## 3 Multi-View Modeling
### Model Implementation  
Because the multi-view object detection model mainly consists of the multi-view module and the merging module, the model is implemented using these two modules. The multi-view module cuts the original image into five regions, each of which is \(1/4\) of the original image in size. Then, an interpolation algorithm is applied to magnify each region by a factor of four in equal proportions to ensure that the detected objects do not become deformed when they are passed to the detection model. Simultaneously, the interpolation algorithm is applied to provide more detail to the detection module rather than performing direct detection on the original image. The integration process of the merging module consists of two stages. In the first stage, the bounding boxes satisfying the distance threshold of horizontal (or vertical) axis are picked out in adjacent views, and the bounding boxes that belong to the same object of them must be determined by combining the overlapping areas of adjacent boundaries. In the paper, the distance threshold of horizontal (or vertical) axis is 10 pixels and the overlapping threshold of adjacent boundaries is 0.3. For the bounding boxes of the same object, a splicing operation must be performed. The formula for evaluating the line overlap \(L_{\text{overlap}}\) between two adjacent bounding boxes is as follows:  
\[L_{\text{overlap}}=(L_{1}\cap L_{2})/(L_{1}\cup L_{2}) \tag{6}\]  
where \(L_{1}\) denotes the bounding line of the candidate box in one view near the horizontal (or vertical) axis and \(L_{2}\) denotes the bounding line of the candidate box in the adjacent view near the horizontal (or vertical) axis. The details are shown in Figure 4.  
As shown in Figure 4, view V\({}_{1}\) contains a car that is jointly detected with view V\({}_{2}\) and a person that is jointly detected with view V\({}_{3}\), whereas another person is jointly detected in views V\({}_{2}\) and V\({}_{4}\). \(L_{1}\), \(L_{2}\), \(L_{1}\cap L_{2}\), and \(L_{1}\cup L_{2}\) are all marked in the figure. For each pair of adjacent views, the \(L_{\text{overlap}}\) results are calculated for the corresponding pairs of bounding boxes, and if the calculated \(L_{\text{overlap}}\) value between two bounding boxes satisfies the line overlap threshold, then those bounding boxes are regarded as representing the same object. Next, the region splicing operation is applied to the chosen bounding boxes to obtain the complete bounding box for each object. Specifically, the region splicing process is first performed in one direction (such as along the horizontal axis); the splicing results are appended to the set of detected object bounding boxes, and the original object bounding boxes on which the splicing operation was performed are removed. Then, region splicing is conducted in the other direction. In the second stage, the region merging algorithm selects object boxes from both the region splicing results of the first stage and the detection results from the center region. The first step of  
Figure 4: Evaluation of adjacent boundary lines in multiple views. the region merging algorithm is to initialize the region-merged object box set \(B_{\text{RM}}\), the object index set \(P\) of \(B_{\text{RM}}\), the overlap threshold \(O_{\text{threshold}}\), and the maximum overlap \(O_{\text{max}}\). The next step is to obtain the index set \(I\) based on the order of the candidate bounding boxes, which are sorted by their \(y_{2}\) coordinates. Then, while \(I\) is not empty, a series of operations are performed as follows. The first operation is to set the suppressed bounding box set \(S\), which includes the last index of \(I\); obtain the index \(i(i\)=\(I[last])\) of \(B\); and append the index \(i\) to \(P\). Then, the operation is repeated to obtain the bounding box \(B[j]\) (where the index \(j\) is in \(I\)) and calculate the overlap between the bounding box \(B[i]\) and the bounding box \(B[j]\).