[MINC-users] determinant of non-linear local deformation fields

[Andrew Janke]

Hi Marc,

On Wed, Jul 30, 2008 at 01:38, Marc BOUFFARD <bouffard at bic.mni.mcgill.ca> wrote:
> I have a question about deformation grids obtained from non-linear
> registration using nlpfit.  These grids contain the 3D displacements at
> each voxel applied to the source to match the template or to the template
> to match the source?

(note that this all presumes you did something like this: where
fred.mnc is our input subject)

   bestlinreg fred.mnc template.mnc linear_part.xfm
   nlpfit -init_xfm linear_part.xfm fred.mnc template.mnc nonlinear_part.xfm

If this is so then the nlxfm is from the source to the target. (after
the linear transformation if there is one). This incidentally is why
we calculate a model to individual transformation when we want to
average a number of transformations during building a model.

> Now if the determinant is calculated from those grids with mincblob and it
> is found that voxel x has a value greater than 1.  Does this mean the
> region in the neighborhood of x has expanded relative to the source  or
> relative to the target?

Perhaps best by example:

0.5 == the area in question is 50% smaller in the template than the source
1 == no change
1.5 == the area in question is 50% larger in the template than the source.

> In a further step, to obtain modulated VBM data should the standard VBM
> data be multiplied by the determinant of the Jacobian matrix or its
> inverse?

You lost me, what do you define as "modulated" VBM data?  I would take
a punt there are a few different takes on it.


-- 
Andrew Janke - andrew.janke at anu.edu.au
Department of Geriatric Medicine, ANU
(a.janke at gmail.com || http://a.janke.googlepages.com/)
Canberra->Australia +61 (402) 700 883