Mathematics involved in Captcha Solving I was wondering if anyone knew about Mathematics involved in Captcha Solvers.  I'm not interested in spamming, I just it would be interesting to see how to classify letters.  I'm certain homology is used to determine the holes of the letter.  I also figure that a line is connected only if at least a certain number of pixels are next to each other.  
 A: Gunnar Carlsson gave a talk many years ago about using algebraic topology to detect handwriting - in particular, handwriting in a particular Indian language.  I'm not sure that anything on this was published, though.  My recollection is that they used the notion of "soft tangent bundles" to distinguish two letters that had been indistinguishable by other methods.  This was presented as a refinement of the idea of using local homology groups (i.e. considering the homology of deleted neighborhoods of points on the letter).  
Googling the phrase "soft tangent bundle" didn't give any hits, so maybe I should say something about what this means.  My memory is a bit fuzzy on this, but I think the idea is to consider vectors that are "almost" tangent to the letter (meaning that the angle they form with the actual tangent is small) which is viewed as a (collection of) curves.
Unfortunately, I have no recollection of what sort of geometry this detected (so as to distinguish the letters) and I don't seem to have notes from the talk...
