## 4 Analysis of Experimental Result  
The Crack500 [24] dataset consists of 3368 crack images divided into subsets of 1896, 348, and 1124 images for training, validation, and testing, respectively. Among these data, 352 images were duplicates; nonetheless, all 3368 images, including the duplicates, were used. This dataset was captured using a mobile phone camera on the main campus of Temple University. Each image was divided into 16 nonoverlapping patches, and only regions containing more than 1000 crack pixels were retained. The input images were resized using the nearest neighbor method, and size-based training was conducted based on the resized images. Detailed information regarding the dataset is presented in Figure 6.  
The following settings were adopted throughout the experiments. Training was conducted for 100 epochs with an initial learning rate of \(2\times 10^{-3}\). A dynamic learning rate adjustment metric was applied to improve the learning rate. The batch size for training was set to 16, and Adam [24] was used as the initialization function. Table 1 provides information on the hardware used in the experiments. The evaluation metrics were based on a confusion matrix. We adopted the F-1 score, which is the harmonic mean of precision and recall, along with the mean intersection over union (mIoU). The F-1 score considers both positive and negative model samples, thereby complementing issues that may arise when considering only precision or recall. \begin{table}
\begin{tabular}{c c c} \hline \hline
**CPU** & **Memory** & **GPU** \\ \hline AMD EYC 2713 & 512 GB & RTX A6000 \\ \hline OS & Python & Tensorflow \\ \hline Ubuntu 20.04 & 3.8 & 2.5.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental hardware. Figure 6: Crack500 dataset samples. \[Precision:\frac{TP}{(TP+FP)} \tag{9}\]  
\[Recall:\frac{TP}{(TP+FN)} \tag{10}\]  
\[F-1\ Score:2\times\frac{Precision\times Recall}{Precision+Recall} \tag{11}\]  
The mIoU is a metric that represents the proportion of overlapping areas between predicted and ground-truth regions, evaluating how accurately objects are detected. The following formula is used for the IoU metric:  
\[\frac{1}{N}{\sum_{i=1}^{N}IoU_{i}} \tag{12}\]  
The confusion matrix for the training results, shown in Figure 7, indicates that while the segmentation of areas without cracks was highly accurate, there was room for improvement in accurately segmenting the crack areas. In particular, incorrect classification was observed in fine cracks, as well as in distinguishing cracks from dark areas such as shadows. Looking at the results in Table 2, our proposed network demonstrated higher performance when low-resolution images from the Crack500 dataset were used as the input. The results show an approximate difference of 0.17 in terms of mIoU between the model trained with 128 \(\times\) 128 input images and that trained with 512 \(\times\) 512 input images. Overall, the model with low-resolution input images exhibited a higher mIoU. Figure 8 presents prediction results with respect to input image size. Here, both test images were predicted to be similar to the ground truth at 64 \(\times\) 64 and 128 \(\times\) 128 resolutions. However, when handling higher-resolution images, the model did not accurately represent crack boundaries and tended to misidentify non-crack areas as cracks. To obtain objective results, comparative experiments were conducted using several models. First, we compared the prediction results across FCN-8s [25], U-Net [26], and our network, with the results shown in Figures 9 and 10. Figure 7: Result of confusion matrix. Figure 8: Segmentation results by input image size.