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

[Nicolas Gallego]

Hi Anja,

Yes, the displacement field is to be applied to the image to warp it to the
fixed image grid, so it is actually the displacement field is used in the
inverse way, it tells the warper for every pixel of the new image where to
look and interpolate from the input image space [1].

The terminology used in actual version is DisplacementField, I saw that the
ExponentialDeformationFieldImageFilter class is being depreciated.


[1]
http://www.itk.org/Doxygen45/html/classitk_1_1WarpImageFilter.html#a75c959bf6fe0d4108a8912723b6337da

Nicolás Gallego-Ortiz
Université catholique de Louvain, Belgium


2014-07-10 18:58 GMT+02:00 Anja Ende <anja.ende at googlemail.com>:

> 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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