How to implement optical flow using belief propagation?

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I'm not sure if I can ask these kind of questions in stackoverflow, but I saw some questions about understanding algorithms here, so I'm posting my question. If it is inappropriate, please let me know.

I'm trying to implement optical flow using BP(Belief Propagation) algorithm, but I'm lost.

I've saw http://www.cs.cornell.edu/~dph/papers/bp-cvpr.pdf this link, and they says that they implemented OF with BP, but I cannot understand how.

They posted their code here, but it only includes stereo vision and image restoration example. I need optical flow!

I understand how they implemented stereo vision with BP. But what I don't understand is: since BP is solving a labeling problem, when using BP you should assign each pixel appropriate label from a set of labels.

Now optical flow is computing 2-D vectors. Are they making a set of vectors as label, i.e {(0,0},(1,0),(2,0),(1,1)...} and assigning each pixel appropriate label?? There will be too many labels and it will take too much time!

If anyone has any insight about how to compute optical flow using BP (specifically, what the set of labels should be), please give me an advice.

Any help will be appreciated.

Thanks!

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