[Insight-users] Regularization of deformable registration

[Luis Ibanez]

Hi Matthias,


Using the Jacobian of the BSplineDeformable transform sounds reasonable,
be careful not to confuse the GetJacobian() method in the transform
classes with the Jacobian that you need.

The Jacobian computed in the Transforms is the jacobian of
point coordinates with respect to the parameters of the transform.

The Jacobian that you need is the one of the output point coordinates
with respect to the input point coordinates. This is the jacobian
computed in the itkDeformationFieldJacobianDeterminantFilter.


Feeding a penalty based on the Jacobian, into the cost of the metric,
is fine *in theory*,...
but it is not straight forward in practice.

You may have to create your own Image metric, and in the GetValue()
method include a penalty value based on the average value of the
Jacobian determinant, or in the standard deviation of that determinant.


However,


Before you engage in this, I will strongly suggest you to write to the
authors of the paper and request their source code. They may also be
willing to contribute their source code as a technical submission to
the Insight Journal.

If *reproducibility* had any value in the Journals of our field, you
shouldn't have to waste time in reverse-engineering the content of
a published paper.



     Regards,



         Luis




--------------------------------------------
matthias.honal at uniklinik-freiburg.de wrote:
> Hi,
> 
> I would like to use regularization terms for deformable BSpline
> registration in ITK. In (Rohlfing et al, Volume-Preserving Nonrigid
> Registration of MR Breast Images Using Free-Form Deformation with an
> Incompressibility Constraint, TMI 22(6), 2003) it is suggested to monitor
> the Jacobian of the deformation field.
> I found the itkDeformationFieldJacobianDeterminantFilter which might be
> helpful in that context. To be able to actually use such a regularization
> however, a penalty term which contains the jacobian must be included in the
> cost function. Now I'm wondering whether something similar (which I
> probably missed) is already implemented in ITK or whether the
> itkDeformationFieldJacobianDeterminantFilter can be used in a more simple
> way to achieve regularization? Otherwise, the ITK way to go would be to
> implement a new cost function which includes the penalty term and an
> efficient way to compute its derivative?
> 
> I would be happy about any comments to that problem or pointers to code
> examples where something similar is already implemented in ITK.
> 
> Thanks a lot,
> Matthias
> 
> ____________________________
> Matthias Honal
> University Hospital Freiburg
> Dept. of Diagnostic Radiology
> Medical Physics
> Hugstetter Str. 55
> 79106 Freiburg, Germany
> 
> Tel: (++49) 761 270 3922
> Fax: (++49) 761 270 3831
> Email: matthias.honal at uniklinik-freiburg.de
> 
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