[Insight-users] Computation of this gradient involving velocity fields

[Anja Ende]

Hello all,

This is more of a general image processing question rather than ITK.
However, I am hoping someone here could still help me with this.

I have been looking at some of the registration toolkit developed in ITK
like ANTs and diffeomorphic demons and one thing that these modern methods
do is parameterise the deformation with velocity fields. Where the moving
image is resampled as F(exp(v)) where exp(v) is the deformation field. Now,
suppose one wants to optimise such a system with gradient descent and has
some energy function which contains this term and just looking at this term
for the moment, one needs to compute its derivative with respect to the
velocity field v.

So, I think one has some expression like dF(exp(v))/dv = exp(v).F'(exp(v)).
Is this correct and would F'(exp(v)) be just the spatial gradient in this
case?

Would really appreciate your input on this.

Many thanks,

Anja
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