[ITK Community] questions about deformation field composition and comparison

[Matt McCormick]

Hi Gavin,

> 1. composition of deformation field
>     I understand the principle of composition. Say I have an inverse DF1
> followed by an inverse DF2 being applied to a floating image. The
> composition will be DF1(DF2(x,y)) for every pixel (x,y) in the coordinate
> system of the fixed image. However, what if DF2(x, y) deforms to an out of
> dimension location (x', y'), then DF1(x', y') is undefined. What is
> DF1(DF2(x,y)) now, should it be DF1(DF2(x,y)) = (x', y')? My worry is that
> the final composed deformation will have a peak at (x, y). Assume DF1 is a
> large deformation, DF2 is a small deformation, make DF1(DF2(x,y)) = (x', y')
> my not follow the overall smoothness introduced by DF1.

If resampling, out-of-bounds issues with displacement field transforms
will causes issues.  However, if the CompositeTransform [1] is used,
these issues can be largely avoided.

> 2. comparison of deformation field
>     I am trying to compare an estimated deformation field with a ground
> truth (synthetic deformation field). My question is related to the out of
> dimension again. If the known deformation at a pixel (x, y) is within image
> range, but my estimated deformation is out of dimension pointing to a really
> large error location, then the error at this pixel largely affects the
> evaluation. How should I treat errors at these out of boundary locations
> when performing such evaluation?

It sounds like a comparison of the resampled images is attempted to
compare the displacement fields?  It may be better to directly compare
the displacement fields directly.

Hope this helps,
Matt

[1] http://www.itk.org/Doxygen/html/classitk_1_1CompositeTransform.html