[Insight-users] Re: about deformation field : Computing the Jacobian of a Deformation Field.

[Luis Ibanez]

Hi Jesse,


There is not a current filter in ITK that will compute the Jacobian
of a deformation field.  However, you can create such a filter by
using the itkVectorGradientMagnitudeImageFilter as a starting point.

http://www.itk.org/Insight/Doxygen/html/classitk_1_1VectorGradientMagnitudeImageFilter.html


If you take the files

    Insight/Code/BasicFilters/itkVectorGradientMagnitudeImageFilter.h
    Insight/Code/BasicFilters/itkVectorGradientMagnitudeImageFilter.txx

rename them, and rename the class inside,

and then modify the method

         EvaluateAtNeighborhood3D()

that is defined in the header file, in order to return a Matrix instead
of a Scalar value, you can simply take the directional derivative values
of the vector components as they are computed in lines 311-316.


BTW, Do you want the "Jacobian Matrix" ?
   or Do you want the "Determinant of the Jacobian Matrix" ?

Unfortunately it is common to misuse the term "Jacobian"....

If what you want is the determinant... well, you can keep
this method returning a scalar, and just need to invoke
the VNL determinant computation.



Please let us know if you find any problems by implementing
this code.


    Thanks



      Luis


---------------------------
Jesse wrote:

> Hi Luis
> 
>  
> 
> I¡¯m using deformation registration on my datasets, Now I want to get 
> the Jacobian of the deformation field,
> 
> SPM can do it well. but I¡¯m not sure if itk can do this too?  
> 
> Thanks
> 
>  
> 
> Jesse 
> 
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