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Re: x-y offsets [message #70954 is a reply to message #70953]

Wed, 19 May 2010 18:45

Craig Markwardt
Messages: 1869
Registered: November 1996

Senior Member

On May 18, 4:29 pm, Gray <grayliketheco...@gmail.com> wrote:
> Hi all,
>
> This is a variation on the 2D matching problem that I'm having trouble
> algorithm-ing (to coin an incredibly awkward word).
>
> I have two sets of XY coordinates of unequal length (i.e., x1/y1/n1,
> x2/y2/n2, n1 ne n2). I want to find offsets in both X and Y that
> match the two sets as closely as possible (there will obviously be
> some unmatched coordinates in the larger set). I'm just looking for
> constant offsets, so basically (for n1 < n2) x1 + Cx -> x2, y1 + Cy ->
> y2, with some elements of x2 and y2 being unmatched. How do I go
> about doing this? I don't think I can use JD's MATCH_2D because I
> don't know a priori what my matching radius is.
>
> Any suggestions? Thanks, as always!

This seems like a fragile problem. It seems like the key thing is to
try to select the matching pairs first, and then you can try to refine
the offset determination. If you match incorrectly, then it's
possible for a spoiler pair to corrupt the offset refinement. If you
had an a priori guess for the offset, that would help immensely.

As far as selecting pairs...

Compute the distances between all pairs of points. For your sample,
that would be N1*N2 distance calculations. The result would be a list
of N1*N2 distances. Presumably the "correct" offset would appear most
frequently. One way to check this is make a histogram of the
distances and look for a peak. Here, having an a priori guess is
helpful to choose the bin size and histogram range. Otherwise you
might have to try those iteratively.

Once you have a preferred offset distance, then you should be able to
go through and match pairs reasonably efficiently. Also, you can
enforce the constraint that a pair can only match once.

From that point, it should be easy to compute the mean offset, or if
you have error bars, then the weighted mean offset. But you will
probably have to check for outliers, which correspond with poorly
matched pairs, and then iteratively recompute offset.

As I said, "fragile."

Craig

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[Message index]

		Re: x-y offsets By: Jeremy Bailin on Thu, 20 May 2010 13:11
		Re: x-y offsets By: Jeremy Bailin on Thu, 20 May 2010 12:20
		Re: x-y offsets By: Gray on Thu, 20 May 2010 08:01
		Re: x-y offsets By: Jeremy Bailin on Wed, 19 May 2010 21:59
		Re: x-y offsets By: Jeremy Bailin on Wed, 19 May 2010 19:56
		Re: x-y offsets By: Craig Markwardt on Wed, 19 May 2010 18:45
		Re: x-y offsets By: Jeremy Bailin on Wed, 19 May 2010 18:38
		Re: x-y offsets By: Gray on Wed, 19 May 2010 12:45
		Re: x-y offsets By: Jeremy Bailin on Tue, 18 May 2010 23:50
		Re: x-y offsets By: Gray on Tue, 18 May 2010 14:08

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