## 4 Results
### Distance Estimation
To compare the performance between different distance estimation models, the trained deep learning model (80:20 split ratio, labeling method 2, and YOLOv4-tiny) was applied in the position-based (relying on the bottom of the object) and the size-based (relying on the height of the object) models, respectively. Table 8 summarizes the estimation results of the two models. The overall performance is shown in Table 9, in which the position-based model in short distances is better as the MAPE (within the effective distance) of the position-based model was 6.18%, but the size-based model was 6.59%. However, when taking the objects out of the effective distance into account, the size-based model gives a much better result. The MAPE of the size-based model was only 5.96% whereas the size-based model climbed to 14.03%. The size-based model shows the capability of estimating distance in dynamic range. Another advantage of the size-based model is that it is free from the assumption of the POI since it refers to the height of the detected objects. One of the limitations of the size-based model is that the detected object has to be completely detected. The misunderstanding of the sizes of occluded and partially out-of-view objects by the deep learning model will lead to a relatively large error. Therefore, a labeling method that ignores the incomplete target object is more suitable for the size-based distance estimation model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multirow{2}{*}{**Obj**} & \multirow{2}{*}{**Ground Truth (m)**} & \multirow{2}{*}{**Class**} & \multicolumn{2}{c}{**Position-Based**} & \multicolumn{2}{c}{**Size-Based**} \\ \cline{5-8}  & & & & **Estimated Distance (m)** & & **Error** & **Estimated Distance (m)** & **Error** \\ \hline \multirow{8}{*}{8} & 1 & 3.73 & 1 & 3.50 & \(-\)6.17\% & 3.07 & \(-\)17.69\% \\  & 2 & 3.82 & 0 & 3.71 & \(-\)2.88\% & 3.26 & \(-\)14.66\% \\  & 3 & 4.71 & 2 & 5.06 & 7.43\% & 4.8 & 1.91\% \\  & 4 & 5.34 & 2 & 5.81 & 8.80\% & 5.07 & -5.06\% \\  & 5 & 13.33 & N & - & - & - & - \\  & 6 & 12.85 & N & - & - & - & - \\  & 7 & 12.67 & N & - & - & - & - \\  & 8 & 12.72 & N & - & - & - & - \\  & 9 & 13.86 & 0 & 17.18 & 23.95\% & 14.04 & 1.30\% \\  & 10 & 14.53 & N & - & - & - & - \\ \hline \multirow{8}{*}{9} & 1 & 3.68 & 2 & 3.29 & \(-\)10.60\% & 3.76 & 2.17\% \\  & 2 & 3.75 & 2 & 3.32 & \(-\)11.47\% & 3.88 & 3.47\% \\ \cline{1-1}  & 3 & 11.11 & N & - & - & - & - \\ \cline{1-1}  & 4 & 11.13 & N & - & - & - & - \\ \cline{1-1}  & 5 & 11.33 & 0 & 10.61 & \(-\)6.35\% & 11.06 & \(-\)2.38\% \\ \cline{1-1}  & 6 & 11.28 & 0 & 11.31 & 0.27\% & 11.06 & \(-\)1.95\% \\ \cline{1-1}  & 7 & 12.10 & 0 & 11.72 & \(-\)3.14\% & 11.41 & \(-\)5.70\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{2}{c}{**MAPE (within**} & \multirow{2}{*}{**Metrics**} & \multirow{2}{*}{**Precision**} & \multirow{2}{*}{**Recall (within**} & \multirow{2}{*}{**Recall**} \\  & **Effective** & & & & **Effective** \\  & **Distance**) & & & **Distance**) & \\ \hline YOLOv4-tiny & 6.18\% & 14.03\% & 100\% & 94.12\% & 72.72\% \\ YOLOv+4 & 6.24\% & 16.08\% & 100\% & 97.06\% & 96.36\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance on object detection models. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{2}{c}{**MAPE (within Effective**} & \multirow{2}{*}{**MAPE**} \\  & **Distance**) & & & \\ \hline Position-based & 6.18\% & 14.03\% \\ Size-based & 6.59\% & 5.96\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance on distance estimation models.