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Casting Doubt On the Hawkeye Ball-Calling System
Human judgment by referees is increasingly being supplemented (and sometimes overridden) by computerized observation systems. nuke-alwin writes "It is obvious that any model is only as accurate as the data in it, and technologies such as Hawkeye can never remove all doubt about the position of a ball. Wimbledon appears to accept the Hawkeye prediction as absolute, but researchers at Cardiff University will soon publish a paper disputing the accuracy of the system."
Why not use a radio transmitter in the tennis ball (or soccer ball or whatever) to record its exact position? I am certain this has been discussed and I wouldn't be surprised if it's already in use. The article's "Hawkeye" just works by optical analysis.
And ultra-accurate GPS like system that tracks the position of balls in nanosecond detail. They can call it Your Object Universal Remote Movement Observance Mechanism, or YOUR MOM for short.
Hawkeye and the like deliver a consistent result. It matters not at all if the ball is in by two Centimetres but is called out, provided that error is consistent throughtout the match.
If both players, or teams, are playing by the same margin of error, the contest is fair.
In cricket for instance, I would accept the computers call over umpires any day of the week!
So if one of the players tries to steal a tennis ball, they won't get very far?
The accuracy has absolutely nothing to do with the overdetermination of the system.
If it had, it would be simple to reduce the number of cameras to three, and boom - perfect position.
That's obviously not how it is.
And of course does the number of cameras increase the precision of the computed position - the principle
is exactly the same as for GPS, where more satellites are better as well.
Using a certain fitting method (least squares, least absolutes etc.) has nothing whatsoever to do
with something like "complementing the equations", that's just necessary because no measurement is perfect -
You are arguing that multiple measurements do not increase the accuracy of a computed average because there
are multiple averaging algorithms to choose from.
Bullshit.
Since we're only dealing with three dimensions, why would any number of satellites > 3 be more precise for GPS?
;-)
Because we are dealing with reality as well - where no measurement is perfect.
Geometrically, three sats indeed are enough, but in reality:
More measurements -> smaller error bars -> better position.
The alternative to more sats would be not to move and to take more measurements over time.
But that would render GPS useless for most applications
Additional trouble with the "stay and wait" method: Those nasty satellites move over time,
introducing different errors that can not be eliminated as easily by simple averaging.
That's also why ultra precise GPS surveying records the satellite data and waits for the week it takes
to make the actual orbital data (as measured, and not just as predicted) available before computing
the position, thereby elimiating (well, at least reducing) another source of error.
In statistics, the only thing beating multiple measurements is even more measurements.
A system such as Hawkeye CANNOT BE MORE ACCURATE than humans. From the link in the article, the Hawkeye system uses 5 cameras to compute the 3D position of the ball. That's an overdetermined system of equations, which cannot have a unique solution due to observation errors in the camera views.
Luckily there's a 100+ year old discipline called statistics, and 60+ years of literature on tracking to help you out in these cases.
So Hawkeye has to complement the equations with an ARBITRARY rule, eg least squares and this arbitrariness makes the Hawkeye estimate neither more accurate nor less accurate than humans, just different. FYI, there are plenty of other arbitrary rules that work, eg least absolute errors, maximum entropy, etc.
While I can't speak for the designers of the Hawkeye, in tracking there are very good reasons to choose one form of error minimization versus another. It only seems arbitrary because you are not informed on the subject, but there's plenty of free papers out there to read and discover.
To explain current methods, please start out with this paper, in particular Figure 2, you'll see that the sort of errors you get from a camera are indeed well fit by a Gaussian. While a camera's perspective transformation is not purely linear (and various forms of distortion make it also non-linear), a good camera with a decent lens estimating the ball location within a limited area is well approximated by a linear model (and you can characterize just how much the error is). Now, a bunch of cameras with a Gaussian error distribution in the image plane with a linear projection out into the world is still a Gaussian (with a transformed covariance matrix). You can then multiply the independent measurements from multiple cameras to get a better estimate. Add a time series to that and apply this recursively and you get a Kalman filter, something invented for aerial tracking and still in widespread use today. If something is good enough for missiles to intercept other missiles, it ought to be good enough for a tennis match.
If the linear approximation not good enough for you, you can use a Rao-Blackwellized Kalman filter. If that's still not good enough because you want to use another error distribution or non-linearizable dynamics, set up a particle filter with a whole lot of particles and enough CPU to simulate it. The point is that what you call arbitrary is a well studied field which is many decades old. You'd be best served by learning about it first before you cast away all that work. I'm not a "tracking" person, just a user of there work. When a field of science has done its job well enough that it has become common engineering, and you can go look up whatever you need in books, with all the derivations, caveats and tradeoffs laid out there for you to see, I would say that that field has done a pretty good job.
The whole media story around this paper is ridiculous. It's a paper from a social sciences department about how the public does not understand the fallibility of these machines due to noise. That's all this paper is about: Hawkeye has error. I hate to break it to the uninformed, but all measurement systems have error. From Galileo to Gravity Probe B, your results can only be as accurate as your measurements, calculations, and statistical models will allow. You can decrease error with various methods, but you can never completely eliminate it. People should not be able to get out of high school without understanding accuracy on measurements, and some rudimentary statistics, but unfortunately our education system hasn't been able to reach that goal. As a result, the public doesn't understand error, and might come to believ
I'm confused. Why would umpires oppose a technology that can automate the refereeing of a game? It just doesn't make any sense.
