3D Pitching Trajectory Reconstruction Using Multiple Unsynchronized Cameras

Abstract

In sports, as the importance of sports data has increased, the necessity of three-dimensional (3D) trajectory analysis system has been increasing. To obtain the trajectory information, the camera-based system is widely used since the camera sensor is relatively inexpensive and easy to use. However, when using a camera in baseball environment, there are many difficulties to consider in order to calculate a trajectory information in 3D. First, in calibration process, it is hard to estimate the extrinsic parameters of the camera accurately because there is no object in the pitching area. Second, it is difficult to use a hardware-based synchronization method because of the long distances between the installed cameras. At last, fast and robust pitching trajectory detection algorithm is required.

This dissertation presents a 3D pitching trajectory reconstruction algorithm for real baseball games using multiple unsynchronized cameras. To calculate the extrinsic parameters, the proposed method uses baseball locations as corresponding points between cameras; thus, calibration process can be completed before the game starts, and the calibration parameter can be updated during the game. In addition, the proposed method estimates the capture delay and correct the baseball locations by considering the capture delay to reconstruct 3D trajectory precisely. To increase the accuracy of pitching trajectory, we proposed quadratic over quadratic rational function model with considers the projection progress of uniformly acceleration movement. In this paper, we analyze the proposed system and verifies the feasibility of proposed method in a simulation space that mimics the multiple unsynchronized system in real environment. To use the proposed method for the real baseball games, an automatic pitching trajectory detection algorithm is implemented.

To evaluate the performance of the proposed method, we conducted the experiment in simulation space and real-world environment. Experimental results in the simulation space showed that the proposed method could estimate precisely the capture delay parameter and calculate extrinsic parameters simultaneously compared to other trajectory models. The proposed method also could estimate the capture delay parameter lower than $0.1$ frame error. In the real-world environment, to compare accuracy of 3D trajectory, we used the Pitching Location Analysis System (PiLAS) that can obtain the 3D baseball locations in a strike zone. For all test sequences, the proposed method could detect 3D pitching trajectory similar with commercialized pitching trajectory system by considering the capture delay parameters. In addition, the pitching trajectory was automatically detected with $99.0\%$ accuracy during the two-hour test in real baseball amateur league.