Hi,
The Gaussian mixture model is on the bias-corrected intensities, not
on the
probabilities. If you take the bias-corrected image, mask by the grey
matter
segmentation, then look at the histogram of the non-zero values, you
will
see a Gaussian-like histogram, although the tails tend to be truncated
because
they mix in with the white matter and CSF. Also, there is the Markov
Random
Field which operates together with the mixture model, so you do not
expect
to get perfect Gaussians.
As for the distribution of probabilities - I would have no particular
concern about
what you say. The distribution of partial volume estimates is the
most useful
quantity and we model that with an additional MRF on the mixel-type,
which will
cause the histograms of these to look quite different, often with a
peak near 1
representing voxels where there is no strong evidence of mixing of
tissues,
but with a lot of entries between 0 and 1 representing the common
mixture
that you see at the edge of the cortical sheet and in the sub-cortical
structures.
I hope this helps explain things for you
All the best,
Mark
On 19 Aug 2009, at 19:55, Mojabi, Pouria wrote:
> Hi all,
>
> I started developing this concern when comparing Segmentation
> results (white matter, grey matter and CSF) between SPM and FSL;
> When looking at for instance Grey matter, as far as the histogram is
> concern, I was expecting to see a Gaussian distribution, is this not
> a correct assumption?
> I could see bell shape histogram for FSL segmented data, but I was
> expecting to see the peak where probability is equal to 1 but the
> peak was at p=0.5
>
> For SPM segmented data, I see a flat histogram with minor peaks at
> p=1 and p=0, not sure why?
>
> I am entirely puzzled by this, based on my understanding of Gaussian
> Mixture Models and Expectation maximization algorithm, you separate
> three Gaussians (ideally speaking, eliminating bias field
> corruption), then you build your probability mask based on the mean
> and standard deviation of the calculated Gaussians, so histogram of
> the Segmented data should somehow reflect this Gaussian nature,
> right ?
>
> Your thoughts on this are highly appreciated
>
> -P
>
>
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