## 4 Experimental Results and Discussion
### Relevant Evaluation Metrics  
In order to completely and objectively evaluate the performance of the proposed model, we used some of the most commonly used metrics in YOLOv5, as indicated below [58; 59; 60; 61]:  
* **Average Precision (AP)--**Measures the detection accuracy at different confidence levels, calculating the area under the Precision-Recall curve. AP is computed as follows: \[\text{AP}=\frac{1}{n}\Sigma_{\text{r}}\text{P}(\text{r})\Delta\text{r}\] (1) where n is the number of threshold points, P(r) is the Precision at recall point r, and \(\Delta\text{r}\) is the recall difference between consecutive points.
* **Mean Average Precision (mAP)--**The average of AP across different object classes, giving an overall performance metric. It is computed as follows: \[\text{mAP}=\frac{1}{C}\sum_{\text{t=1}}^{\text{c}}\text{AP}_{\text{t}}\] (2) where C represents the number of categories. Variants include mAP@.5 (IoU = 0.50) and mAP5:95 (average over IoU thresholds from 0.5 to 0.95).
* **IoU (Intersection over Union)--**measures the overlap between the predicted and ground truth bounding boxes: \[\text{IoU}=\frac{\text{Intersection Area}}{\text{Union Area}}\] (3)
* **Accuracy--**The proportion of correct detections relative to total detections, calculated as:  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Specification** \\ \hline Image size & 1280 \(\times\) 1280 pixels \\ Optimizer & Stochastic gradient descent (SGD) \\ Learning rate & 0.01 \\ Batch size & 16 \\ Epochs & 100 \\ Training time & 2 h 21 m 39 s \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters settings of the training configuration.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Hardware and Operating** & **Specification** \\
**System (OS) and Specific Environment** & UBUNTU 22.04.2 LTS \\ CPU & TWO CPUS INTEL(R) XEON(R) CPU @ \\  & 2.00 GHZ \\ GPU & NVIDIA TESLA T4 WITH \\ RAM MEMORY & 16 GB \\ FRAMEWORK & PYTORCH 1.13.1 \\ CUDA & 12.0 \\ CUDNN & 8700 \\ PYTHON VERSION & 3.7.9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The development environment and software tools environment.  
\[\text{Accuracy}=\frac{\text{Number of Correct Detections}}{(\text{Total Number of Detections})}\] (4) or \[\text{Accuracy}=(\text{TP}+\text{TN})/(\text{TP}+\text{TN}+\text{FP}+\text{FN})\] (5) where \[\odot\] True Positive (TP): the number of samples correctly classified as positive. \[\odot\] False Positive (FP): the number of samples incorrectly classified as positive. \[\odot\] False Negative (FN): the number of samples incorrectly classified as negative. \[\odot\] True Negative (TN): the number of samples correctly classified as negative.
* **Precision**--measures the proportion of correct positive detections: \[\text{Precision}=\frac{\text{TP}}{(\text{TP}+\text{FP})}\] (6)
* **Recall**--measures the proportion of correct detections among true objects: \[\text{Recall}=\frac{\text{TP}}{(\text{TP}+\text{FN})}\] (7)
* **F1-Score**--harmonic mean of Precision and Recall: \[\text{F1}-\text{Score}=\frac{2\times\text{Precision}\times\text{Recall}}{ \text{Precision}+\text{Recall}}\] (8)
* **Confusion Matrix**--a table showing correct and incorrect detections for each class.
* **Performance metrics curves during training and validation model--graphs visualizing metrics during training and validation to assess model effectiveness and detect overfitting [63; 64].