## 4 Evaluation
### Bounding Box Similarity Check  
The KITTI dataset provides occlusion values for each object. In this study, the time and the occlusion value required to estimate the distance of each object were evaluated to measure the efficiency of the methods. YOLOv8 was used as the object detection method, and it provided the bounding box and the segmentation mask for detected objects, including persons, bicycles, cars, buses, and trucks. To ensure an accurate evaluation, the bounding box information of objects with occlusion values from the KITTI dataset must match the bounding box information provided by YOLOv8. Figure 17 illustrates the bounding boxes drawn in the image using coordinate information from both KITTI and YOLOv8.  
As shown in Figure 17, YOLOv8 detects more objects, whereas the KITTI dataset provides fewer object annotations and includes information about a foreign object outside the defined categories of person, bicycle, car, bus, and truck. Furthermore, while YOLOv8's bounding box coordinates closely match the exact size of the object, the KITTI dataset's annotation bounding boxes tend to be larger than the actual object size. To address this discrepancy and ensure a high-accuracy evaluation, similarity checks were performed between the bounding box annotations from the KITTI object detection benchmark dataset and the bounding boxes provided by YOLOv8 for each object in the image.  
\[\text{KITTI}=(x_{1}^{1},y_{1}^{1},x_{2}^{1},y_{2}^{1}),\quad and\quad\text{ YOLOv8}=(x_{1}^{2},y_{1}^{2},x_{2}^{2},y_{2}^{2}) \tag{17}\]  
The similarity between the KITTI and YOLOv8 bounding boxes was compared by computing the absolute differences between their corresponding bounding box coordinates. The differences in the top-left coordinates were calculated as \(\Delta x_{1}=|x_{1}^{1}-x_{1}^{2}|\) for the x-coordinates and \(\Delta y_{1}=|y_{1}^{1}-y_{1}^{2}|\) for the y-coordinates. Similarly, the differences in the bottom-right coordinates were calculated as \(\Delta x_{2}=|x_{2}^{1}-x_{2}^{2}|\) for the x-coordinates and \(\Delta y_{2}=|y_{2}^{1}-y_{2}^{2}|\) for the y-coordinates. These differences helped to quantify the spatial  
Figure 17: Bounding boxes overlaid on the image, showing the detection results from both KITTI and YOLOv8 datasets. The position of irrelevant objects is shown with red arrows.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Image Feature** & **Easy** & **Moderate** & **Hard** \\ \hline Max. occlusion level: & Fully visible & Partly occluded & Difficult to see \\ Min. bounding box height: & 40 Px & 25 Px & 25 Px \\ Max. truncation: & 15 & 30 & 50 \\ Number of Object: & 14550 & 6428 & 3511 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The KITTI object detection benchmark.  
deviation between two bounding boxes, allowing a threshold-based similarity condition to be defined.  
\[\text{is\_similar}(\text{KITTI},\text{YOLOv8})=\begin{cases}\text{True},&\text{ if }\Delta x_{1}\leq T\text{ and }\Delta y_{1}\leq T\\ &\text{ and }\Delta x_{2}\leq T\text{ and }\Delta y_{2}\leq T\\ \text{False},&\text{otherwise}\end{cases} \tag{18}\]  
To determine whether two bounding boxes were similar, a predefined threshold (\(T\)) was applied to the coordinate differences. The similarity condition required that the absolute differences between the corresponding coordinates of the two bounding boxes remain within this threshold. When all these conditions were satisfied, the bounding boxes were considered similar. Mathematically, this was expressed in Equation (18).  
Figure 18 shows the refined bounding box data after the elimination of irrelevant objects. All KITTI and YOLO bounding boxes have been successfully matched, ensuring consistency between the data. In this way, the final bounding box and segmentation mask information is optimized for input into our methods.