# Rebar Recognition Using Multi-Hyperbolic Attention in Faster R-CNN
## 3 Experimental Study  
During the training phase of the Faster R-CNN model based on the hyperbolic attention mechanism, the Adam optimization strategy was employed, with a maximum learning rate set at 0.0001 and a minimum learning rate at 0.01 of the maximum learning rate. The input images were segmented into 38x38 grids, with each grid containing 9 anchor boxes of varying sizes. In the RPN, the length, width, and aspect ratios of the true bounding boxes of the target images in the dataset were analyzed to establish three different anchors with base scales of 8, 16, and 32, and aspect ratios of 1:0.5, 1:1, and 1:2. For the classification and regression network of the model, the condition for an ROI to be classified as reinforcing bars is that its IoU with the ground truth box is \(\geq\)0.5, with all other regions designated as background. Given that this network contains a relatively large number of parameters while the dataset is relatively small, transfer learning was employed to train the model in order to mitigate the risk of overfitting, which is particularly crucial for small datasets. A pre-trained model from VOC2007 ImageNet [20] was utilized to initialize the model parameters. Subsequently, the ground-penetrating radar dataset was applied for further fine-tuning of the model. During the generation of target candidate boxes, it is necessary to calculate the degree of overlap between all proposed boxes and the ground truth boxes, followed by filtering. If the overlap degree between a specific ground truth box and a proposed box exceeds 0.5, the proposed box is classified as a positive sample; conversely, if the overlap is less than 0.5, it is classified as a negative sample. Subsequently, non-maximum suppression (NMS) is applied to reduce overlapping regions generated by the Region Proposal Network (RPN). All generated candidate boxes are ranked based on their object scores, ultimately resulting in the recommended candidate regions. The model is trained and evaluated using radar images obtained from both field collection and simulation data. To validate the effectiveness of the model, comparative experiments were conducted, with Table 1 summarizing the training results of various models, including SSD, YOLOv5, and Faster R-CNN, in terms of their \(F1\) scores and \(AP\) values. In object detection tasks, Precision refers to the proportion of correctly identified rebar among all detected instances, while Recall measures the proportion of correctly identified rebar among all actual rebar present in the image. Since the goal in this study is to ensure that all rebar is detected, even at the expense of some false positives, we prioritized Recall over Precision. Consequently, Faster R-CNN, which achieved the highest Recall, was selected as the baseline for this work. Additionally, Faster R-CNN demonstrated competitive \(F1\) scores and \(AP\) values, further confirming its effectiveness for rebar detection. Furthermore, to substantiate the efficacy of the DAS and HAT modules in enhancing the Faster R-CNN model's ability to identify the hyperbolic features of steel bars within images, ablation experiments were conducted. Specifically, we evaluated three configurations: the first involved adding the DAS module solely to the feature extraction module, the second involved incorporating the HAT module into the network, and the third assessed the combined effect of both modules. The results, as delineated in Table 2, indicate that the incorporation of the DAS and HAT modules individually resulted in an increase in \(AP\) values of 1.19% and 1.82%, respectively. Moreover, the simultaneous addition of both modules yielded a cumulative increase of 3.23% in the \(AP\) value. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & \(F1\)**Scores** & **Accuracy** & **Recall** & \(AP\) \\ \hline SSD & 0.73 & 96.64\% & 58.54\% & 89.90\% \\ YOLOv5 & 0.75 & 96.28\% & 61.56\% & 90.24\% \\ Faster R-CNN & 0.77 & 65.08\% & 94.72\% & 91.79\% \\ \hline \hline \end{tabular}
\end{table}