Merging multiple adjacent rectangles into one polygon?

O'Rourke has studied a problem that is related to this one (along many others that relate to Computational Geometry) and as a consequence, produced a very beautiful method to efficiently solve it. His method is described in the paper Uniqueness of orthogonal connect-the-dots and is also clearly illustrated at cs.mcgill.ca/~cs644/Godfried/2005/Fall/s... . Note that it says that the polygon shouldn't share vertices in order to apply this method, but this happens very often in the problem we are discussing here.

Thus, all we need to do is to eliminate vertices that are shared. Note that this still produces a polygon, and it is the polygon that is wanted as result. Also observe that the list of rectangles must not contain duplicates (I will assume that is the case, otherwise preprocess it to make the list unique).

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