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
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