In 2019, the Premier League first started using the Video Assistant Referee (VAR) to assist the on-field referee in making crucial decisions, such as verifying a goal or giving a penalty. The VAR system records the whole game, not only assisting the referee in making calls but also advising teams and sports broadcasters after the game. A key part of the VAR system involves 3D tracking of the soccer ball and players, which is what A General Framework for 3D Soccer Ball Estimation and Tracking by Ren, Orwell, Jones, and Xu is about. 3D tracking uses snapshots from multiple cameras viewing the field to pinpoint the exact position of the ball in a moment of time. The article states that although you can easily track players in the game using distinct shapes and colors, it’s challenging to track the soccer ball using these methods since the ball is blocked by players or moving too fast for multiple cameras to detect a clear color and shape.
Because of these difficulties, the researchers use different methods of tracking in order to estimate the ball’s position. The authors’ reason that if the ball is only kicked once, then the ball’s direction won’t drastically change unless it hits another object (hits a goal post or another player). Because of this, the trajectory can be viewed as a continuous planar curve on consecutive vertical planes. If the position of the camera is located at c and the ball has known positions a and d, you can use properties of a similar triangle and orthogonal lines to estimate a third point on the curve. Once you have three points on the curve, you can find the polynomial for the planar curve that predicts the ball’s trajectory.
Figure 1: Given points a and d and a given plane 𝝅, you can find point b on the plane 𝝅 using properties of similar triangles
In this experiment, mathematics is used to estimate the ball after it has been kicked eight times. Then the estimated path is compared to the actual trajectory of the ball, which is measured using manually derived ground truth. The results are compiled into this histogram below (Fig. 2), which shows that the estimations are within 2.5 meters of the actual position 90% of the time.
Figure 2: The ball is predicted to be within 2.5 meters of the actual position within 90% of the time
Although this is a start to 3D tracking of a fast-moving soccer ball, there is room for improvement. For example, their way of estimating the ball’s position is very limited in that it is only able to provide an accurate estimation of the ball after it is touched exactly once. This is useful in games like baseball and golf, where the ball in question is touched a very few times in each trajectory. However, it is not as useful in a fast-paced soccer game, where the ball is being passed from one player to the next without a pattern. If we can figure out the mathematics to estimate the ball’s position throughout the game regardless of how many touches the ball receives, then the applications of 3D tracking can be expanded. Once we achieve this, we can use this method to track soccer balls, but we can track and estimate the position of volleyball and basketball too.
Not only does 3D tracking have applications in different sports, but it has many applications outside athletics as well. For example, 3D tracking can be used in flight simulation and pilot training. Flight training simulators utilize 3D tracking which uses similar mathematics as described above, which mimics a real-life environment to allow pilots the best training possible. 3D tracking also has applications in the medical field. For instance, 3D tracking provides surgeons with the most accurate scenarios so they can plan out at practice new surgeries. 3D tracking also creates accurate ultrasounds, as well as plays a key part in biomechanics. This shows that VAR has lots of potential not just in the world of athletics, but in other industries as well, proving that we need to adopt it more into our everyday society.
References
- Ren, J., Orwell, J., Jones, G. A., & Xu, M. (2004). A general framework for 3D Soccer Ball estimation and tracking. 2004 International Conference on Image Processing, 2004. ICIP ’04. https://doi.org/10.1109/icip.2004.1421458
