## 4 Experiment Results and Analysis
### Model Performance Analysis  
The performance of MDD-YOLOv8 significantly surpasses that of the base model, as illustrated in Figure 9. Specifically, MDD-YOLOv8 achieved 87.7% precision, 76.1% recall, 78.9% mAP@50, and 47.0% mAP@50:95 across all classes (as shown in Table 4). When examining individual categories, the model demonstrates more balanced performance in detecting ships and planes compared to bridges and oil tanks. The latter two categories are more prone to confusion with background elements, making it challenging to improve the recall rates for these classes.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Metrics** & **Formulas** & **Contents** \\ \hline Precision & \(P=\frac{TP}{TP+FP}\) & TP (True Positive):The count of samples that are actually positive and correctly predicted as positive. \\  & \(P=\frac{TP}{TP+FP}\) & FP (False Positive): The count of samples that are actually negative but incorrectly predicted as positive. \\ \hline Recall & \(R=\frac{TP}{TP+FN}\) & FN (False Negative): The count of samples that are actually positive but incorrectly predicted as negative. \\ \hline Average Precision & \(AP=\int_{0}^{1}P(R)dR\) & AP (Average Precision): The average precision of the model for predicting a single category, calculated as the integral of the Precision–Recall (P-R) curve. \\ \hline Mean Average Precision & \(mAP=\frac{1}{n}\sum\limits_{i=1}^{n}AP_{i}\) & mAP (Mean Average Precision): The mean AP across all n categories. \\ \hline F1 Score & \(F1=\frac{2\times P\times R}{P+R}\) & F1 Score: A metric to evaluate the overall quality of the model, calculated as the harmonic mean of precision and recall. The score ranges from 0 to 1, with higher values indicating better performance. \\ \hline \hline \end{tabular}
\end{table}
Table 3: The metrics for model performance evaluation.  
Figure 9: The results of model training.  
As shown in Figure 10, the confusion matrix highlights that the square grid colors become progressively darker from YOLOv8 to MDD-YOLOv8, indicating improved object detection performance. The most significant improvement is observed in the \"planes\" category, as the M-FPN-PAN module enhances the algorithm's ability to identify tiny targets effectively.  
Table 5 presents typical scenes for each category and the detection results of YOLOv8 and MDD-YOLOv8. In the first row, MDD-YOLOv8 successfully identifies all eight ships in the image, whereas YOLOv8 misses one. In the second row, while both models detect the bridge, MDD-YOLOv8 demonstrates a higher confidence coefficient. The third row reveals that YOLOv8 produces more false positives when detecting oil tanks and suffers greater losses when detecting planes compared to MDD-YOLOv8. This clearly shows that MDD-YOLOv8 achieves higher precision and recall rates than the baseline model.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Class** & **P (\%)** & **R (\%)** & **mAP@50 (\%)** & **mAP@50:95 (\%)** \\ \hline All & 87.7 & 76.1 & 78.9 & 47.0 \\ Ship & 87.1 & 87.2 & 90.1 & 55.9 \\ Bridge & 84.7 & 65.8 & 67.0 & 39.3 \\ Oil tank & 97.0 & 61.8 & 69.8 & 58.8 \\ Plane & 81.9 & 89.7 & 88.7 & 34.1 \\ \hline \end{tabular}
\end{table}
Table 4: The results of MDD-YOLOv8.  
Figure 10: The confusion matrixes of YOLOv8 and MDD-YOLOv8. (**a**) YOLOv8; (**b**) MDD-YOLOv8.