Reconstructing the 3D Trajectory of a Ball with Unsynchronized Cameras

The 3D trajectory of the ball is one of the most important performance indicators in ball games. However, it often cannot be measured because of the requirements: synchronized cameras and control points within the playing field. Thus, this paper proposes a method that reconstructs the 3D trajectory of a ball with unsynchronized cameras. The proposed method consists of ball detection, camera calibration, and trajectory reconstruction. At first, ball candidates are detected on the basis of their appearance. Balls are then extracted from the candidates on the basis of their motion. After the extraction, ball trajectories are reconstructed in image spaces. The corresponding points in two views are estimated on the basis of the ball trajectory in image spaces and the temporal offset between cameras, which is supposed to be recorded with a few erroneous frames. The matrix including the geometrical relationship between cameras, namely the fundamental matrix, is then computed from the corresponding points. The estimated one is inaccurate due to the error of the temporal offset. The key feature of this method is to optimize the temporal offset and fundamental matrix simultaneously. After the optimization, the geometrical relationship between cameras is computed from the matrix. Balls are extracted again by using the temporal offsets and the geometrical relationship between cameras. A ball trajectory is finally reconstructed as connected trajectories that are separated at collisions. It is experimentally demonstrated that the proposed method accurately calibrates cameras and successfully reconstructs the 3D trajectory of the ball.