> Ah yes, ... I had to check wikipedia again to be sure I understood, but
> now I think I do. I have another question, though, which I think I need
> in order to proceed here: what is the origin that the volume is rotated
> around? In other words, is every single fMRI volume rotated around its
> center, or one of the corners? I would expect the former, but I have
> been wrong before. I checked spm_realign but did not find a clue, so any
> hint is appreciated.

Around the "origins" of the images would be a bit closer.  The overall affine 
transform is parameterised in terms of a rigid-body transform inserted 
between a couple of voxel-to-world mappings

    M2\R*M1

where M1 and M2 are the mappings from the voxels in one image to the current 
best guess of "world space".  So a voxel in image 1 is mapped to world space 
(by M1), rotated by the estimated rigid-body transform (R) and then mapped 
back to voxels in image 2 (by inv(M2)).

After registration, depending which image is considered as fixed, the voxel to 
world mappings would be modified.  If image 1 is fixed, then M2 would be 
replaced by R\M2.  If image 2 is fixed, then M1 is replaced by R*M1.  Either 
way, the result is that the new M2\M1 should be a better map from voxels in 
image 1 to voxels in image 2.  The general idea is to get all the images of a 
subject into alignment with each other according to the same scheme.  For 
example, if there is an image 3, and its voxels map to those of image 2 (by 
M2\M3), and image 2 maps to image 1 (by M1\M2), then you can go from image 1 
to image 3 by multiplying by M3\M1 (= inv(M3)*M1 = inv(M3)*M2*inv(M2)*M1 = 
(M3\M2)*(M2\M1) = inv(M2\M3)*inv(M1\M2) ).

Best regards,
-John