# YOLO-Type Neural Networks in the Process of Adapting Mathematical Graphs to the Needs of the Blind
## 2 Development of YOLO Neural Networks
This helps to ensure that the evaluation of each model's performance is more rounded and provides a more complete picture than if all errors were grouped into one category. The last factor determines the probability with which an element in the image can be said to have been recognized correctly. This aspect is represented by a metric called IoU (Intersection over Union) and is important from the point of view of the result when assessing the quality of the prediction. The output of the YOLO network is an image with classified objects marked by rectangular areas called bounding boxes, which represent the relative position of the detected object in the analyzed space. The numerical value of IoU represents the intersection of two objects--the predicted and the actual object location bounding boxes. The higher the metric value is, the greater the confidence in the correctness of the classification. A simplified computational schematic of the calculation of the IoU value is shown in Figure 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**YOLO Version** & **Scaled Models** & **AP** & **AP\({}_{\text{50}}\)** \\ \hline  & n & 38.5\% & - \\  & s & 46.3\% & - \\  & m & 51.1\% & - \\ YOLOv10 & b & 52.5\% & - \\  & l & 53.2\% & - \\  & x & 54.4\% & - \\ \hline  & n & 39.5\% & - \\  & s & 47.0\% & - \\ YOLOv11 & m & 51.5\% & - \\  & l & 53.4\% & - \\  & x & 54.7\% & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 1: The schematics of computing the IoU value for YOLO networks. To better illustrate how all three factors contribute to the final value of the AP metric, an example can be made on the model Microsoft COCO dataset [45]. The main characteristics of this data are that it consists of 80 object classes and has a 101-point interpolation, which allows the precision of 101 recall thresholds from 0 to 1 in 0.01 intervals. These factors allow the AP to be calculated over multiple IoU values, resulting in more accurate results than a common AP\({}_{50}\) metric, which is limited to a threshold of 0.5. The example steps for the final calculations can be described as below:  
1. Compute the recall-precision curve for each class with a varying threshold;
2. Calculate the AP value for each category with 101-point thresholds;
3. Compute the AP with different IoU thresholds--in most cases, from 0.5 up to 0.95 with 0.05 intervals;
4. Calculate the mean AP for every IoU threshold from step 3;
5. Compute the final average value by taking into account all the above metrics. Another important aspect related to YOLO neural networks is Non-Maximum Suppression (NMS). This is a process that takes place after the detection of objects and allows one to discard less-precise bounding boxes in the case where there are multiple instances of them on a single element. The algorithm is based on the IoU parameter and selects a bounding box with the highest confidence score for a detected class, removing the excess ones so that the result is one per element. An example of the Non-Maximum Suppression is shown in Figure 2.  
In this publication, several of the networks described above were selected to compare the effectiveness of their application in the context of analyzing mathematical graphs. The selected versions were YOLOv5, YOLOv6, YOLOv7, YOLOv8, YOLOv9, YOLOv10, and YOLOv11.