# Addressing the Gaps of IoU Loss in 3D Object Detection with IIoU
## 7 Evaluation
\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 \(L_{IoU}\) & 92.01 82.84 78.01 & 66.43 59.55 54.62 & 89.13 66.91 62.31 & 72.42 \\ \hline \(L_{DIoU}\) & 91.99 **82.81** 78.01 & **66.51** **60.24** **55.15** & 89.10 67.92 63.75 & 72.83 \\ \hline \(L_{IIoU}\) & **92.18** 82.84 **79.80** & 64.02 58.57 53.67 & **89.77** **69.43** **66.06** & **72.93** \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental evaluation of Camera-Fusion 3D detector network trained using \(L_{IoU}\), \(L_{DIoU}\), and \(L_{IIoU}\) losses. AP_40 results are reported on the KITTI val dataset. Tables 4 and 5 demonstrate the performance of the proposed loss function against IoU loss. NDS is a consolidated metric that captures metrics such as IoU, box location, size, and orientation. As we can observe, the NDS score of the proposed method has improved in both single-stage and two-stage LIDAR networks. Area Orientation Error (AOE) measures the difference in yaw angles between the ground truth and predictions, and ATE measures the Euclidean distance between the centers in 2D. A low AOE and ATE error from the proposed method indicates the network could regress the boxes more accurately. The classification accuracy is measured by AAE, which has improved in the two-stage LIDAR network. For the next phase of evaluation and to compare our proposed method with other state-of-the-art detectors, the fusion network was trained with the proposed loss function \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Loss** & **NDS** & **ATE** & **ASE** & **AOE** & **AAE** \\ \hline \(L_{IoU}\) & 0.0244 & 0.447 & 0.320 & 0.964 & 0.166 \\ \hline \(L_{IIIoU}\) & **0.0295** & **0.324** & 0.344 & **0.687** & 0.186 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental evaluation of single-stage LiDAR 3D detector network trained using \(L_{IoU}\) and \(L_{IIIoU}\) losses. Results are reported on the nuScenes val dataset. Figure 3: Loss convergence of single-stage 3D LiDAR network during training phases. (**a**) Localization loss; (**b**) Overall training loss (CLS + LOC). \begin{table}
\begin{tabular}{c c c c c} \hline \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 \(L_{IoU}\) & 69.96 62.55 62.43 & 49.96 45.78 43.56 & 69.51 56.55 52.16 & 56.94 \\ \hline \(L_{DIoU}\) & 73.65 64.63 64.16 & 55.35 52.76 48.24 & 73.43 60.44 55.20 & 60.87 \\ \hline \(L_{RIoU}\) & **87.6 77.71 76.8** & 58.45 52.71 47.3 & 81.22 **67.57** 62.34 & 67.96 \\ \hline \(L_{IIoU}\) & 87.39 77.01 75.78 & **59.99 54.22 48.63** & **83.56** 64.69 **63.52** & **76.27** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental evaluation of single stage LiDAR 3D detector network trained using \(L_{IoU}\), \(L_{DiolU}\), \(L_{RIoU}\) and \(L_{IIoU}\) losses. Results are reported on the KITTI val dataset. using the KITTI train+val dataset. The total number of training samples was 7480. No additional data split and data augmentation were carried out. The train settings were kept constant throughout the execution across Tables 1-3 and 6. Table 6 provides the evaluation results for the 3D pedestrian class across easy, moderate, and hard categories in the test set. Our proposed loss method achieves optimal performance in easy and hard categories, surpassing many state-of-the-art detectors such as PointGNN [45], Frustum-PointPillars [40] and Part-\(A^{2}\)[52]. **Discussion and Limitations:** Machine learning, especially deep learning, has shown significant promise in feature extraction and pattern recognition, which could complement our geometric approach. For instance, integrating deep learning-based feature extraction with our IIoU loss could enhance the model's ability to discern subtle variations in object orientation and position, leading to more accurate predictions.