## 2 Materials and Methods
### Evaluation Metrics  
In the different annotated data sets used by object detection challenges and the scientific community, the metric most commonly used to measure the accuracy of detections is the mean average precision (\(mAP\)) [42]. To understand \(mAP\), you need to bear in mind the concepts of true positive, false positive, and false negative, which are defined as follows:  
* **True Positive (TP):** Correct detection of a true bounding box;
* **False Positive (FP):** An incorrect detection of a nonexistent object or a misplaced detection of an existing object;
* **False Negative (FN):** An undetected ground-truth bounding box;  
The previous definitions also require establishment of what are correct and incorrect detections. A common method for this is the use of the intersection over union (_IoU_). According to [43] the _IoU_ is a measure based on Jaccard's index which measures the area of overlap between the predicted bounding box \(B_{p}\) and the true bounding box \(B_{gt}\) divided by the area of union between them, as described mathematically in Equation (1) and illustrated in Figure 4.  
\[IoU=\frac{area(B_{p}\cap B_{gt})}{area(B_{p}\cup B_{gt})} \tag{1}\]  
The value of _IoU_ is then compared with a defined threshold \(t\) in order to establish when a detection is correct or incorrect. If \(IoU\geq t\), then the detection is considered correct. If \(IoU<t\), the detection is considered incorrect.  
In addition to \(mAP\), other evaluation metrics frequently used in detection problems are precision and recall [42], which are also adopted in the evaluation process. Each of these detection metrics will be explained below.  
\begin{table}
\begin{tabular}{c c} \hline
**Hyperparameter** & **Value** \\ \hline Epochs & 100 \\ Batch Size & 16 \\ Image Size & 640 \(\times\) 640 \\ Learning Rate & 0.01 \\ Momentum & 0.937 \\ \hline \end{tabular}
\end{table}
Table 3: Hyperparameters of the experiment.  
Figure 4: Illustration describing the calculation of the \(IoU\).  
* **Precision:** It measures the quality of the model through its ability to find true positives among all positive predictions [42]. Mathematically, accuracy is given by Equation (2), where \(TP\) is the number of true positives and \(FP\) is the number of false positives. \[Precision=\frac{TP}{TP+FP}=\frac{TP}{\textit{all detections}}\] (2)
* **Recall:** It is related to quantity and measures the model's ability to find true positives in relation to the total number of positives [42]. Mathematically, sensitivity is given by Equation (3), where \(TP\) is the number of true positives and \(FN\) is the number of false negatives. \[Recall=\frac{TP}{TP+FN}=\frac{TP}{\textit{all ground truths}}\] (3)
* **mAP:** It is an evaluation metric that has been widely used for evaluating the quality of object detectors [44]. This metric is the most popular among benchmark challenges, such as the COCO and ImageNet challenges. The \(mAP\) measure, used in multiclass problems, is defined from the Average Precision (\(AP\)) of each class. The \(AP\) is calculated by Equation (4) and is defined as the area under the precision (P) \(\times\) recall (R) curve, where \(M\) is the number of interpolated points. \[AP=\sum_{m=1}^{M}(R_{m}-R_{m-1})\cdot P(R_{m})\] (4)  
Therefore, the \(mAP\) metric calculates the \(AP\) of each category separately and then averages these APs across all categories. This approach ensures that the model's performance is assessed for each category individually, providing a more comprehensive assessment of the model's overall performance [43]. The \(mAP\) is expressed mathematically by Equation (5), where \(N\) is the number of classes in the problem.  
\[mAP=\frac{1}{N}\cdot\sum_{i=1}^{N}AP_{i} \tag{5}\]  
It is important to note that for this work, a threshold of 50% was selected when evaluating the architectures. In this case, the notation \(mAP50\) is used to indicate the threshold.