The values are indeed related to mixing proportions, means and
variances, but note that the mixing proportion is a slightly modified
version, which takes into account the prior belonging probabilities (see
the Unified Segmentation paper in NeuroImage).
1) Note that there are usually multiple Gaussians per class (as
specified via the Custom part of the UI). By default, there should be
two Gaussians for each tissue type, plus a bunch of others for modeling
the background. Therefore, the first two mg, mn and vr of one
seg_sn.mat file should model a similar intensity distribution to those
from another seg_sn.mat file. Similarly for the second two, etc.
There are no hyper-priors within the segmentation (i.e. priors on the
means, variances and "mixing prioportions"), so the model is pretty free
to do what it wants. In an ideal world, computers would have loads and
loads of memory, and it would be possible to more easily implement a
hierarchical modeling strategy, so that parameter estimates were biased
according to the parameters estimated from the other subjects. As the
code currently stands, the estimation is done independently for each
subject, which means that the approach is not as powerful as it would be
if information from all subjects was properly combined.
2) The intensity distributions are essentially those of the bias
corrected images.
Best regards,
-John
-----Original Message-----
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]]
On Behalf Of Burak Ozkalayci
Sent: Thursday, February 22, 2007 6:20 PM
To: [log in to unmask]
Subject: [SPM] gaussian of mixture parameters in segmentation
Dear everyone,
I use the SPM5 for segmenting the brain tissues. I believe the mg, mn,
vr fields in the resultant files *_seg_sn.mat are the parameters of the
Gaussians used for modeling the density distribution of tissue
intensities, that are weight coefficient, mean and variance
respectively.
I guess the probability density function of the intensity values in the
volume is estimated by this formula. If i am wrong please correct me
pdf = SUM { mg(i) * N(mn(i), vr(i)) }
(the summation is over i`s.)
I have two questions about them.
1- Why these parameters vary between the *_seg_sn.mat files for each
tissue?
2- The fitted intensity distribution of the volume belongs to the
original volume to be segmented or the bias corrected volume?
Thanks for your help in advance
Burak
