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

[Nicolas Gallego]

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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