[Insight-users] Concatenation of deformation fields?

Sat Mar 27 14:30:23 EDT 2010

Hi Gerald,

This process might actually be eased by a utility class called
  DisplacementFieldCompositionFilter
that you will find in the following IJ paper:
  http://www.insight-journal.org/browse/publication/644

This filter does exactly the combination of steps 2 and 3 proposed by Luis.

Hope this helps,
Tom

On Sat, Mar 27, 2010 at 17:04, Luis Ibanez <luis.ibanez at kitware.com> wrote:
> Hi Gerald,
>
> Thanks for your very detailed clarification.
>
> Just to simplify the email notation,
> let me add the following two definitions:
>
> A  :=  D_r^-1
> B  :=  D_n^-1
> C  :=  D_n,r^-1
>
>
> so the deformation field "C" is the result
> of composing the deformation field "A"
> with "B".
>
> Therefore, for every point x, its deformed
> target x" will be computed as:
>
>           x" =  C(x) = B( A (x) )
>
> that is
>
>           x'   = A( x )
>           x"  = B( x' )
>
>        x"  = C( x ) = B( x' ) = B( A ( x ) )
>
>
> Let's now name the coordinate frames:
>
> F1 := The original image from
>          which the points "x" are taken.
>          This is the undeformed image.
>
> F2 := The deformed image that results
>         from applying the field A to all the
>         points of  F1.
>
> F3 := The deformed image that results
>         from applying the field B to all the
>         points of F2.
>
>
> With your current processing you have
> direct access to the fields "A" and "C".
>
>   "A" maps the coordinate system F1 to F2
>   "C" maps the coordinate system F1 to F3
>
> and you are interested in finding the field B
> where
>
>   "B" maps the coordinate system F2 to F3
>
> So one way to *estimate* the field "B" is
> the following.
>
> 1) Use the filter
>
>     Insight/Code/BasicFilter/
>         itkIterativeInverseDeformationFieldImageFilter.h
>
>    in order to estimate A^-1, (let's call it A' so it looks
>    better in an email:   A' = A^-1.
>
>       A'  maps the coordinates from F2 to F1
>
> 2) Having A' you can now visit all the points x' of F2,
>    map them to x in F1 via A', and then map their
>    destinations to F3 via C.
>
>                         x'' =   C ( A'( x' ) )
>
>    Therefore you can build an estimation of B by
>    composing   C with A'
>
> 3) Note that when you apply A' to a point x', the
>    resulting point x will not land exactly in the grid
>    node of the image F1, and therefore, you will
>    have to interpolate from C in order to find the
>    corresponding destination.
>
>    For this purpose you can use the class
>
>       Insight/Code/Common/
>           itkVectorLinearInterpolateImageFunction.h
>
>
>
> If you compose steps (1),(2),(3) in to an ITK filter,
> that will make a very nice contribution to the
> Insight Journal    :-)
>
>
>
>    Regards,
>
>
>         Luis
>
>
> ----------------------------------------------------------------------------------------------------
> On Fri, Mar 19, 2010 at 3:30 AM, Lodron, Gerald
> <Gerald.Lodron at joanneum.at> wrote:
>> Hi
>>
>> I do not exactly know what you mean but i will try to explain my pipline in a little more detail:
>>
>> In principle i have two 3D data sets with I1 = 512 x 512 x z1  and I2 = 512 x 512 x z2. The origin and pixel spacing could be different. So the first thing i do is to calculate a new image I2iso = f(I1) and I2iso = f(I2) so that the pixel spacing becomes isotrophic, i mean pixel spacing in x y and z is now the same and also equal for I2iso and I1iso (spacingX1=spacingY1=spacingZ1=spacingX2=spacingY2=spacingZ2). I need an isotrophic pixel spacing because i use the demon registration in my nonrigid step (and the usepixelspacing function of the filter always leads to an error).
>>
>>
>> Now i made two registrations, a coarse one (i called it rigid which is wrong) and a fine one where the coarse one is implemented via two subregistrations. First i make a versor registration, so i compute translation and rotation. Then i make a coarse Bspline like in the examples with 4 grid points and the versor result as initial parameters. The result is converted into a deformation field (for sure in reference to the fixed image), this is called my D_r^-1 (i know it is not pure rigid, but nearly).
>>
>> Now i make my nonrigid registration using a multiscale demon registration filter with the initial deformation field of the quasi rigid step (D_r^-1). So the result is the combination of the known D_r^-1 and the unknown D_n^-1 which is called D_n,r^-1.
>>
>> I want to display changes (which should refer to the norm of D_n-1) in the registered image (so I1 transformed with D_n,r^-1) so i need to extract D_n-1 from D_n,r^-1 using D_r^-1 and thats not a simply substraction...
>>
>>
>>
>>
>>
>> -----Ursprüngliche Nachricht-----
>> Von: Luis Ibanez [mailto:luis.ibanez at kitware.com]
>> Gesendet: Donnerstag, 18. März 2010 17:32
>> An: Lodron, Gerald
>> Cc: insight-users at itk.org
>> Betreff: Re: [Insight-users] Concatenation of deformation fields?
>>
>> Hi Gerald,
>>
>> It should be possible to separate the non rigid component from the final deformation field.
>>
>> Did you compute both the
>>
>> 1) D_r^1      and
>> 2) D_n^1
>>
>> in the same image grid ?
>>
>> Note however that the key point here is a problem of reference systems.  The non-ridig deformation field will be one with respect to the rotated image, not with respect to the original image.
>>
>>
>>      Luis
>>
>>
>> --------------------------------------------------------------------------------------
>> On Wed, Mar 10, 2010 at 11:52 AM, Lodron, Gerald <Gerald.Lodron at joanneum.at> wrote:
>>>
>>> Hi,
>>>
>>> I have a quite interresting problem and I am not sure if it is solveable but maybe someone can help:
>>>
>>> I made a rigid registration and converted the output to a deformation field, let us name it D_r^-1 (it is the inverse deformation because of inverse mapping). After that i made a nonrigid registration with the R_rigid^-1 as start deformation value, the output is the inverse deformation field of the rigid and the nonrigid registration, let us call it D_r,n^-1.
>>>
>>>  My question is, is it possible to calculate the pure nonrigid deformation field D_n^-1 ?
>>>
>>> Best regards
>>>
>>>
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