[Insight-users] Find the inverse of a deformation field

[Torsten Rohlfing]

Guillaume:

Two problems with this idea from the top of my head:

a) it would only be approximate, since you8 would need to interpolate 
from the deformation field.

More importantly (this is the killer actually):

b) in oder to interpolate the deformation field in the direction you're 
proposing, you actually need the inverse deformation field already. This 
is the old "paradox" that the pixel values (here: deformation vectors) 
in some sense "travel" in the opposite direction of the coordinates. 
Which is why the pixel value mapping is sometimes called a "pullback" 
mapping.

Best,
  Torsten

>Hi,
>
>I would like to find the inverse of a 3D-displacement field that I've
>computed with a deformable registration done with ITK. I saw that there
>was a method in ITK, but that some bugs remained. So I was thinking about
>another method but I wonder if this is really a good way to invert a field
>:/
>/The inversion could be done in 2 steps : - Deformation of the 3 components
>(each component is stored as a 3D-image) of the 3D-field by the field
>itself.
>- Multiplication of the deformed components of the field by -1.0, so that
>you get the displacement that go back to your original position. And you
>should have the inverse field, if I'm right.
>
>But it seems to be too simple to be correct, so I wonder what could be
>wrong in this method ?
>
>Every opinion would be greatly appreciated.
>
>Guillaume.
>
>  
>
> ------------------------------------------------------------------------


-- 
Torsten Rohlfing, PhD          SRI International, Neuroscience Program
 Research Scientist             333 Ravenswood Ave, Menlo Park, CA 94025
  Phone: ++1 (650) 859-3379      Fax: ++1 (650) 859-2743
   torsten at synapse.sri.com        http://www.stanford.edu/~rohlfing/

     "Though this be madness, yet there is a method in't"