Information theory is life. The rest is just the KL divergence.
For a system like Hawkeye to be useful, it doesn't need to be perfect. It just needs to consistently be more accurate and impartial than a referee can be.
Nor is it required for the system to be fully automatic and autonomic. Referees can sit in front of their monitors, observe the cameras from all angles, with any time slowdown, and ultimately come to a better decision than a single person could make while the ball buzzes past them at Warp 9.
But from the social aspect, one has to decide on what is the referee's role, and what kind of influence, if any, do we want to delegate to a computer. And that depends on the type of sport.
For non-interactive sports such as sprinting, an automatic system works very efficiently, and most people readily accept it as better than a human time tracker.
But for many GAME sports (soccer and boxing come to mind) many people consider that a referee is PART of the game rather than just an observer. As long as a referee is comparatively competent, and acts in good faith, he has the authority to judge events in the game, and while mistakes are unavoidable, they are considered part of the game as well.
I'm not sure why this position is popular in these kinds of sports. Maybe it's the whole "humans should be judged by humans and not machines" aspect. Or maybe it's because having a Review Comission in front of CCTV monitors be judging every little move just feels too 1984-rish for spectators and players alike. Or maybe its something else. But this is a rather popular feeling.
Depending on the features and benchmarks of the electronic system, it may or may not be more accurate than a human observer. In the long term, a joint human-computer analysis system would be certainly more accurate than a human referee alone, especially in team or high-speed sports. But one has to ultimately question, whether, by gaining mathematical precision, we lost some human touch of sport that makes it enjoyable to play and watch. Fun can't be generated with a mathematical formula. And sometimes sitting on the couch and thinking "OMG that referee is such a dumbass" is part of the fun as well.
I'm willing to concede that you are talking theory at some level I don't fully grok. What I think you're completely missing in this discussion stems from your original statement that"system such as Hawkeye CANNOT BE MORE ACCURATE than humans", which does not seem to be possibly true by any standard definition of these words that I am familiar with.
You can talk about "error criterions" and odd offtopic tangents about targeting algorithms etc, but the bottom line is, your original statement is completely wrong.
You say "So Hawkeye has to complement the equations with an ARBITRARY rule, eg least squares, and this arbitrariness makes the Hawkeye estimate neither more accurate nor less accurate than humans".
That's both wrong and illogical. Yes, Hawkeye is estimating a solution, and using a "arbitrary" (again, this is utterly bizarre and incorrect word choice--the makers of Hawkeye have presumably done a great deal of testing to pick an algorithm, which is NOT arbitrary) method to estimate. However, if Hawkeye ESTIMATES the correct answer more often than a human judge then, Hawkeye is more accurate than a human judge. The methods it uses are really completely irrelevant to the final answer.
So in short, it seems that this is a discussion in your usages of "accurate," "error," "arbitrary," etc are different than the rest of the people in the thread.. Please let me know if I'm misinterpreting something though!
Just because an umpire is the final word doesn't mean that a system can't do better than him, That is because the umpire is in fact he trying to measure something with a right/wrong answer. Specifically the umpire is the person who decides if event X happened or not which means that the goal is to see if X happened or not (not to see if the umpire thought X happened or not). The umpire isn't an inherent part of the rules but simply a judge to determine if something specified in a certain rule happened or not. As a result it's a perfectly valid problem to predict this event X in a method that is better (ie: lower misclassification) than the umpire. Finding the winner in a horse raise is one example of where technology is more accurate despite the rules likely having a person originally be the final judge.
One problem is that sometimes one can't measure the true answer in some way so there is no way to truly measure accuracy for a problem. That is a valid problem however I have no clue if that or something else is the actual problem you're so concerned about (your posts are as clear as black mud). In this case there probably are more accurate systems of measuring the truth although these take excessive money, time or preparation. One could for example cover the ground around the line with wet paint (or some such) and then check for breakages, or simply cover the ground with pressure sensors. The article implies they can measure the accuracy of the system compared to the true impact point which means that one can devise experiments in which one can measure the truth of where the ball lands.
Yes, some people also want to use Hawkeye for some decisions in cricket, the sport that first used it. However the margin of error is far greater (approximately +- 2 inches) in cricket as the cameras have to be a lot further away due to the size of the pitch.
Also Hawkeye finds it hard to pick up swinging, seaming and spinning balls. Basically anything that deviates off its theoretical trajectory either in the air or off the playing surface. Both of which are vital in the LBW decisions where the TV companies and doubtless the Hawkeye people would want to see it used.
Obviously cricket is a far more useful game than tennis so does this answer your question?
another Roadkill on the Information Superhighway
This assumes there is another method, such as post-analysis of videotape, that can find almost all uncorrected errors or at least give some good indication of the uncorrected error rate.
Another method would be to use Radar instead of Hawkeye. Probably faster and more efficient as well.
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