## 3 Results and Discussions
### Ablation Tests with the Adapted Loss Function  
To demonstrate the effects of the box loss function on the model performance, we compare results from the detectors with the CIOU loss, the EIOU loss, and the revised EIOU loss. It should be noted that the new formulation of the loss function has certain flexibility in the parameters \(\gamma\) and \(\beta\). Based on prior testing on a variety of cases, we set \(\gamma=0.5\) and \(\beta=0.1\) as the default parameters for the revised EIOU loss in the comparative studies. Results using \(\beta=0.1\) and different values of \(\gamma\) for Baseline Model 2 with the loss function altered to the adapted EIOU loss have been appended in Table 3. Considering the reference result with the unaltered EIOU loss (Table 4), the new formulation achieves considerable growth in mAP score when \(\gamma\) is around \(\ 0.4\ \sim\ 0.6\), which indicates that improvements provided by the proposed algorithm are stable and sufficiently consistent  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & **Augmentation** & \multirow{2}{*}{**Setting**} & \multirow{2}{*}{**Pr**} & **Re** & **mAP (\%)** \\  & **Groups** & & & & \\ \hline A1 & A, B, C & I & 0.825 & 0.786 & 50.4 \\ A2 & A, B, C & II & 0.835 & 0.787 & 50.9 \\ A3 & D, E & I & 0.815 & 0.777 & 50.8 \\ A4 & D, E & II & 0.826 & 0.797 & 51.3 \\ A5 & C(H), D, E & I & 0.813  
over the hyperparameter range. \(\gamma=0.5\) is in the middle of this range and has been shown to be robust in the model performance among various cases. The test cases and results with EIOU loss or revised EIOU loss are shown in Table 4, where the threshold setting II has been applied as the default setting. Figure 4 shows the learning curves for the model trained with the adapted loss function (Test M3). The training losses generally drop steadily during the entire process, while losses for validation all reach the minimum values prior to the last epoch. Similarly, the mAP curves obtain their peaks before going down near the end of the training. These trends verify that settings, including the total number of epochs and our proposed form of the loss function, are appropriate for the experiments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multirow{2}{*}{**Loss Function**} & \multicolumn{2}{c}{**Augmentation**} & \multirow{2}{*}{**Additional Techniques**} & \multirow{2}{*}{**mAP (\%)**} \\  & & & & \\ \hline M1 & \(L_{EIOU}\) & \(-\) & Setting I & 49.8 \\ M2 & \(L_{EIOU}\) & \(-\) & \(-\) & 50.1 \\ M3 & \(\widetilde{L}_{EIOU}\) & \(-\) & \(-\) & 50.9 \\ M4 & \(\widetilde{L}_{EIOU}\) & D, E & \(-\) & 50.7 \\ M5 & \(\widetilde{L}_{EIOU}\) & A, B, C, D, E & \(-\) & 51.6 \\ M6 & \(\widetilde{L}_{EIOU}\) & A, B, C & \(-\) & 51.6 \\ M7 & \(\widetilde{L}_{EIOU}\) & A, B, C & mixup, label smoothing & 51.9 \\ M8 & \(\widetilde{L}_{EIOU}\) & A, B, C, D, E & mixup, label smoothing & 51.4 \\ M9 & \(\widetilde{L}_{EIOU}\) & D, E & mixup, label smoothing & 52.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Test results using different loss functions, augmentation sets, and other settings. Figure 4: Curves of the loss functions for the training and validation sets and the metrics during training using the revised EIOU loss function (model M3): (**a**) box loss; (**b**) confidence loss; (**c**) classification loss; (**d**) mAP. The original EIOU loss produces a mAP score similar to the CIOU loss (Baseline 2), with a difference of merely 0.2% between the two different forms, while selecting the adapted form with NMS setting II leads to an overall improvement of 1.3% compared to Baseline Model 2. This trend is maintained for the tests augmented with the first three groups of image transformation methods, where the mAP score reaches 51.6%, growing by 0.7% compared to the model using the default CIOU loss. The situation changes when sets D and E (representing the local distortions and sharpening of the images) are incorporated in the pre-processing steps.