[ITK] [ITK-users] deformation, displacement and velocity field transforms

[Anja Ende]

Thanks Nicolas!

So, the transformation through the exponentiation is to the actual
displacement/translation of the point rather than the point's new position.


On 10 July 2014 15:07, Nicolas Gallego <nicgallego at gmail.com> wrote:

> Hi Anja,
>
> Yes, as far as I understand the concept, the velocity field lives in the
> tangent space of the manifold, while the displacement field is the actual
> manifold, arbitrarily curved. In practice the transformation between the
> velocity field (tanget space) and the displacement field (curved manifold)
> is done via the exponential chart, and the inverse via the logaritmic.
>
> The exponential is a k times recursive composition of the field with
> itself starting from a scaled version of it by 2^(-K), such that the
> initial field is small enough [1]. That is the equivalent of integrating
> over the unit interval.
>
> [1]
> http://www.itk.org/Doxygen45/html/classitk_1_1ExponentialDisplacementFieldImageFilter.html
>
> hope that helps
>
>
> Nicolás Gallego-Ortiz
> Université catholique de Louvain, Belgium
>
>
> 2014-07-10 12:43 GMT+02:00 Anja Ende <anja.ende at googlemail.com>:
>
>> Hello,
>>
>> I am slightly confused by some terminology in ITK and I was wondering if
>> someone would be kind enough to help me out on this.
>>
>> As far as I understand, a deformation field is the vector field which
>> describes the new <position> of a given point.
>>
>> A displacement field, on the other hand, the distance and the direction
>> that the point has moved.
>>
>> ITK has this ConstantVelocityFieldTransform object. My question is what
>> does the velocity field in ITK encode? If I integrate the velocity field
>> over unit time would I get a deformation or a displacement field?
>>
>> Thanks for any help you can give me.
>>
>> --
>> Cheers,
>>
>> Anja
>>
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>


-- 
Cheers,

Anja
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