Trying to use CMTK fit_spline_xform to fit the inverse of an existing transform

cmtk_bspline_example.sh

#!/bin/bash

# Setup
mkdir images
mkdir refbrain
curl -o images/A.nrrd http://flybrain.mrc-lmb.cam.ac.uk/cmtk/A.nrrd
curl -o refbrain/B.nrrd http://flybrain.mrc-lmb.cam.ac.uk/cmtk/B.nrrd

AREG="B_A_9dof.list"
REG="B_A_warp.list"

# Generate registration 1 for A onto B
# munger -b /opt/local/bin/ -aw -l f -C 20 -R 1 -A '--accuracy 2' -W '--accuracy 2' -s 'refbrain/B.nrrd' 'images'
registration -i -v --dofs 6 --dofs 9 --accuracy 2 -o "$AREG" refbrain/B.nrrd images/A.nrrd
warp -v --fast -e 16 --grid-spacing 40 --energy-weight 1e-1 --refine 1 --coarsest 20 --accuracy 2 -o "$REG" "$AREG"
# Reformat A onto B using registration 1
reformatx --outfile A_onto_B.nrrd --floating 'images/A.nrrd' 'refbrain/B.nrrd' "$REG"
# Invert our previous step, giving an A' similar to A
reformatx --outfile A_prime.nrrd --floating 'A_onto_B.nrrd' 'images/A.nrrd' --inverse "$REG"

# Fit B-spline to transformation of A onto B using image B to define output domain
fit_spline_xform --fit-affine-first --final-cp-dims '10,6,4' --levels 3 --output A_onto_B_spline 'refbrain/B.nrrd' "$REG"
# Now produce an image A_onto_B_spline.nrrd, using the spline fit
reformatx --outfile A_onto_B_spline.nrrd --floating 'images/A.nrrd' 'refbrain/B.nrrd' A_onto_B_spline
# not identical to A_onto_B.nrrd, but certainly similar

# OK ALL FINE SO FAR BUT ...
# now we want to fit_spline_xform to the INVERSE of our original image-based transform

# Fit B-spline to inverse transformation (ie we want A to be the reference image)
fit_spline_xform --fit-affine-first --final-cp-dims '10,6,4' --levels 3 --output inverse_spline 'images/A.nrrd' -- --inverse "$REG"
# Hmm, what's odd here is that the initial affine is (almost) the identity transform
# and the spline component is a completely regular grid
# Well let's go ahead and produce an image A'_spline, using the B-spline fit
reformatx --outfile A_prime_spline.nrrd --floating 'A_onto_B.nrrd' 'images/A.nrrd' inverse_spline
# yes, no joy there

# just in case, check without fitting initial affine
fit_spline_xform --final-cp-dims '10,6,4' --levels 3 --output inverse_spline_noaff 'images/A.nrrd' -- --inverse "$REG"
reformatx --outfile A_prime_spline_noaff.nrrd --floating 'A_onto_B.nrrd' 'images/A.nrrd' inverse_spline_noaff
# same deal - completely regular spline grid

# just in case, check with a full size B spline field
fit_spline_xform --fit-affine-first --final-cp-dims '33,17,9' --levels 3 --output inverse_spline_full 'images/A.nrrd' -- --inverse "$REG"
# Produce an image A'_spline, using the B-spline fit
reformatx --outfile A_prime_spline_full.nrrd --floating 'A_onto_B.nrrd' 'images/A.nrrd' inverse_spline_full

# maybe we should still be giving B as the reference image (since it _is_ the reference for the registration we are inverting)
fit_spline_xform --fit-affine-first --final-cp-dims '10,6,4' --levels 3 --output inverse_spline_B 'refbrain/B.nrrd' -- --inverse "$REG"
# do the reformating
reformatx --outfile A_prime_spline_BA.nrrd --floating 'A_onto_B.nrrd' 'images/A.nrrd' inverse_spline_B
# nope that didn't do the trick!

# SO HOW DO WE USE FIT_SPLINE_XFORM ON THE _INVERSE_ OF AN EXISTING REGISTRATION?