If we apply conventional unregularized
3D image registration using B-splines
to warp the inhale images
onto the exhale images
then we would get the following results.
The grid
shown on the right
illustrates that the
estimated deformation
is unrealistically irregular,
and not locally invertible.
This is physically implausible.
Graduate student Se Young Chun
developed an improved image registration algorithm
(to be presented at ISBI 2008)
that constrains the deformation
to be locally invertible
by including a special regularization function
in the cost function that is optimized.
His method is faster than the Jacobian penalty functions
used previously
and yields the following results.
The estimated deformation is much more realistic
for breathing motion.
CT of thorax at exhale and inhale, and estimated 3D deformations with and without invertibility constraint.