[Insight-users] Inversion of transformation fields

[Jens Fisseler]

Hi Ralf,

> I am working on different registration approaches. Some of them consists
> of more then one registration steps (e.g. rigid preregistration and non
> rigid registration). All of them are data driven, so working directly on
> the image. But in some cases, there are some additional information like
> reference points (e.g. fiducals) attached. To keep them up to date
> through out the whole registration process, they also must be
> transformed.
> Now the problem. ITK uses back transform to ensure dense images. This is
> appropriate for the registration of the image itself, but to transform
> meta information (like reference points, to have them up to date in
> interim registration steps) a transform from moving to result image is
> needed. In cases of a rigid registrations I could use the back transform
> function for every single point to achieve this. But the fem, for
> example, only produces a transformation field and has no back transform
> or inversion capabilities.
> Are there any suitable methods to invert this field to achieve a
> transform of points from the moving image space to the result image
> space?
> The easy way: inverting all vectors of the field would only be a
> solution, if the spacing was infinitesimal (whish it was so). So this
> would be no solution.

I don't know which non-rigid registration algorithm (demons, b-splines,
FEM, level-sets) you use, but can't you just simply swap the fixed and
moving images?

If I'm getting you right you wan't to transform the position of the
additional information (e.g. fiducials) from one image to another, which
does not contain this information. So you could use the image _with_ the
additional information as the fixed and the other as the moving image.
The computed transformation T maps physical points from the fixed image
to the moving image, so you could use this to calculate the fiducial
position in the moving image.

Regards,

	Jens