# Point-Graph Neural Network Based Novel Visual Positioning System for Indoor Navigation
## 2 Related Research
### D Intersection over Union (IoU)  
IoU is widely adopted as an evaluation indicator in several visual tasks, such as object detection, segmentation, and visual tracking. Additionally, it is generally computed independently of the neural network training loop without participating in the backpropagation process. To regress the parameters of the rotated bounding box, the conventional 3D object detection approach regresses the translation, scale, and yaw angle separately,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **One-Stage** \\ **Method** \\ \end{tabular} } & \multirow{2}{*}{**Reference**} & \multirow{2}{*}{**Modality**} & \multicolumn{5}{c}{**3D Object Detection AP**} & \multirow{2}{*}{**Time (ms)**} \\ \cline{3-4} \cline{6-9}  & & & **Easy** & & **Moderate** & **Hard** & **mAP** \\ \hline VoxelNet [15] & CVPR 2018 & LiDAR & 77.82 & 64.17 & 57.51 & 66.5 & 220 \\ ContFuse [16] & ECCV 2018 & LiDAR+RGB & 83.68 & 68.78 & 61.67 & 71.38 & 60 \\ SECOND [17] & Sensors 2018 & LiDAR & 83.34 & 72.55 & 65.82 & 73.9 & 50 \\ PointPillars [18] & CVPR 2019 & LiDAR & 82.58 & 74.31 & 68.99 & 75.29 & 23.6 \\ TANet [19] & AAAI 2020 & LiDAR & 84.39 & 75.94 & 68.82 & 76.38 & 34.75 \\ Associate-3 Ddet [20] & CVPR 2020 & LiDAR & 85.99 & 77.40 & 70.53 & 77.97 & 60 \\ HotSpotNet [21] & ECCV 2020 & LiDAR & 87.60 & 78.31 & 73.34 & 79.75 & 40 \\
3 DSSD [22] & CVPR 2020 & LiDAR & 88.36 & 79.57 & 74.55 & 80.83 & 38 \\ SA-SSD [23] & CVPR 2020 & LiDAR & 88.75 & 79.79 & 74.16 & 80.90 & 40.1 \\ CIA-SSD [24] & AAAI 2021 & LiDAR & 89.59 & 80.28 & 72.87 & 80.91 & 30.76 \\ SE-SSD [25] & CVPR 2021 & LiDAR & 91.49 & 82.54 & 77.15 & 83.73 & 30.56 \\ Point-GNN [4] & CVPR 2020 & LiDAR & 88.33 & 79.47 & 72.29 & 80.03 & 643 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance comparison of the KITTI test set by submitting to the official test server.  
using Smooth-L1 Loss [26] based on the L1-norm of the parameter distance. As IoU does not change with the scale of the problem, a study [27] attempted to learn the IoU directly, such as predicting the IoU as a metric of non-maximum suppression (NMS) rather than calculating the IoU between the detected bounding box and ground truth bounding box. Another study [28] proposed a fitting quality network (RQNet) to directly predict 3D IoU between the sample and object in monocular 3D object data. Additionally, an algorithm for estimating the exact 3D IoU value of the bounding box was proposed [29]. The accurate 3D IoU values of 3D boxes in 3D object detection can be computed using a three-part algorithm. First, the Sutherland-Hodgman polygon clipping algorithm calculates the intersection point between the faces of two boxes. Second, the volume of intersection uses the convex hull algorithm of all truncated polygons. Third, IoU is computed based on the intersection and union volumes of the two boxes. Figure 1a illustrates the computation of the intersection points of each side by clipping the polygon to the box, and Figure 1b depicts the computation of the intersection volume using the convex hull algorithm of all intersections (green).