# Multi-Player Tracking for Multi-View Sports Videos with Improved K-Shortest Path Algorithm
## 3 Methodology
### Feature Extraction and Fusion  
In our tracking framework, we firstly detect the players in different views frame by frame, which can be done by Faster RCNN [47]. Then we send the 2D detections into POM algorithm [44], and it outputs the player occupied probability for each discrete grid of the court, as shown in Figure 2. Afterwards, the locations where the probability of being occupied by a player surpasses 80% are selected out and mapped into different views as rectangle boxes, as shown in Figure 5.  
For one location (i.e., one player), it might correspond to several bounding boxes cropped from different cameras. Thus, the appearance feature can be jointly determined based on these cropped images, which can avoid some interferences caused by occlusions to some extent. The appearance feature used in this paper is the jersey color and jersey number. For the jersey color, assume the output of color feature for one cropped image can be represented as \((L_{c},p)\) where \(L_{c}\in\)[1 (yellow), 2 (blue), 3 (yellow and blue), and 4 (none)], and \(p\) means its probability. Then, we need to fuse multiple color feature candidates into one, which can be considered as a vote issue that needs to determine which team the player should belong to. This problem can be easily solved by the classic Boyer-Moore voting algorithm [47]. Similarly, the jersey number as well as its probability can be obtained in the same way. However, it is worth mentioning that before the jersey number extraction for each cropped image, we need to ensure the player's color label is the same as the winning color label after voting. If not, the jersey number might be wrong due to occlusion (see the player 3 in Camera 2 and 4 in Figure 5).  
As to how to extract the jersey color and jersey number for each cropped image, many existing methods can be available. In this paper, we adopted a pre-trained person re-identification (re-ID) network [48] to obtain a descriptor for the bounding box (a 128-dimensional vector) and then classified the players as four classes using SVM algorithm [49]: 1 (yellow player), 2 (blue player), 3 (yellow and blue player), and 4 (none). For the jersey number, we first train a detection model to locate the jersey number and then classify the jersey number images with a six-layer convolutional neural  
Figure 5: The illustration of feature extraction and fusion: players 1, 2 and 3 are taken as three examples that correspond three locations in the probability occupancy map, respectively. For each player, it can be mapped into several views to crop its image patches. The jersey color and jersey number can be jointly determined by all the cropped images, which can be done by Boyer–Moore voting algorithm. The output of color feature can be represented as \((L_{c},p)\) where \(L_{c}\in\)[1 (yellow), 2 (blue), 3 (yellow and blue), 4 (none)] and \(p\) means its probability. The output of number feature can be denoted as \((L_{n},q)\) where \(L_{n}\) and \(q\) is the jersey number and its probability, respectively.  
network which is borrowed from an jersey number recognition approach crafted for soccer players [50]. Other relative works related to jersey number recognition can be seen in [51; 52]. An accurate feature extraction is very important for our tracking framework, and how to further improve its accuracy is our future work while this paper mainly focus on how to improve the problem of identity switches by taking full advantage of the appearance features. Thus, before the implement of our tracking method, two prerequisite knowledge should be given: (1) player occupied probability for each location in the court (provided by POM algorithm [44]); (2) the label of jersey color and jersey number and its corresponding probabilities (provided by re-ID [48] + SVM [49] and jersey number recognition based on CNN [50]).