[Insight-users] Re: Jacobian determinant image of the deformation field

[Luis Ibanez]

Hi Mathieu, Tom,

Thanks a lot for pointing out this problem.

We are trying to figure out what is the best way to fix this issue.



There seems to be three issues here:


1) Mismatch documentation between the filter
    and its actual computation

2) Whether the filter is intended for

    Deformation field versus Transformation

    Deformation field will have zeros for an identity transformation
    while the Transformation will have an identity matrix.

3) Misnaming of the filter.


---

About (1), we should just remove the comment about adding 1.0
to the output, since it is not really equivalent to adding
the Identity matrix to the Jacobian before computing the
determinant.

 From Tom comment, it seems that the filter name is actually
correct, so (3) may not be an issue.

The filter is indeed intended for a Deformation field and
not for a transformation. This seems to be clear in the
documentation.


However, an additional filter is needed where an Identity
matrix is added to the Jacobian before computing the
determinant.

We could factorize the common code of both filters, and
only have to overload the method:


        EvaluateAtNeighborhood()


So, here are the proposed action items:


1) Create a base class X with the current code of the
    DeformationFieldJacobianDeterminantFilter.

2) Add a class WarpJacobianDeterminantFilter that derives
    from X, and overload  EvaluateAtNeighborhood().

3) Make DeformationFieldJacobianDeterminantFilter derive
    from X too and overload EvaluateAtNeighborhood().

4) Remove the comment about adding 1.0 from the documentation
    of the DeformationFieldJacobianDeterminantFilter.


If that make sense we can log this as a feature request/bug fix
in the phpBugTracker.



   Please let us know what you think,



      Thanks



          Luis


----------------------
Tom Vercauteren wrote:
> Hi Mathieu,
> 
> Just my two cents about it. I do agree with you that the current
> implementation is not computing a really meaningful quantity. However,
> the current name is misleading. Without adding an Id matrix, it
> actually computes the Jacobian of the deformation field, but what we
> usually need is the Jacobian of the spatial transformation... In my
> code, I have added an itk::WarpJacobianDeterminantFilter to make
> things a bit clearer.
> 
> Best,
> Tom
> 
> On 9/6/07, Mathieu De Craene <decraene at tele.ucl.ac.be> wrote:
> 
> Hi ITK folks,
> 
> 
> I found this email on the mailing list
> 
>        
> http://public.kitware.com/pipermail/insight-users/2006-August/019246.html
> 
> and I think these two users are right.
> 
> I was wondering if we shouldn't add the following line at line 250 of
> itkDeformationFieldJacobianDeterminantFilter.h to correct the problem
> 
>        if (i == j) J[i][j] += 1.;
> 
> 
> so that we effectively compute
> 
> 
>        det[ dT/dx ] = det[ I + du/dx ]
> 
> 
> 
> Thanks for any comment,
> 
> 
> 
> Mathieu
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