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Let me reply based on your comments

Now, a number plate is, by essence, unique.

That is true, but by providing many samples, you let the boosting look for features that are general to the class, and not specific to one plate.

So just out of curiosity here (because I know some LBP detector do work for ANPR) : is that why the detector need soooo many examples ?

Yes because basically it wants to generalize. To have a clue on what it does, take 1000 images of numberplates and convert them to their LBP counterpart. Then normalize/average over the 1000 plates. The resulting average plate will have the features used in your learned model.

Would not it be "easier" to train it to find objects looking like number plates : find the rectangular shape but not caring about "what's inside" ?

No, because you are tackling it visually. Features are capable of capturing relations that we do not see with our eyes. If we just use rectangular shapes, you will have way more false positives to get rid off somehow.