Biomedical Engineering Reference
In-Depth Information
and reverse transformations, respectively. This term penalizes large derivatives
of the displacement fields and provides the smooth interpolation away from
the landmarks. The second integral is the inverse consistency constraint (ICC)
and is minimized when the forward and reverse transformations are inverses
of one another. This integral couples the estimation of the forward and reverse
transformations together and penalizes transformations that are not inverses
of one another. The constants
ρ
and
χ
define the relative importance of the
bending energy minimization and the inverse consistency terms of the cost
function.
The cost function in Eq. (6.14) is iteratively minimized until the landmark
error and the inverse consistency error fall below problem specific thresholds
or until a specified number of iterations are reached. In practice, this algorithm
converges to an acceptable solution within five to 10 iterations and therefore
we use a maximum number of iterations as our stopping criteria. See [34] for
more details of this algorithm.
6.4.3
Combined Intensity and Feature-Based Inverse
Consistent Registration
Landmark based registration algorithms provide good registration at landmark
points where correspondence is known, but use interpolation away from the
landmarks to define correspondence. The correspondence defined by the inter-
plolation function does not always give acceptable correspondence away from
the landmarks. On the other hand, intensity based registration provides good
registration of intensity features contained in the images. However, intensity
based correspondence funtions provide correspondence without regard to the
structure of the objects being matched causing noncorresponding structures to
be registered. Combining landmark and information from other features such as
contours, surfaces, and subvolumes with intensity information helps avoid regis-
tration errors in uncertain or ambiguous areas of the respective cost functions.
For example, landmarks are good at getting corresponding points registered
and the intensity based cost function is good at registering points in between
landmarks. In general, the more information that the registration algorithm has
to define correspondences, the better the registration result will be. Examples
of inverse consistent image registration combining landmark, subvolume, and
intensity information can be found in [34-38].
