[Insight-users] Question about workings of ExponentialDeformationFieldImageFilter

[Anja Ende]

Hi Tom,

Many thanks for the reply! Much clearer now.
>
> Correct. Mathematically you have
>  exp(Phi/2^N) \approx Identity + Phi/2^N
> but in the code you always use a vector field which is a deviation
> from the identity (displacement field) hence
> you represent the spatial transformation Identity + Phi/2^N by
>  Identity + Phi/2^N - Identity = Phi/2^N

Ahhhh...so we are using displacement fields rather than position fields.

>> - The last question is that when the number of iterations is 0, the
>> output of the filter is set to the input deformation field. Why is
>> that? I am a bit confused on this point.
>
> If the number of iterations is zero, you simply use the Taylor
> expansion you mention. This is thus the same question as the first
> one.

Ahhhh...that was silly of me. Thanks.

I have a small related question. I was reading your SPIE paper from
last year where you use NMI forces to adapt the registration for
inter-modal registrations. In this paper, you use a conjugate gradient
based optimisation scheme where you use the NMI gradient as the
driving force. I wanted to ask whether it is theoretically sound to
use the conjugate gradient scheme as there is a line in the mentioned
paper about maybe this approach being on a bit shaky mathematical
foundation. I was wondering if you would be kind enough to comment on
that as I am quite keen to try and implement this in the ITK
framework. I was looking for a subsequent publication regarding this
but there seems to be very little work on this. I would like to try
and code this up in the ITK framework.

Many thanks again for your replies.

Anja