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Andy,

> I'd like to ask how programs like SPM or VBM8 can segment the image into
> GM, WM, CSF partitions. Based on greyscale value of each voxel, how do
> they determine which partition should be assigned to?

Signal intensity is one of the parameters that are used to determine a 
voxel's tissue class ("it looks like GM so it is GM"). Another one is 
spatial location , which is where the priors come into play ("it is 
where I am expecting GM so ii is GM"). These information are usually 
combined in order to come to a final decision, as described in a couple 
of classical papers by Ashburner & Friston (2000, 2005, and most 
recently, the Malone et al, 2015 paper).

> Also, if everyone's GM image is normalized into standard MNI template,
> may I ask why each participant's value is different for the same voxel?

They don't necessarily have to be different, they may be very close (but 
even small differences may of course be meaningful). And yes, if 
normalization was perfect, and perfect registration was aimed for, then 
the value for the likelihood at a given voxel should be very close (in 
which case you could investigate the deformation field instead, c.f. 
DBM). But alas, the algorithm is not perfect, and perfect registration 
is not usually aimed for. Also, modulation (i.e., integrating the amount 
of non-linear deformation at the voxel level) would still make a 
difference.

Cheers,
Marko
-- 
____________________________________________________
PD Dr. med. Marko Wilke
  Facharzt für Kinder- und Jugendmedizin
  Leiter, Experimentelle Pädiatrische Neurobildgebung
  Universitäts-Kinderklinik
  Abt. III (Neuropädiatrie)

Marko Wilke, MD, PhD
  Pediatrician
  Head, Experimental Pediatric Neuroimaging
  University Children's Hospital
  Dept. III (Pediatric Neurology)

Hoppe-Seyler-Str. 1
  D - 72076 Tübingen, Germany
  Tel. +49 7071 29-83416
  Fax  +49 7071 29-5473
  [log in to unmask]

  http://www.medizin.uni-tuebingen.de/kinder/epn/
____________________________________________________