[ITK Community] questions about deformation field composition and comparison

[Matt McCormick]

Hi Gavin,

>
>
> 1. I have checked out the CompositeTransform code, however, I can not
> find where the problem is treated. I am trying to understand how
> deformation at out of bound locations are treated. My current solution is:
>
>         T2(T1(x)) = T2(T1(x)),    if T1(x) within dimension of T2
>         T2(T1(x)) = T1(x),          if T1(x) is out of dimension of T2
>
> Assuming the dimension of T2 is the image size. My current problem is that
> discontinuity happens at locations where T1(x) out of dimension in the
> final composited deformation field.
>

This is a reasonable solution.  Note that T1(x) is not actually being
computed in continuous space, but a discrete sampled space, and an
interpolator is used on T2.  A slight improvement is then to use an
extrapolator for T2 when T1(x) is outside T2.  Depending on the situation,
throwing an exception and not counting the point may be most appropriate.


> 2. Yes, I am comparing the displacement field directly. My problem here is
> also with the out of bound displacements. |T1-T2| will be large if there is
> some locations in T2 has large out of bound displacements. My question is
> whether these out of bound displacement should be reduced in their
> contribution to the displacement error. Because the out of bound
> displacement does not affect the re-sampled image.
>

If comparing two displacement fields that are defined on the same input
domain, it should not matter if any of the displacements end at location
that is out of bounds of the input domain.

Hope this helps,
Matt
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