[ITK-users] Regularization of itkDemonsRegistration

[alexlovesmath]

All,

I appear to be having troubles with my ITK-users login. I apologize in
advance if I have mistakenly sent multiple copies of this post to the group.

Here is my question:

I am using ITK 4.2 and have a question about the implementation of
itkDemonsRegistrationFilter. 

My question relates to the order of regularization of the accumulated field
in each iteration of Demons. 

What I conjecture is happening in itkDemonsRegistrationFilter is that
regularization of the accumulated field must happen at the beginning of each
iteration. I believe this implies that in the last iteration of the filter,
the displacement field returned by filter->GetOutput() is the result of the
composition of a regularized accumulated field from all past iterations and
the update field, but that a final regularization is not performed. 

I have tested my hypothesis by running the DeminsRegistrationFilter for one
iteration starting with the identity transformation (all zeros) as the
initial condition for the displacement field, once with
SmoothDisplacementFieldOff() and once with SmoothDisplacementFieldOn() (I'm
using the default where SmoothUpdateField is off). In both cases, I obtain
the same result. I think this has to imply that the regularization of the
accumulated field is done at the start of each iteration. 

My questions: 

1) Am I correct that at the end of each iteration, the previously
regularized accumulated field is composed with the update field and that
this is the result returned by filter->GetOutput(). 

2) Is there some reason not to regularize the accumulated field "on the way
out" at the end of each iteration? Is there some algorithmic advantage to
this? I do understand that if a non-identity displacement field was
specified as the initial condition, that the current architecture has the
advantage of regularizing the initial condition. However, it is possible to
regularize the initial condition outside the iterative loop and still
achieve regularization of the accumulated field at the end of the last
iteration. 

Thanks! 

- Alex



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