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I've seen this story before. NASCAR infamously has been trying to integrate technology, yet they can't track the speed or position of any of the 42 cars on the track at a specific moment in time...

That's a solved problem. That technology has been deployed since 1982. When we were doing a DARPA Grand Challenge vehicle, we went to talk to the Sportsvision people about precision real-time GPS. They use some tricks we couldn't; for example, they have a model of the track and can get precision GPS with fewer satellites because they know altitude for each point on the track.

Not being a sports fan, I don't see much of this stuff, but I once visited the company in Silicon Valley that makes the gear. The "yellow line" is one of the easier applications. It's basically a camera with encoders driving a fairly simple video processor. Calibration is manual; there's a setup display that shows the normal lines of a football field, and someone aligns the corners to match the real image from the camera. When the generated image matches the real one, the system is in alignment.

That's 1998 technology. The newer systems have gone way beyond that. Ads on billboards are sometimes replaced using the same system. Ads you see on the air may not be what people in the stadium are seeing. There's player tracking, ball tracking, the "virtual strike zone" for baseball, GPS-based tracking for NASCAR, and virtual billboard insertion into everything.

The company that does it is Sportvision they have some fairly interesting technologies other than just the first down line.

I work for Sportvision and I do the live internet production of our Ironman coverage. We encode the entire finishline stream in Real Video - about 8 hours @ 350 megs. We use a script to generate files based on the timing data that reference the correct minute or so of video around the finisher. Go to live.ironmanlive.com to check it out. Go to any athlete that finished any race and you can watch them finish!

those finishline cams have been available for most (if not all) races of the Ironman series for quite some time now. the site that's covering them (live.ironmanlive.com) also provides updates during the race, including up-to-date swim/bike/run split times. (for my performance at Ironman California this year, look for athlete #213 :-)
I tried to find more technical info on the sportvision homepage, but a quick glance didn't reveal any specifics on their approach.

I guess it can tell the Jets from the grass.

How it Works

The central computer in the 1st & Ten system examines every frame of video in real time (i.e. 30 times per second) and determines which pixels to change to yellow. These are all the points in the image where an actual painted-on-the-field first down line would be visible, such as grass along the line that is not obscured by a player or referee. It determines which pixels to change based on very precise information about the camera's view, a 3D model of the field, which camera is on air, and a palette of colors for the field and another palette for players.

Pixels along the line with colors from the field palette are changed to yellow unless that color is also in the palette for players. Player colors and other colors not on the field palette are left unchanged. This makes the virtual line visible where the field is visible and hidden where the field is obscured, just as a real line would be.

Each camera in the 1st & Ten system, is instrumented with very precise encoders for pan, tilt, zoom, focus and extender (1x or 2x doubler). A computer at each camera reads the encoders and transmits these readings to the Sportvision production truck 30 times per second. Another computer in the truck gathers readings from all the cameras and transmits a consolidated data stream to the central computer. These readings and the 3D field model go into a geometrical calculation that determines which pixels in the video frame would be in an unobstructed view of a real first down line.

Yet another computer determines, also 30 times per second, which camera is tallied (on air). It does this by comparing the video streams from each of the 1st & Ten cameras to the program video. This computer allows for graphics, such as the constant time and score box, that are not in the camera view but are introduced into the program video. The result, camera 1, 2, 3 or none of them, is transmitted to the same computer that is consolidating data from the three cameras, and it adds tally to the data stream going to the central computer.

The final computer has only one simple but crucial task, draw the yellow line in video 60 times per second (every field, not just frame) and send that to a linear keyer to superimpose the yellow onto the program video.


Need more

http://www.howstuffworks.com/question2 25.htm

And since the line is added by the broadcaster, there isn't just one company doing it. Each of the 3 broadcasters has their own system, I think.

ESPN (and MNF) use SporTVision for example, not PVI.