How Accurate is the Hawk-Eye System for Tennis Line Calls

The US Open Tennis 2009 is in full swing. Once again the likes of Federer, Nadal and Murray are playing well and the men's championships looks set for an exciting second week.
We know and have seen how video analysis can be used to analyze a tennis players performance, but it can also be used in real time or almost real time to track the ball and even make close line calls. Of course I am talking about the "Shot Spot" or Hawk-Eye system.

If you have watched any Major Tennis since 2006, you will know exactly what Hawk-Eye is. The Hawk-Eye is used to make decisions on line calls that are challenged by the tennis player. Each player (or team if playing doubles) can challenge a line call on any point. They get a maximum of 2 incorrect challenges each set. If the set goes to a tie break an extra challenge is allowed. Basically the Hawk-Eye challenge enables the tennis players to use technology to challenge line calls they think are incorrect.

The technology being used by the Hawk-Eye system is Video Analysis. Here is how it works.

1. Multiple cameras are placed around the court and players. These cameras are usually placed high up, so that there is less chance that a player will be blocking the ball from the camera view.
2. Multiple cameras are used to ensure accuracy of tracking the ball and to account for possible occlusion (the ball being hidden from the camera view by the players body...)
3. The system uses at least 4 high speed video cameras, with a capture rate presumed to be 500 frames per second.
4. The camera position is calibrated to determine its position in space and relative to the other cameras in the system. The lines on the court are also used in calibration and to compensate for any camera movement.
5. The center of the ball is tracked in 2D by each camera. The ball therefore is like a reflective marker or point on the body. Using the information from all the cameras, the Hawk-Eye system then triangulates the 3D position of the ball.
6. This process is done for each captured frame so that a trajectory of the ball can be created and then overlayed on an animated background containing the lines of the tennis court.
7. Finally the skid and compression of the ball is measured by examining the position and trajectory of the ball prior to the bounce and its position and trajectory after the bounce. In this way they can determine how long the ball was on the ground and how it skidded over the ground.
8. The Hawk-Eye system is said to have an accuracy of 3.6 mm.

I believe that the use of video technology in this way is great for the sport of tennis and for the players piece of mind as well as spectator enjoyment. However we have seen a number of controversial calls with the Hawk-Eye system. Take a look at video of 2 big ones here.

In this first video we see a very tight call for Mikhail Youzhny over Rafael Nadal at Dubai in 2007.


This second video is from the Wimbledon final in 2007. Rafael Nadal benefiting from a very close one over Roger Federer.


In both cases we would have to say that the ball likely looked out to the lines judge who made the call. In both cases the player is most likely only challenging the call because it is a crucial point (Yozhny vs Nadal - Set Point, Nadal vs Federer - Break point). The Hawk-Eye system suggests that in both cases these calls were measured as being 1mm IN, meaning the ball was 1mm from being out.

Have a look what the manufacturers of Hawk-Eye have to say about these two controversial calls at here.

Could Hawk-Eye have been wrong in either or both of these calls and what does it mean that it is 2-3 mm accurate but can suggest that the ball was in by only 1mm?

Here are some points that may effect the accuracy of the system.

1. The camera capture rate of 500 frames per second may be too slow for the hard hitting tennis game of today. Andy Roddick has recorded a fastest serve at 155 mph and ground strokes are often hit with a similar speed. Assuming a capture speed of 500 frames per second or 1 frame every 0.002 seconds, the ball will have moved about 139 mm for every video frame. This may not be sufficient data to determine the position of the ball to within 1 mm.
2. The more cameras that are used the better the chance of tracking the ball and the higher the accuracy. However there are possibilities of occlusion by players, tennis rackets and the net, which will lead to reduced accuracy.
3. High speed video capture also needs excellent lighting. We have discussed the importance of lighting for high speed capture in a previous post . Therefore the system will work best under a roof with artificial bright lighting and will possibly have a problem tracking the ball outdoors, particularly when there is cloud cover or as it gets later into the evening.
4. Assuming everything is perfect for capture, the center of the ball has to be identified as accurately as possible too. If a camera sees the ball at a funny angle or partly occluded the center may not be correctly defined by this one camera and the position of the ball will be inaccurate.
5. The skid and compression of the ball is being estimated and extrapolated based on the trajectory of the ball before and after the bounce. Any inaccuracies in tracking the position and flight of the ball will become larger during an extrapolation (estimation of the movement).

The Hawk-Eye system may not be perfect but it is definitely a step up from the eyeball view of a line judge, particularly when the ball is moving at high speed. We believe Hawk-Eye has improved the line calls in Tennis and this is great for the players and spectators alike. However it still leaves room to debate exciting points and close matches. Enjoy the US Open Tennis and hopefully we will not see any controversial Hawk-Eye calls.