[ITK Community] questions about deformation field composition and comparison

[Gavin Ubuntu]

Matt,

Thank you for your help.

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

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.

I have not done much work in this area, please excuse for inaccuracy in my
questions.

Please let me know if you have further comment. Thank you for your time.

Best Regards,
Gavin


On Tue, Feb 11, 2014 at 9:31 AM, Matt McCormick
<matt.mccormick at kitware.com>wrote:

> 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
>
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