Imaging analysis Tools

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All these different tools indeed interpret NIFTI headers differently and hence can display images differently. Apparently ITK (by the way, ANTs registration tools follow ITK convention) has a different way of seeing "registered" compared to SPM or AFNI. 

First thing to check is that the origin and direction are the same between your images -- if they are not, then they are not considered coregistered. I guess you can use either ITK::c3d, ANTs::PrintHeader, or FSL::fslhd commands, or even Matlab or SPM to check your NIFTI headers. I'm assuming that the voxel spacing and image dimensions between your images are the same because ITK-Snap will not allow you to overlay a segmentation on an image with those being different in the two (BUT note you can open the segmentation as an "additional image" even if the voxel spacing and image dimensions are not the same for all images opened, similarly in SPM's coreg check display).

(For others who might have the same problem I had: my ASHS segmentations did not look coregistered to my TSE structural in ITK-snap, although theoretically they were coregistered -- and this ended up being a problem that they ended up in different physical spaces, as indicated by them having different origins -- even though I had coregistered all my images and then ran ASHS, at least I thought so, for some reason, the origin between my ASHS segmentations were different to my TSEs -- I fixed this by using ANTs::CopyImageHeaderInformation to copy just the origin of my TSE images to my ASHS segmentations)

SPM, MRIcron, ASHS, ITK a nd FSL have different ways of working with DICOM orientation information and encoding native space.  There is the sform (linear) and qform (rotatation/quarternion) matrices which encode space/how to convert between voxel coordinates and "real world"/mm coordinates. Each has its own advantages -- apparently sform is better for figuring out starting alignment estimates, and qform for figuring out native space. Therefore, warping might work with qform (ignoring any sform of the fixed image) and registration will actually have worked properly but depending on how your viewer interprets the NIFTI header, it might just look like it didn't work.

ITK (like ANTs registration tools) works in LPS space like DICOM images and works with rotation (quarternion/qform) rather than affine transformation (sform). It ignores sform and during certain processes even replaces existing sform with zeros, so you'll lose any info in the sform.

AFNI works in RAI-/LPI+ coordinate order by default, SPM in LPI. Not sure about AFNI, but SPM, MRIcro, FSL and Mango prefer the sform matrix, and only newer SPM versions update both sform and qform to try and keep things consistent.