# A Novel Dataset for Multi-View Multi-Player Tracking in Soccer Scenarios
## 3 The System and The Datasets
### Calibration of the Cameras  
Since multi-view tracking relies on integrating information using unified world coordinates, it is crucial to have a reliable calibration method that provides stable and accurate data. We used surveillance-level zoomable cameras, but we were unable to locate the calibration parameters for our specific models in the equipment manual or on the official website. As a result, we utilized the pinhole camera model, as described in [79], to jointly calibrate the cameras for each field. For a specific field, given a set of existing landmark points \(\mathcal{W}=\{\mathbf{w}_{i}\}\), \(\mathbf{w}_{i}=[x_{i},y_{i},z_{i}=0]\in\mathbb{R}^{3}\), we manually annotated their corresponding pixel coordinates \(\mathcal{M}=\{M^{c}\}\), \(M^{c}=\{\mathbf{m}_{i}^{c}\}\), \(\mathbf{m}_{i}^{c}=[x_{i}^{c},y_{i}^{c}]\in\mathbb{R}^{2}\) on the image plane of each camera, more precisely, \(\mathcal{C}=\{c_{i}\}\) denotes the number of cameras in this field. Let \(\mathbf{P}=\{\mathbf{P}^{c}\}=\{\{\mathbf{I}^{c},\mathbf{E}^{c}\}\}\) denote the calibration parameters of each camera, where \(\mathbf{I}\) and \(\mathbf{E}\) denote the intrinsic and the extrinsic parameters, respectively. To this end, we  
Figure 2: Synchronization of multi-cameras. solved the projection relationship between \(\mathcal{W}\) and \(\mathcal{M}=\{M^{c}\}\) jointly through bundle adjustment [80] to achieve \(\mathbf{P}\), as we explain in Equation (2). \[\mathbf{m}_{i}^{c}=\mathbf{P}^{c}\cdot\mathbf{w}_{i} \tag{1}\]  
\[\mathbf{P}^{\star}=\operatorname*{arg\,min}_{\mathbf{P},\mathcal{W},\mathcal{ M}}\sum_{c=1}^{|\mathcal{C}|}\sum_{i=1}^{|W|}\alpha_{i}^{c}\|\mathbf{m}_{i}^{c}- \mathbf{P}^{c}\cdot\mathbf{w}_{i}\| \tag{2}\]  
\(\|\cdot\|\) denotes the Euclidean distance in the image plane, and \(\alpha_{i}^{c}\) is the indicator variable equal to 0 when the landmark point \(w_{i}\) is not available in view \(c\), and equal to 1 when the landmark point \(w_{i}\) is visible. In other words, we have formulated this problem as a non-linear least squares approach. In this approach, the error is represented as the squared \(L2\) norm of the difference between the projection points of the real world \(3D\) points \(\mathbf{w}\) on the image plane and their corresponding annotated pixel coordinates \(\mathbf{m}^{c}\). To improve the versatility and robustness of the calibration method, we exclusively utilized the original landmarks on the field to calibrate the camera. These landmarks comprised the penalty point, the kick-off point, the intersection of the marking line, the intersection of the boundary line between the deep and shallow turf and the marking line, etc. For the 11-a-side set, camera-1 used four pinhole cameras to stitch the image plane, and therefore we calibrated each part of the image plane separately. Similarly, we used a similar method to calibrate the 8-a-side camera-1, which was stitched from two pinhole cameras. Take the 11-a-side field as an example, Figure 3 illustrates the calibration precision of this method. (1) The field areas actually observed by each camera are sampled at an interval of 0.2 m to obtain \(D^{c}=\{\mathbf{d}_{i}^{c}\}\), \(\mathbf{d}_{i}^{c}=[x_{i}^{d},y_{i}^{d},z_{i}^{d}=0]\in\mathbb{R}^{3}\). Then the projection results of \(D^{c}\) on each image plane, \(J^{c}=\{\mathbf{j}_{i}^{c}\}\), \(\mathbf{j}_{i}^{c}=[x_{i}^{d},y_{i}^{d}]\in\mathbb{R}^{2}\) are calculated using Equation (1). We draw \(J^{c}\) on the image plane in the form of small red dots, as shown in Figure 3. (2) Based on landmark points \(W^{c}\) and manually annotated pixel coordinates \(M^{c}\), we re-projected \(M^{c}\) to the world plane to obtain \(K^{c}=\{\mathbf{k}_{i}^{c}\}\), \(\mathbf{k}_{i}^{c}=[x_{i}^{k},y_{i}^{k},y_{i}^{k}=0]\in\mathbb{R}^{3}\) using Equation (1). \(W^{c}\) and \(K^{c}\) were drawn on the world plane using big red dots and small blue dots, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Game Type** & **Game ID** & **Cameras** & **Players** & **Length/Fps** & \