| Re: yet another 2d matching question [message #71993 is a reply to message #71991] |
Fri, 30 July 2010 09:12   |
pgrigis
Messages: 436
Registered: September 2007
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Senior Member |
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On Jul 30, 12:06 pm, Gray <grayliketheco...@gmail.com> wrote:
> On Jul 30, 11:59 am, Paolo <pgri...@gmail.com> wrote:
>
>
>
>> On Jul 30, 11:41 am, Gray <grayliketheco...@gmail.com> wrote:
>
>>> On Jul 30, 11:25 am, Gray <grayliketheco...@gmail.com> wrote:
>
>>>> On Jul 30, 11:23 am, Gray <grayliketheco...@gmail.com> wrote:
>
>>>> > 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.
>
>> what is the "best" match you would like to obtain?
>
>> Ciao,
>> Paolo
>
> Smallest distance between two points.
In the sense that the sum of all distances between matched points of
list (1) and (2) is minimal?
Ciao,
Paolo
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