# Dist-YOLO: Fast Object Detection with Distance Estimation
## 3 Benchmark and Results
### Ablation Study  
Firstly, we investigated the dependency of the distance error on the object's real distance. Because class-aware Dist-YOLO showed a poor result in the previous experiment, we considered only class-agnostic Dist-YOLO. The absolute and relative distance errors are visualized in Figures 3 and 4, respectively. Concerning Figure 3, we can claim that the absolute error grows according to a polynomial curve until distances higher than 80, where the trend is broken. The reason is that few objects lie in this interval and, therefore, the measured value was not computed from a statistically significant number of samples. Similar behavior is also reflected in Figure 4. Here, we can see that the relative error was almost constant for all distances except one meter. That is caused by the fact that even a 30 cm distance error on such a distance yields an error of 0.3, which makes the task extremely difficult and is probably also affected by the inaccuracy of the distance capturing process itself.  
The next investigated aspect was the correlation between variables. Firstly, we measured the correlation between the quality of bounding box detection and the distance error. It was \(-0.27\) for IoU and \(\varepsilon_{A}\) and 0.05 for IoU and \(\varepsilon_{R}\). Secondly, we measured that the correlation between the height of an object and \(\varepsilon_{A}\) was \(-0.55\), i.e., the lower the box is, the larger the absolute error produced, which is consistent with the values in Figure 3. For height and \(\varepsilon_{R}\), it was 0.11, which is again consistent with the values in Figure 4; the positive correlation is caused by the large error for close boxes. Note, all of these correlations are computed for class 'car', and IoU \(>0.5\) between the predictions and labels.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Class**} & \multicolumn{8}{c}{**Dist-YOLOv3 G**} & \multicolumn{8}{c}{**Dist-YOLOv3 W**} \\ \cline{2-13}  & \# & **Min** & **Mean** & **Max** & \(\varepsilon_{A}\) & \(\varepsilon_{R}\) & \# & **Min** & **Mean** & **Max** & \(\varepsilon_{A}\) & \(\varepsilon_{R}\) \\ \hline Pedestrian & 1150 & \(-16.81\) & \(-0.54\) & 7.73 & 1.75 & 0.11 & 1117 & \(-8.93\) & 3.83 & 39.48 & 4.87 & 0.41 \\ Car & 7682 & \(-24.87\) & \(-0.81\) & 14.47 & 2.49 & 0.11 & 7798 & \(-13.24\) & 8.75 & 42.10 & 10.68 & 0.44 \\ Van & 749 & \(-20.49\) & 0.46 & 18.00 & 3.55 & 0.15 & 751 & \(-26.88\) & 13.94 & 42.25 & 14.17 & 0.64 \\ Truck & 318 & \(-34.36\) & 1.16 & 15.93 & 4.63 & 0.14 & 319 & \(-27.33\) & 4.51 & 26.30 & 6.49 & 0.21 \\ Person sitting & 57 & \(-7.09\) & \(-0.59\) & 4.74 & 1.84 & 0.22 & 56 & \(-2.27\) & 4.35 & 16.15 & 4.64 & 0.64 \\ Cyclist & 406 & \(-17.79\) & \(-1.25\) & 14.66 & 2.37 & 0.11 & 409 & \(-4.16\) & 14.32 & 46.80 & 14.38 & 0.85 \\ Tram & 135 & \(-26.66\) & 1.85 & 19.57 & 4.72 & 0.19 & 132 & \(-22.37\) & \(-2.65\) & 11.36 & 4.41 & 0.17 \\ \hline All & 10,497 & \(-34.36\) & \(-0.61\) & 19.57 & 2.57 & 0.11 & 10,582 & \(-27.33\) & 8.52 & 46.80 & 10.22 & 0.46 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Measurement of distance error in meters for Dist-YOLOv3 G/W. The values in columns Min, Mean, and Max, \(\varepsilon_{A}\) are expressed in meters. The value of column \(\varepsilon_{R}\) is relative, where \(\varepsilon_{R}=1\) equals to 100%.  
The last aspect we evaluated was the computation speed. We measured the time on an RTX2060 SUPER graphics card, where the time represents the duration of executing the _predict_() method with a batch size equal to one and without further optimization such as conversion into TensorRT. The prediction time was equal for all three models, 22 ms per image, i.e., it ran approx 45 frames per second. The equal processing time confirmed that the increase in parameters in the output prediction vectors was negligible compared to the complexity of the rest of the model.