[Insight-users] Generating a velocity field from a deformation/displacement field

[brian avants]

hi anja

there are a few ways to look at this .... and a few things to consider

1. a velocity field is just a regularized displacement field that may
or may not be constant in time.

2. the required regularity in the field is related to the amount of
time and the way in which you will integrate the field

3. the velocity and deformation are related, most generally, through
an ODE such as

D(x,t) = v(D(x,t),t) .

A crude way to convert a deformation to a velocity field and integrate it is :

v_0 = 1/n * D , where D is the deformation and w is the v_0 is the
constant velocity
w_0 = v_0
w_{j+1} = w_j( v_0 )   where j runs from 0 to (n-1).

w_{n-1} gives you a weak, approximate diffeomorphic version of D if D
is regular enough.

and this is valid only over small time interval.   ITK probably has
some tools for this --- ANTs (google "ants picsl") certainly does.  in
itk you can probably apply the WarpImageFilter to an image with vector
voxels.  and then add it as in the above algorithm ...


brian


On Wed, Sep 1, 2010 at 9:30 AM, Anja Ende <anja.ende at googlemail.com> wrote:
> Hello everyone,
>
> Is there an easy way in ITK to generate a velocity field from a
> deformation field? I have a displacement field where each voxel
> contains a displacement vector (transformed position - initial
> position). What would be an easy way to estimate the velocity field? I
> am guessing the velocity field would just be the first derivative of
> this deformation field. Is that correct?
>
> Cheers,
>
> Anja
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