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From: tristram.scott@ntlworld.com (Tristram Scott)
Subject: Re: Find gaussian humps in a 3D dataset
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Xref: news.mathworks.com comp.soft-sys.matlab:490451


Thomas Clark <t.clarkremove_spam@cantab.net> wrote:
> One fortunate feature is that particles don't tend to clump together, and
> of course they can't be in the same place... so any two peaks will occur at
> least two standard deviations apart. Hopefully that'll help re. overlapping
> peaks.

That is very useful.

> 
> Thanks for the additional idea, I'd not come across that before. I'll
> store it away for the future, but not implement that yet... as I see it,
> I'd still have to make some kind of fit to detect the exact location of the
> peak (thresholding could only ever give voxel-scale accuracy, rather than
> sub-voxel).

I am assuming that your intensity data can be interpreted as a probability
density function for the Gaussian.  Assuming that is the case, then your
discrete approximation to the PDF should be usable to find the mean by
looking at the moments of the PDF.

mean = \int (x.p) .dx

Presumably for a symmetric distribution of intensities you can do this in
each dimensions independently of the others?


> And yes, ~1000 particles per frame, ~1000 frames per test, ~100 tests to
> get a PhD. It'll need to be relatively quick :( !
> 

Perhaps it is not so much that the process needs to be fast, but rather
that it needs to operate without manual intervention.

Drop me an email if you want more details on any of my vague ideas.

-- 
Dr Tristram J. Scott               
Energy Consultant