Hi, Harriet-
I for one can’t see these images, because they require a google login. Can you please try attaching them here again?
A general point about alignment; there is only so far that affine alignment—12 degrees of freedom, 3 dimensions of rotation, translation, shear and scale–can go. We generally use affine to align data from one subject to other data of that subject—e.g., an EPI to an anatomical of sub-000. Why might that not provide exact alignment? EPIs can be distorted by B0 inhomogeneity and other effects; DWI images (also typically from an EPI sequence) can have even more distortions. Also, EPI images tend to be lower spatial resolution than an antomical, so there is partial voluming and loss of structural detail. Also also, EPI images (and also structural images) can have brightness inhomogeneities (separate from geometric distortion), which change their appearance and potential alignability. Scanning on a different day or in a different scanner can also lead to different distortions/effects. In short, life can be hard sometimes.
So, sometimes higher order alignment is necessary, depending on the data, even for data within the same subject, depending on the degree of alignment you need. But this depends a lot on the data, data quality, goals, etc.
To align data from different subjects (e.g., sub-000 to sub-001 or sub-000 to a template), we would typically recommend using nonlinear alignment, because the degree of expected difference is pretty large.
In all of this, the relative contrast of your data (and presence of inhomogeneities/oddities) can also inform what cost function is used to guide the alignment.
A lot of alignment issues in MRI are discussed here:
https://www.youtube.com/watch?v=PaZinetFKGY&list=PL_CD549H9kgqJ1GDXAs1BWkgEimAHZeNX
Again, these are just general points, because I cannot see the images you have linked above.
–pt