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Re: match_2d [message #66363 is a reply to message #66227]

Wed, 29 April 2009 13:29

JDS
Messages: 94
Registered: March 2009

Member

On Apr 28, 10:44 pm, Jeremy Bailin <astroco...@gmail.com> wrote:
> On Apr 27, 3:06 pm, JDS <jdtsmith.nos...@yahoo.com> wrote:
>
>>> I'm pretty sure there's a HIST_ND-based algorithm of doing this
>>> similar toMATCH_2Dbut taking spherical trig into account, but I
>>> don't have the patience to figure it out.
>
>> That would be challenging for the whole sphere, since histogram can
>> only evaluate monotonic coordinate fields. You can always first remap
>> your coordinates using some projection which puts the ill-behaved
>> parts (nominally, the poles) far away, and preserves distance
>> locally. For example, if you have a small field (a degree or so) near
>> the pole, this would be a nice way of solving the converging longitude
>> lines issues. But generally? Sounds tough.
>
>> JD
>
> How about if it was done in 3D? Instead of 2D angular coordinates, use
> the 3D coordinates of the relevant points on the surface of a unit
> sphere, and then use HIST_ND to determine which 3D bin the points are
> in and build the algorithm analogously to MATCH_2D?
>
> The main problem I see is that, for small bin sizes (ie. small desired
> angular separations), there's a lot of wasted memory storing the
> histogram in locations that don't lie on the surface of the sphere and
> therefore are necessarily zero. But maybe there's a way of enumerating
> the bins that do contain part of the surface - if so, then you could
> use that enumeration to map the 3D positions into a simple number that
> you can run HISTOGRAM on.

I thought of that and rejected it for the reason you mention. The
vast majority of memory would be devoted to empty volume, and as the
resolution grew, the fraction of wasted memory would grow as well.
The mapping you describe to do away with the empty space is equivalent
to spherical projection, for which there is no unique mapping for the
whole sphere. One possibility would be to project iteratively,
forming low distortion projections over the sphere to push the poles
off out of the way, matching against a subset of the data, rotate the
projection, repeat. Some heuristic for deciding which projection, how
large, and where to center it, would be needed.

At some point, it would become simpler to use pattern matching via
Delauney triangulation or other patterns formed from the target list.

JD

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[Message index]

		match_2d By: vino on Mon, 20 April 2009 06:40
		Re: match_2d By: Jeremy Bailin on Tue, 28 April 2009 19:44
		Re: match_2d By: JDS on Wed, 29 April 2009 13:29
		Re: match_2d By: JDS on Mon, 27 April 2009 12:06
		Re: match_2d By: vino on Mon, 27 April 2009 03:53
		Re: match_2d By: Jeremy Bailin on Wed, 29 April 2009 17:00
		Re: match_2d By: Jeremy Bailin on Fri, 08 May 2009 22:02
		Re: match_2d By: Jeremy Bailin on Wed, 29 April 2009 16:30
		Re: match_2d By: wlandsman on Thu, 06 May 2010 11:11
		Re: match_2d By: d.poreh on Fri, 07 May 2010 05:06
		Re: match_2d By: d.poreh on Thu, 06 May 2010 05:25
		Re: match_2d By: vino on Thu, 06 May 2010 04:27
		Re: match_2d By: d.poreh on Fri, 07 May 2010 05:55
		Re: match_2d By: Jeremy Bailin on Fri, 07 May 2010 05:30

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