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

Tom Vercauteren tom.vercauteren at m4x.org
Thu Sep 2 12:10:00 EDT 2010


Sorry, sent a  wrong link for Arsigny et al.'s paper. Here is the right one
http://www.inria.fr/sophia/asclepios/Publications/Arsigny/arsigny_miccai06.pdf

Tom

On Thu, Sep 2, 2010 at 17:29, Anja Ende <anja.ende at googlemail.com> wrote:
> 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_miccai06.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
>>> _____________________________________
>>> Powered by www.kitware.com
>>>
>>> Visit other Kitware open-source projects at
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>>> Kitware offers ITK Training Courses, for more information visit:
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>>
>
>
>
> --
> Cheers,
>
> Anja
>


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