[Insight-developers] Vector field to Jacobian determinant filter

[Torsten Rohlfing]

Hi --

it seems to me that it would be nice to have a filter that takes a 
vector field (i.e., an n-dimensional image of n-dimensional vectors) and 
produces an image of the local Jacobian determinants (for deformation 
morphometry etc). In fact, this was suggested a few weeks back on the 
itk-users mailing list I believe. As proposed there, I have taken the 
VectorGradientMagnitudeImageFilter and modified it accordingly. I would 
be happy to contribute this code if there is any interest.

Beyond that, I was wondering: one may consider the Jacobian determinant 
as an alternative measure of gradient magnitude, albeit one that is only 
well-defined for cases where the dimensionality of the image equals that 
of the vectors at each pixel. So maybe it would make more sense to 
include this computation as an alternative operating mode in the 
VectorGradientMagnitudeImageFilter itself rather than create a new 
class? The actual code is actually fairly small, thanks to vxl's 
determinant computation.

Best,
  Torsten