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

[Anja Ende]

Thanks Tom. I think I will need to read these papers and try to get my
head around some of these concepts.

Many thanks,

Anja

On 2 September 2010 08:33, Tom Vercauteren <tom.vercauteren at m4x.org> wrote:
> Hi Anja,
>
> As an alternative to what Brian proposed, if what you need is a
> velocity field which is constant in time and if your displacement
> field is diffeomorphic (i.e. using Arsigny et al.'s terminology, you
> want the logarithm of the displacement field), then you might rely on
> Arsigny et al.'s algorithm
>  http://www.inria.fr/sophia/asclepios/Publications/Arsigny/arsigny_mrm_2006.pdf
> or on the more computationally efficient one from Bossa at al.
>  http://diec.unizar.es/intranet/articulos/uploads/mfca08.pdf.pdf
>
> Pierre Fillard just wrote an initial ITK version of Bossa's algorithm
> and we have just integrated it in the following IJ submission:
>  http://hdl.handle.net/10380/3060
>
> Hope this helps,
> Tom
>
> On Thu, Sep 2, 2010 at 07:57, Anja Ende <anja.ende at googlemail.com> wrote:
>> 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
>> _____________________________________
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>> Visit other Kitware open-source projects at
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>



-- 
Cheers,

Anja