[ITK] On the deformable model

[Nicolás Barnafi]

Hi Matt,

Thanks the quick answer and welcome :) . That is indeed the ppt. There they
define two energies and then write an integral in terms of some
"similarity" which wasn't really defined. Maybe it is the E_D term?
Hopefully the same applies for smoothness (E_S), but I'm not sure. In the
code I had trouble because RunRegistration uses MultiResSolve, and there
they instantiate a solver which uses Update(). I couldn't find Update in
either .h or .hxx files, and apparently update is redirected (somehow) to
AssembleKandM. The Doxygen page for the CrankNicolson solver shows a
formulation of the method but not for what problem, and that leaves other
questions without answer, such as the boundary conditions, elements used
for the FEM formulation, etc. Thanks so much for your time.

Best regards

On 23 March 2017 at 18:34, Matt McCormick <matt.mccormick at kitware.com>
wrote:

> Hi Nicolás,
>
> Welcome to ITK!
>
>
> Is this the PowerPoint?
>
>   https://itk.org/CourseWare/Training/NonRigidRegistrationMethods
>
> Note that DeformableRegistration1.cxx (FEM registration) is discussed
> after the optical flow example.
>
>
> Some more information on the FEMRegistrationFilter can be found in its
> class documentation:
>
>   https://itk.org/Doxygen/html/classitk_1_1fem_1_
> 1FEMRegistrationFilter.html
>
> Multiple metrics are available:
>
>   https://itk.org/Doxygen/html/classitk_1_1fem_1_
> 1FEMRegistrationFilter.html#acc636f4752e592cd780503a5fbfeba82
>
>
> In general, "the code reveals all" and should be given the highest
> amount of trust.
>
>
> Hope this helps,
> Matt
>
> On Thu, Mar 23, 2017 at 4:32 PM, Nicolás Barnafi <nabw91 at gmail.com> wrote:
> > Hi everyone,
> >
> > I have been trying to understand exactly what is happening in the
> > DeformableRegistration1.h file without much success. The problem is:
> > according to the software guide, the problem being solved comes from the
> > variational problem given by
> >
> > min D[image1, image2; u] + S[u]
> >
> > where D is just the SSD (or the L2 norm of (Im1 - Im2 o phi), with phi
> the
> > unknown displacement field) and S is a linear elastic potential. From
> here
> > you get  the euler lagrange equations (asuming some unspecified boundary
> > ocndition) and solve it using some semi implicit newton-raphson scheme.
> This
> > is where it starts getting blurry, because the ITK ppt on deformable
> > registration first shows an optical flow formulation, which would mean
> that
> > the SSD metric isn't really what is being used, and also if I dig deeper
> in
> > the code, I find actually a Crank-Nicolson scheme being used, which
> really
> > implies some kind of temporality that really does not exist in the
> > variational formulation. The only hint I have found was in Modersitzki's
> > book where a fixed point scheme is artificially stabilized:
> >
> > A(u[k+1]) = f_u[k]
> >
> > => u[k+1] + t A(u[k+1]) = t f_u[k] + u[k].
> >
> > I would want to know what is exactly happening in that example to be
> able to
> > validate an example I implemented in python. Thanks for your time.
> >
> > Best regards
> >
> >
> >
> > --
> > Nicolás Alejandro Barnafi Wittwer
> >
> > _______________________________________________
> > Community mailing list
> > Community at itk.org
> > http://public.kitware.com/mailman/listinfo/community
> >
>



-- 
Nicolás Alejandro Barnafi Wittwer
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