Precise 3D Baseball Pitching Trajectory Estimation Using Multiple Unsynchronized Cameras

Abstract

We developed a method for the precise estimation of the 3D trajectory of a baseball by modeling the movement of the baseball and estimating the capture delay, using multiple unsynchronized cameras. To develop the proposed algorithm, we mimicked the real-world process of capturing a baseball in simulation space, and analyzed the capture process using a multiple unsynchronized camera system. We represented the movement of the baseball using a piece-wise spline model, and predicted the position of the baseball in the subframes in a manner which is robust to position error and change in direction of movement of the baseball. This method accurately predicts the baseball position over time by modeling the movement of the baseball in a real baseball game environment, and improves the accuracy of the reconstructed 3D baseball trajectories. We defined an objective function to estimate the capture delay, and estimate the optimal capture delay parameter using non-linear optimization method. In addition, we evaluated the performance of the proposed method in simulation space and in a real-world situation. The experimental results show that the proposed method can estimate a 3D baseball trajectory precisely using a multiple unsynchronized camera system and is robust to variations in capture delay, both in the simulation space and in real-world situations.

Keywords

• Stereo vision
• 3D pitching trajectory
• multiple unsynchronized cameras
• camera calibration