| Re: yet another 2d matching question [message #71997 is a reply to message #71995] |
Fri, 30 July 2010 08:41   |
Gray
Messages: 253
Registered: February 2010
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Senior Member |
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On Jul 30, 11:25 am, Gray <grayliketheco...@gmail.com> wrote:
> On Jul 30, 11:23 am, Gray <grayliketheco...@gmail.com> wrote:
>
>
>
>
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>> On Jul 30, 11:15 am, Paolo <pgri...@gmail.com> wrote:
>
>>> On Jul 30, 10:01 am, Gray <grayliketheco...@gmail.com> wrote:
>
>>>> Hi all,
>
>>>> For quite a while I've been using JD Smith's match_2d routine to match
>>>> xy coords between lists. However, this and all the other matching
>>>> codes I've seen out there suffer from a variation of the uniqueness of
>>>> matches problem.
>
>>>> Codes like SRCOR in the NASA IDL library let you specify a one-to-one
>>>> match, i.e. enforcing that each element in list 2 only be matched to
>>>> one element in list 1; using match_2d's match_distance keyword one
>>>> could implement the same effect oneself. However, while that excludes
>>>> multiple matches to the same element, it's all done after the fact,
>>>> after the original match was determined.
>
>>>> What I'm looking for is an algorithm that matches 2 lists, identifies
>>>> multiple-matches, and then looks for additional matches within the
>>>> search radius for elements which would become unmatched after
>>>> enforcing a one-to-one relationship. What I mean is, say element 0 in
>>>> list 2 is matched to both element 3 and element 5 in list 1, and that
>>>> the distance between 2_0 and 1_3 is smaller than the distance between
>>>> 2_0 and 1_5. In that case, 1_5 would become unmatched; but what if
>>>> there is element 2_1 which is also within the search radius of 1_5?
>>>> Then, 1_5 should be re-matched with 2_1.
>
>>>> My best idea thus far is to run match_2d once, identify multiple-
>>>> matches, keep the matches with minimum distance using match_distance,
>>>> then iterate with the remaining elements until match_2d returns no
>>>> matches. Can anyone come up with a better solution?
>
>>> Hmmm... what about starting with first point (a) in list 1, finding
>>> the nearest
>>> point (b) to (a) in list 2, removing (b) from list 2 and repeat for
>>> all points
>>> in list 1? [this assumes list 1 and list 2 have the same number of
>>> elements N,
>>> which is a necessary condition for a one-to-one matching].
>
>>> With some smart partitioning of list 1 it will take ~log(N) to find
>>> the nearest
>>> point, so we are looking at ~ N log(N) operations...
>
>>> Ciao,
>>> Paolo
>
>>>> --Gray
>
>> I'm fine with having there be points which don't match at all w/in the
>> search radius, I'm just looking to force any matches that exist to be
>> recognized.
>
>> The straight FOR-loop method is certainly serviceable, but I had hoped
>> there was a more efficient way to do it... but it's certainly possible
>> (or even likely) that anything fancier I try to do is LESS efficient.
>
>> --Gray
>
> Though I have trouble believing that FOR is the way to go when I have
> ~50k elements in each list.
AND... there's no guarantee that the first match you find for a given
element in list 2 is the best one.
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