There is a lot of ambiguity about ordering of rotations, so that is why
we didn't chose Euler angle representations.  The headers already have a
field for voxel sizes, so we didn't want to replicate this information
elsewhere.


I think the original intention was to use the S-form for affine mappings
to MNI/T&T space, and just use the Q-forms for the rigid stuff.  A few
people only use 9 parameter affine transforms. Depending of the order of
the rotations and zooms, such 9 parameter transforms can sometimes be
represented by zooms, rotations and a translation.


The headers also contain a bunch of fields for slice timing information
and statistical codes (F maps, t maps etc).  These are not used by SPM
yet, and as far as I know, DICOM headers don't seem to store the
relevant slice timing info.   If you are interested, you can manipulate
some of the additional information in the headers by the nifti utilities
in SPM5.  Type the following for more info...

     help nifti/contents

Best regards,
-John


-----Original Message-----
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]]
On Behalf Of Ged Ridgway
Sent: Thursday, May 24, 2007 7:08 PM
To: [log in to unmask]
Subject: Re: [SPM] [FSL] DICOM (DIR?) to NIFTI

Alle Meije Wink wrote:
> Ashburner John (PSYCHOLOGY) wrote:
>> The Q-form is a bit limited.
>> [...]
>> Many CT images are skewed.
> 
> [...] was there a rationale for having 2 separate 
> forms and making 1 more limited?

My first guess is that some people favoured using quaternions for the 
rotation matrix (this is where name Q-form comes from, I believe), as 
these have some advantages. See e.g.
   http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q47

My second guess is that maybe the idea was, as John and I have 
mentioned is possible, to have the q-form for the scanner mapping and 
the s-form for the standard-space mapping.

However, neither guess entirely makes sense to me...

As described in the above link, quaternions are usually converted to 
standard rotation matrices when it comes to using them. I can't 
(currently) see why a separate skew matrix couldn't proceed the rest 
of the transformation. See, for example, spm_matrix.m, where a 
complete 12 DF affine transformation matrix in homogeneous form is 
built by multiplying homogeneous matrices for skew/shear (S) then 
scaling/zoom (Z) then rotation and translation, i.e. A=T*R*S*Z. In 
spm_matrix, the rotation matrix R comes from a combination of simpler 
rotation matrices (with the pitch/roll/yaw convention), but it could 
easily come from quaternions, if preferred, as far as I can see.

And my second guess seems daft in light of
  (a) the q-form intent code can specify MNI-space, while the s-form 
one can specify scanner anatomical.
  (b) John mentions that CT data can have skews in the voxel-world 
mapping, which would leave you with a useless q-form and potentially 
two things you might want to put in the single s-form.

I must be missing something though -- the NIfTI format seems very well 
thought out to me in all other regards, from what little I've read 
about it.

Best,
Ged