Dear Hedok,
>
> Just curious. How could there be negative Jacobian determinant?
> From what I understand, it's a volumetric scaling to match a voxel
> with a template during registration, so it is counter intuitive for
> me to interpret what negative Jacobian determinant means.
I think this is equally non-intuitive to everyone. Let us think of
two spaces, the original space and the "warped" space. When we create
the warped image we visit each coordinate in the original space and
calculate what point in the warped space that coordinate maps/
corresponds to.
When we move from one coordinate to the next on the original space,
that also corresponds to going from one point to another in the
warped space. Let us say we take a 2mm step to the right in the
original space, and that we find that that corresponds to a 2mm step
in the warped space. We will then have a Jacobian of 1, i.e. volume
is preserved. If instead we find that that corresponds to a 1mm step
to the right, then the Jacobian is 0.5, i.e. the volume has shrunk to
half. If (god forbid) we find that it corresponds to a 1mm step to
the LEFT, that means that the warps has collapsed onto themselves and
the Jacobian is negative.
This collapse is generally considered a very bad thing and there is a
whole field of research dedicated to preventing that from happening.
When it does happen (as it can in e.g. IRTK, SPM5 and in the coming
FNIRT) it is an indication that things are a little wonky in the
estimation of the warps. When observing this behaviour one can i)
ignore it if it is outside the brain or ii) increase the amount of
regularisation that is used.
Good luck Jesper
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