A stereo audio file only has two channels, mixed from any number of sources: L+R. This described process essentially converts the track (we'll call X) to mid/side (M/S) form, which is used by some microphones and other outboard equipment. We're exploiting properties of both forms of the audio to produce our isolated center.
Also if you have the removed data all you have to do is invert it and sum it against hte original material and it will cancel out
I described it slightly incorrectly in the original post but I have used this process to extract vocals for remixing
The first inversion produces one channel containing nothing but stereo data, as you're summing L+Ri to produce S -- the center channel data (technically, anything equivalent in both stereo channels) cancelled itself out. (Note that if you combine L+Ri you should get a zero-ed out waveform)
The second inversion, produced by combining the first inversion (Ri) and the original source converted to mono (L+R), produces the isolated center channel (M). It works because you are essentially only cancelling out stereo data you generated in the first inversion
If you don't believe me, load up a copy of Audacity or Sound Forge and try it. (Note the music needs to be uncompressed) One track this works with is the original mix of "Day n Nite" by "Kid Cudi" if you can find a WAV copy somewhere. It doesn't work with a lot of music
So...
L, R = stereo_split(X)
Ri = inverse(R)
S = L+Ri
Si = inverse(S)
M = Si+(L+R)
Note: L+Ri should result in empty waveform