[ITK Community] questions about deformation field composition and comparison

[Gavin Ubuntu]

Hi, all,

I have two questions regarding deformation field, I hope someone can help
me understand.

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.

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?

I am confused and can not find related answer, thank you for helping.
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