# Addressing the Gaps of IoU Loss in 3D Object Detection with IIoU
## 7 Evaluation  
The performance of the proposed IIoU was evaluated on both the LiDAR-based detection network and the fusion detector network. Due to testing constraints in the KITTI benchmark test set [14], performance evaluation was carried out on the KITTI val dataset. Three classes of the KITTI dataset, such as 3D car, pedestrian, and cyclist, were evaluated with different IoU thresholds, 0.7, 0.5, and 0.5. The testing thresholds were adapted from previous studies [38; 40; 43]. The results are displayed in average precision (AP) and meanaverage precision (mAP), a cumulative average of different APs. This section calculates the relative improvement (R.L.) to IoU loss. The highest prediction result in each category is highlighted in bold. Table 1 displays the improved performance of IIoU against IoU and DIoU losses in a 3D fusion network. The initial analysis phase revealed a performance gap between networks trained from scratch and pre-trained model weights [17; 46; 70]. To conduct a fair evaluation, we trained all the networks from scratch. All the training parameters, including the hyper-parameters, training, and testing environments, were kept constant during the network training and evaluation phase. Table 1 shows that the proposed IIoU performs well for all easy, moderate, and hard categories of the 3D cyclist class. We can observe an R.L. of 3.4% in the hard class. Table 2 measures the A.P. at 40 sampling recall positions. IIoU performs significantly better than IoU and DIoU in the 3D car and cyclist classes. The hard category of the 3D car class shows an R.L. of 2.29%. 3D cyclist shows a R.L. of 0.71%, 3.76%, 6.01% demonstrating a significant performance change for smaller objects. In both Tables 1 and 2, the 3D cyclist class attains the best performance for the proposed loss function. Figure 3 displays the loss convergence of IoU, DIoU, RIoU, and proposed IIoU loss. Figure 3a represents the localization loss estimation at each iteration step. IoU and DIoU almost converge at the same rate. However, the proposed IIoU loss converges much faster and minimizes the loss values. Figure 3b showcases overall training loss. This sums up both classification and localization loss. Better convergence is observed at the proposed IIoU loss compared to IoU, DIoU, and RIoU losses. Table 3 displays the improved performance of IIoU against IoU, DIoU, and RIoU losses in the 3D LiDAR detection network. The table shows that the DIoU loss performs well across all categories compared to the IoU loss. This is because DIoU loss considers center distance estimation and aids in better localization. However, RIoU loss shows consistent improvement compared to DIoU loss. Our proposed IIoU loss attains higher results in the 3D pedestrian class with an R.L. of 20%, 18.43%, and 11.63%. IIoU loss has the highest mAP of 76.27 when compared to its counterparts. \begin{table}
\begin{tabular}{l l l l l} \hline
**Loss** & **3D Car (IoU = 0.7)** & **3D Pedestrian (IoU = 0.5)** & **3D Cyclist (IoU = 0.5)** & **mAP** \\ \hline  & Easy Mod Hard & Easy Mod Hard & Easy Mod Hard & \\ \hline \(L_{IoU}\) & 89.20 **79.08** 77.6 & 65.75 59.87 56.32 & 86.22 66.32 63.17 & 71.50 \\ \hline \(L_{DIoU}\) & 89.20 78.97 77.71 & **66.56** **60.86** **57.00** & 86.27 66.55 64.16 & 71.92 \\ \hline \(L_{IIoU}\) & **89.20** 79.02 **77.93** & 64.54 59.11 55.60 & **86.64** **67.66** **65.36** & 71.67 \\ \hline \end{tabular}
\end{table} 
Table 1: Experimental evaluation of Camera-Fusion 3D detector network trained using \(L_{IoU}\), \(L_{DIoU}\), and \(L_{IIoU}\) losses. Results are reported on the KITTI val dataset.