[Insight-users] Adding a penalty to deformable registration

[Kris Thielemans]

Hi all

Short question: how do I add a penalty to a deformable image registration ?


I don't think there is a facility for this in ImageToImageMetric. I could
make a new derived class (e.g. from MeanSquaresImageToImageMetric) that adds
a penalty on the basis of the transform parameters (for instance in terms of
the determinant of the jacobian). But I expect that this must be present
already somewhere...


Long question:

In my continuing quest to get a good deformable registration for my
piece-wise constant images, I believe I should add a penalty to the
registration algorithm. At present, I'm getting some reasonable results
after 5 iterations of a sligthly modified version of DeformableRegistration7
(i.e. BSplineTransform, MeanSquaresImageToImageMetric, LBFGSBOptimizer), but
then it seems to go all wrong.

In any case, my problem is not very well-defined, as especially with
piece-wise constant images there are arbitrary deformations that leave
uniform regions untouched, for example some internal stretching/compression
that leaves the boundary intact. 

[ side note: I'm still a bit unclear if the transform includes the
volume-change (that is, a stretched voxel would decrease its activity). If
so, I guess this non-uniqueness would mostly disappear. I can still imagine
a spherical object though that would be left intact by rotations. ]

In any case, I feel it would be best to add some penalty on the deformation
parameters as I'm only interested in not-too-crazy deformations. Moreover it
should make the problem numerically more stable.

So, a penalty seems a good thing to do.

I'd appreciate any help

Kris Thielemans
Hammersmith Imanet, part of GE Healthcare
London, United Kingdom