## 4 Experimental Results
### Comparison of YOLO Models
#### 4.3.1 Quantitative Comparisons  
Table 5 presents the quantitative results of the detection performance of the models, measured by the precision, recall, and mAP metrics. For comparison purposes, it also displays the inference time of the trained models, reflecting the average time per image in the test set.  
Among the detection results, the YOLOv9s model demonstrated excellent performance, with a precision and recall of 97.6% and a mAP of 98.7%. This indicates that, due to its more robust architecture and greater number of layers, the model achieves a remarkable balance between precision and recall, effectively detecting objects and minimizing false detections. Conversely, the YOLOv8s, YOLOv10s, and YOLOv11s models showed positive results, with YOLOv11s achieving the lowest performance in comparison to the others. With the lowest average inference time, the YOLOv11s model stands out. Despite its superior performance, the YOLOv9s model exhibits an average prediction time approximately twice as long as the other models, likely due to its more robust architecture and higher FLOPS count. Meanwhile, the YOLOv8s model strikes an effective balance between high performance (97.3%) and low inference time (13.9 ms).  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Models** & **Complete Epochs** & **Train Time (min)** & **Time per Epoch (min)** \\ \hline YOLOv8s & 227 & 32.4 & 0.14 \\ YOLOv9s & 330 & 361.2 & 1.09 \\ YOLOv10s & 327 & 64.8 & 0.20 \\ YOLOv11s & 179 & 27.6 & 0.15 \\ \hline \hline \end{tabular}
\end{table}
Table 4: YOLO models training performance.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Models** & **\#Param. (M)** & **Layers** & **FLOPS (G)** & **Size (MB)** \\ \hline YOLOv8s & 11.14 & 225 & 28.6 & 22.0 \\ YOLOv9s & 9.76 & 1269 & 40.4 & 19.9 \\ YOLOv10s & 8.07 & 402 & 24.8 & 16.2 \\ YOLOv11s & 9.43 & 319 & 21.5 & 18.7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Characteristics of the YOLO models architectures.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Models** & **Precision (\%)** & **Recall (\%)** & **mAP (\%)** & **Inference Time** (ms)** \\ \hline YOLOv8s & 95.8 & 95.6 & 97.3 & 13.9 \\ YOLOv9s & **97.6** & **97.6** & **98.7** & 33.1 \\ YOLOv10s & 97.0 & 93.5 & 97.5 & 14.5 \\ YOLOv11s & 95.8 & 91.7 & 96.5 & **13.8** \\ \hline \hline \end{tabular}
\end{table}
Table 5: Quantitative results of the models in stamp detection.  
To analyze the detection performance and error patterns, confusion matrices were generated for each model, as shown in Figure 9. These matrices display the correct detection rates (values along the main diagonal) and the types of errors (values off the diagonal). According to the confusion matrix, the YOLOv9s model demonstrated robust performance, achieving a high true positive rate for stamp detection (98%), surpassing the other models. The YOLOv8s model achieved a true positive rate of 95%, followed by YOLOv10s (93%) and YOLOv11s (92%). These values are inversely proportional to the number of false negatives, with the models showing the least occurrence of this error listed in order. Regarding false positives, the YOLOv9s model exhibited the lowest occurrence (2%), while the YOLOv8s and YOLOv11s models showed the highest (4%).