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

[Anja Ende]

Thanks a lot Brian. I still need to get my head over such
diffeomorphic schemes but this helps a lot.

I will spend some time checking out ANT in detail.

Many thanks,
Anja

On 1 September 2010 14:57, brian avants <stnava at gmail.com> wrote:
> 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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>
>
> --
> ß®∫∆π
>



-- 
Cheers,

Anja