Images are deformed by scanning over the voxels of the image to be created,
and figuring out where to pull the intensity from in the original image. The
alternative would be to scan through the voxels of the original image, and
put the values in the appropriate locations of the warped image. This is not
done (usually), as it could leave gaps in the warped image in those voxels
that don't get filled in. Therefore, the deformations are actually the
inverses of those that you had in mind.
So if a voxel in the template image had its voxel volume expanded by 2
relative to the image to be spatially normalised, then the value at that
voxel in the jacobian determinant will be 2. A voxel in the image to be
normalised therefore has its volume halved during spatial normalisation. If
we then want to apply modulation then we should multiply by the jacobian
It takes a while to get ones head around this stuff, so I hope it makes sense
On Wednesday 30 July 2008 19:00, Marc BOUFFARD wrote:
> I have a question about multiplying jacobian determinants by the tissue
> classified images.
> From what I understand the jacobian determinants are obtained from the
> deformation fields. If the deformation fields are relative to the source
> image (not relative to the template) then jacobian determinants will also
> be relative to the source as well. So if a voxel in the source image had
> its voxel volume expanded by 2 relative to the target then the value at
> that voxel in the jacobian determinant will be 2.
> If we then want to apply modulation then should'nt we multiply by 1 over
> the jacobian determinants (at each voxel) to preserve volume information
> rather than by the jacobian determinant itself?
> Marc Bouffard