A method for reconstructing 3D trajectory of ball with unsynchronized cameras

Sho Tamaki, Hideo Saito

Research output: Contribution to journalArticlepeer-review


Ball trajectory is an important performance indicator in ball game. However, Measuring 3D trajectories is often unusable because synchronized cameras and control points inside the playing field are generally required. A method that reconstructs 3D trajectory of ball with unsynchronized cameras is proposed in this paper. Proposed method consists of ball detection, camera calibration, and trajectory reconstruction. At first, ball candidates are detected based on the appearance. For the camera calibration, highly probable balls are extracted from the candidates based on the motion. Imaged ball trajectories are then reconstructed. Next, fundamental matrix is computed from the corresponding points, which are estimated with the ball trajectories, and roughly estimated temporal offset, which is estimated manually. The estimated fundamental matrix is assumed to be inaccurate due to the inaccuracy of the temporal offset. The key feature of this method is to accurately estimate temporal offset and fundamental matrix by optimizing them iteratively based on the error of fundamental matrix. After the calibration, balls are extracted robustly with geometrical and temporal relationship between cameras. A ball trajectory is finally reconstructed as connected trajectories which separated at collisions. It is experimentally demonstrated that the proposed method can calibrate cameras precisely and reconstruct accurate ball trajectories.

Original languageEnglish
Pages (from-to)1157-1165
Number of pages9
JournalSeimitsu Kogaku Kaishi/Journal of the Japan Society for Precision Engineering
Issue number12
Publication statusPublished - 2014 Dec 1
Externally publishedYes


  • Ball
  • Calibration
  • Table tennis
  • Trajectory
  • Unsynchronized camera

ASJC Scopus subject areas

  • Mechanical Engineering


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