[Insight-users] multi-modality with FEM or with Demons ?

[Luis Ibanez]

Hi Edi,


Answer to question (1):

When you use the FEM-based deformable registration
you are modeling the image as a block of elastic
material on which you apply forces. The forces are
computed based on the local derivatives of image
metrics on points of a coarse grid.

The parameters that control the behavior of the
elastic material are

         Elasticity  (E)
         Density x capacity (Rhoc)

since they are critical on the conversion of forces
into local displacements of the elastic material.

The challenge (and the fun) of deformable registration
is to figure out appropriate range for these values.
You may want to get familiar with the elasticity
equations where the parameters above are used.
In general terms, subject to the same forces, higher
elasticity results in smaller displacements, and
higher density results also in smaller displacements.

You must drive the method by starting with conservative
values and if the resulting displacements are not
enough for correcting the deformations you need, then
reduce the elasticity until you get significant
deformations.



Answer to question (2):

Yes, it is true that Demons is not appropriate for
multi-modality registration. The Demons algorithms
implemented in ITK minimize the Sum of Squared Differences
between the Fixed and deformed Moving image.  The image
must have similar gray level distributions.  It is
recommended to match their histograms first using
the HistogramMatchingImageFilter
http://www.itk.org/Insight/Doxygen/html/classitk_1_1HistogramMatchingImageFilter.html


Answer to question (3):

DEMONS doesn't have a direct equivalent among the
physical models of FEM-Based registration. Demons
is based on heuristics of local deformation exerted
by local forces that are regularized by smoothing
them with a low pass filter (like a Gaussian filter).
It is closer to the optical flow model used in
computer vision. Demons do not model a fluid, since
there is no notion of volume nor mass preservation,
not even prevention of folds, (the method relies on
the smoothing for preventing folds from happening).

You can configure a viscous fluid model using
FEM though. It will require some coffee and patience
on your part since you have to put together the
elements representing the equations of the viscous
fluid.

Note that all of these models are totally artificial
and do not represent the reality of the patient's anatomy.
So, to be pragmatic, it is not worth to suffer much
trying to match the math of the models since they are
simply heuristic approximations intended to produce
deformation fields that are relatively easy to control.
At the end *ANY* algorithm that allows you to locally
deform the image is good enough to be used for image
registration. So, what matter the most is how easy
is for the user to figure out the parameters controlling
the deformation.

Along those lines of reasoning, you may want to look
at the BSpline transform for managing deformable
registration. In this method, a BSpline is used to
interpolate deformations over a coarse grid overlapped
on top of the image. you control the deformation by
initializing the nodes of the grid.




Regards,



    Luis



---------------------------
Schreibmann Eduard wrote:

> Hello everybody,
> 
> Question 1 :
> I want to use FEM to register some CT and MRI images, 
> using the  DeformableRegistration1.exe. With the 
> demo images, it works great but...
> 
> When using some CT and MRI images that came with ITK (
> BrainT1Slice and BrainProtonDensitySlice.png ), and
> with setting the metric to 3 (MI) in the configuration
> file, the application finishes after 2-3 iterations
> without doing something visible to the input image.
> Basically, the only thing changed in the parameter
> file was file names and metric type.
> 
> What parameters control this behavior ? 
> What settings are appropriate for this job ?
> 
> Question 2: Is it true that demons can not be used for
> multi-modality registration ?
> 
> Question 3: The "viscous fluid landmark" registration
> has anything to do with demons or FEM ?
> 
> Thank you in advance,
> 
> A nice day,
> Edi
> 
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