmentation evaluation for each image category are presented in Table 1. It is evident that the proposed method achieves significantly higher accuracy compared to the other methods. This indicates that the proposed method achieves a high correct detection rate for cracks while also minimizing false detections. Figure 7.0 Comparison of recognition results for different images using semantic segmentation network. In Figure 9, it can be observed that the falsely positive (_FP_) pixels in the results of the proposed method are mainly located around the actual cracks. This occurrence can be attributed to resolution inconsistencies, resulting in slight errors in crack width estimation. However, these _FP_ pixels do not significantly affect the recognition of the crack skeleton. Conversely, in the original image and those generated by the comparison algorithm, the _FP_ pixels are predominantly distributed in the background, leading to significant interference in crack recognition. As indicated by the objective index, the proposed method exhibits the highest specificity, reflecting a low rate of false recognition in the background. Both ResU-Net and R2U-Net demonstrate high recall for all segmented images. This, along with the observations in Figure 9, suggests that the prediction results for crack positions closely align with the ground truth, resulting in a low miss detection rate for the model. The high resolution of the proposed method, combined with the visible image information at crack locations, results in a small number of missed pixels at the crack edges. However, this has no significant impact on the overall detection results, as there are no substantial instances of continuous or extensive missed pixels. In summary, without altering the structure of the semantic segmentation network model and the training samples, using the proposed method to fuse images as input samples can effectively enhance the crack recognition performance of the semantic segmentation network. When compared to the original image and the image generated by the comparison method, the sample preprocessed using the proposed method offers several advantages, including high detection precision, a low miss detection rate, and a low false detection rate. These advantages significantly improve the accuracy and adaptability of the semantic segmentation network. It is necessary to emphasize that the results presented in Table 1 solely indicate that utilizing processed samples from infrared image fusion in a specific scenario enhances the crack prediction performance of U-Net. However, this does not imply that combining the proposed method with R2U-Net or ResU-Net is the optimal solution for this problem.