[ITK] On the deformable model

[Matt McCormick]

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
>
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