Results
Why is Affine Registration Performing Poorly?
Affine transformation should have a least-squares optimal solution
at least as good as the rigid-body, since it has more
parameters. At worst it could find the rigid-body solution, which has lower error!
One possibility: linearized matrix is nearly singular. If a matrix is
poorly conditioned (if it has a large condition number), it will be very sensitive
to noise (Golub). The rigid-body matrix (3XN) is well-conditioned, but
the affine matrix (6XN) is not.
- linearized rigid-body matrix:
cond(L) ~ 20 - 40
- linearized affine transformation matrix:
cond(L) ~ 10^17 - 10^19
This may mean that the linearization of the affine transformation is
an inherently unstable approximation, or it may reflect a bug in my
affine registration code. If the matrix were nearly singular for most
images (as my affine data matrix was for every image pair i gave it),
it would likely mean that a number of existing algorithms need to find
a method of approximation other than the Taylor approximation.