[ITK] On the deformable model

[Nicolás Barnafi]

Hi Matt,

That clarifies everything, thanks for the references and time.

Best regards!

On 3 April 2017 at 18:00, Matt McCormick <matt.mccormick at kitware.com> wrote:

> Hi Nicolás,
>
>
> > I think I haven't explained myself correctly. At the end of the
> presentation
> > there is a variational formulation of the problem, different to the one
> > shown at the Optical Flow section. In that one, the problem reads
> >
> > D[R,T;u] + a S[u],
> >
> > which you can derivate to get a nonlinear system of equations
> >
> > Au = f(u).
> >
> > This is an SSD metric with an elastic penalization (assuming S is such a
> > functional) and as far as I understand it should be the default metric as
> > stated in the software guide. This setting has no temporal evolution, and
> > can be solved by a fixed point iterative scheme as
> >
> > A u[k+1] = f(u[k])
> >
> > or through a Newton-Raphson iterative scheme by looking for solutions of
> >
> > F(u) := Au - f(u) = 0,
> >
> > where you take a derivative and then iterate taking F(u[k+1]) = 0. Up to
> > this point, there is no time in any sense, which is confusing from the
> > example. When I read the code from DeformableRegistration1.h (the
> example I
> > mentioned before) and follow all the way what is happening, first the
> metric
> > is loaded
> >
> > https://github.com/InsightSoftwareConsortium/ITK/blob/
> aecfac233e8815cdd0121fd2351dd3fef80d2e1b/Modules/Registration/FEM/include/
> itkFEMRegistrationFilter.hxx#L536-L538
> >
> > and then the solver is called to iterate
> >
> > https://github.com/InsightSoftwareConsortium/ITK/blob/
> aecfac233e8815cdd0121fd2351dd3fef80d2e1b/Modules/Registration/FEM/include/
> itkFEMRegistrationFilter.hxx#L547-L549.
> >
> > Now, if I go to check the kind of solver used, it is the CrankNicolson
> > Solver
> >
> > https://github.com/InsightSoftwareConsortium/ITK/blob/
> aecfac233e8815cdd0121fd2351dd3fef80d2e1b/Modules/Registration/FEM/include/
> itkFEMRegistrationFilter.h#L145
> >
> > and checking the documentation for it says explicitly it is used for time
> > dependent problems
> > (https://itk.org/Doxygen/html/classitk_1_1fem_1_
> 1SolverCrankNicolson.html),
> > which the mentioned formulation is not.
>
> While SolverCrankNicolson can be used for time dependent problems, in
> the context of the presentation (Au = f) and the example,
>
>   https://github.com/InsightSoftwareConsortium/ITK/blob/
> f9110a0046a9d07a921767ba000443ad006a2c9b/Examples/RegistrationITKv4/
> DeformableRegistration1.cxx#L131
>
> you are correct -- it is not being used for time-dependent problems,
> because they are only using a stiffness matrix and not a mass matrix.
>
> https://github.com/InsightSoftwareConsortium/ITK/blob/
> f9110a0046a9d07a921767ba000443ad006a2c9b/Modules/Numerics/FEM/include/
> itkFEMSolverCrankNicolson.hxx#L298-L318
>
>
> > Now, in the variational Registration
> > filter
> > (https://itk.org/Doxygen/html/classitk_1_1VariationalRegistrationFilter
> .html),
> > [...]
>
> To clarify, there are five different registration frameworks within ITK.
>
> 1) The Variational Registration framework
>
> 2) The ITKv3 Registration framework
>
> 3) The ITKv4 Registration framework (classes have "v4" suffix).
>
> 4) The PDE deformable registration filters (these include optical flow
> algorithms)
>
> 5) The FEM Registration
>
> The VariationalRegistrationFilter is from the Variational Registration
> framework and is not used by FEM Registration.
>
>
> It sounds like you are most interested in variational registration,
> and the Variational Registration and ITKv4 Registration could help.
> More information can be found here:
>
>   http://hdl.handle.net/10380/3460
>   https://itk.org/Doxygen/html/group__VariationalRegistration.html
>
>   https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4009425/
>   https://itk.org/Doxygen/html/group__ITKMetricsv4.html
>   https://itk.org/Doxygen/html/group__ITKRegistrationMethodsv4.html
>   https://itk.org/Doxygen/html/group__ITKOptimizersv4.html
>
>
> I hope this helps.
>
> Matt
>



-- 
Nicolás Alejandro Barnafi Wittwer
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