Hi Chiara,
> Is there a way to see whether intensities for some voxels are
> concentrated at particular values, e.g. at zero (SPM2)? I have been
> asked to check this to address the problem of clumping of data which may
> suggest non-normal models.
There may well be a rather non-normal clump of voxels in the histogram
at 0, however, I think these are masked out (e.g. SPM5's version of
spm_segment.m line 497: the mask will excluse zero voxels).
There could *possibly* be a similarly saturated clump at e.g. 255 if
8-bit data are used and some of the white matter (or artefacts?) is
very bright, but I wouldn't expect this to happen -- I think most MR
operators would probably avoid clipping the data like this.
Another potential source of concentration at particular values would
be very clean (low noise, low bias, low partial-volume effect) data,
as discussed in this thread:
http://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0701&L=SPM&P=53408
Lastly, the problem of non-normality is of course not just limited to
concentration around certain values, it could also be manifest as
heavy-tailed (high-kurtosis) distributions, or skewed ones, or bimodal
distributions (for example, I believe deep grey matter structures have
a different distributional mean/mode to cortical GM). Although, note
that non-normal images might actually still be segmented very well by
a GMM; just because the data doesn't match the model perfectly doesn't
mean that the three tissues can't end up mostly correct (e.g.
saturated bright white matter would be badly modelled, but almost
certainly still classified as WM).
SPM5 attempts to reduce the problem of non-normality by modelling
individual tissue classes with multiple Gaussians, as I think I
mentioned in previous reply to you. Jose, in the last post of the
thread linked above, suggests that these problems are better handled
by non-parametric classification. I wouldn't claim to know much about
this, but one method which avoids Gaussian Mixture Models that appears
to have been quite successful is the Fuzzy C-Means algorithm -- the
following are quite informative:
http://scholar.google.com/scholar?hl=en&q=fcm+clustering
http://scholar.google.com/scholar?hl=en&q=fcm+segmentation
Look out for the many Bezdek articles on fuzzy methods, the Pham and
Prince articles of (A)FCM segmentation, and the Pal & Pal review.
Hope that helps,
Ged.
P.S. I have potentially-rubbish Matlab code that I cobbled up to test
bog-standard non-adaptive FCM image segmentation if you are
interested, though hopefully you can find better...
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