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Re: fitting many linear eqs simultaneously with outliers [message #77967 is a reply to message #77957]

Fri, 14 October 2011 02:32

Bringfried Stecklum is currently offline

Bringfried Stecklum
Messages: 75
Registered: January 1996

Member

Jeremy Bailin wrote:
> So I have a large number of very simple linear equations, which all look
> like:
>
> a_i + b_i x_ij = a_k + b_k x_kj
>
> for i,k=1..N (all unique combinations of i and k), j=1..M. The data
> values x_ij and x_kj are measurements of the brightness of object j in
> images i and k respectively, where the images have an unknown zero point
> and scalings that I am trying to determine.
>
> (aside to astronomers: this may sound suspiciously like re-implementing
> mscimatch)
>
> Not all objects appear in all images, so there are different numbers of
> equations relating each pair of images. In principle, any number of
> linear solvers should work... BUT: it needs to be extremely robust to
> outliers. I know for a fact that there are many many many outliers, and
> there are some pairs of images where it looks like pure scatter. So I
> need some sort of solver that will do sigma clipping. Essentially, I
> want a sigma-clipping linear least squares solver that can solve more
> than one line at once.
>
> Does anyone know of such a beast already existing? Or something that's
> vaguely similar enough that I can use it as a basis?
>
> -Jeremy.

Perhaps fitting a line in 3D may serve as a starting point. From looking at the
equations a generalization to higher dimensions seems feasible.

http://www.scribd.com/doc/31477970/Regressions-et-trajectoir es-3D

cheers, Bringfried

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[Message index]

		Re: fitting many linear eqs simultaneously with outliers By: Jeremy Bailin on Mon, 17 October 2011 23:56
		Re: fitting many linear eqs simultaneously with outliers By: Craig Markwardt on Fri, 14 October 2011 18:46
		Re: fitting many linear eqs simultaneously with outliers By: Bringfried Stecklum on Fri, 14 October 2011 02:32
		Re: fitting many linear eqs simultaneously with outliers By: Matt Francis on Thu, 13 October 2011 22:37

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