From my experience, if you use BRAINS registration, a cropped region of the head does not register well to a volume the overall head. By the way, this does not work well in ANTs either (both methods are ITK based). I have had success with BRAINS if you switch the role of “moving” and “fixed”, i.e. if you set the cropped volume to be the “fixed” volume and the whole head is the “moving” volume, it often works (not always though). Afterwards, you have to invert the resulting transform.
I haven’t tried it in Elastix (also ITK-based), and it’s interesting to hear that it doesn’t work there either. I think that the problem lies in the base ITK classes that all these registration frameworks rely on - I assume that the moving volume gets resampled to the fixed volume (i.e. the cropped volume gets resampled into the whole-head fixed voxel-space) and there are a lot of “black regions” (all zeros) in the non-overlap regions. That would throw off the similarity functions if they wrongly assume those zero-voxels to be image intensities. The reason may be more complex though, I’m not familiar with the source-code of ITK.
I also know that SPM (not ITK-based) handles this case gracefully. It would be interesting if this could be fixed in ITK eventually. It’s a limitation, especially because cropped volumes with limited overlap are a very common scenario in image registration. Sometimes, the inverse-transform trick (see above) works, but often enough, I need to solve this with a cumbersome workaround.