Biomedical Engineering Reference
In-Depth Information
solution by gradual refinements. We first solve a reduced problem using a small
amount of data, then use the solution as an initial guess for the problem at a finer
level. This is repeated until the finest (original) level is reached.
Multiresolution on the search space works similarly, adding degrees of free-
dom to the warping model at each step. We start with a simple model leading to
a simple and easy to solve problem. Then gradually add a manageable amount
of complexity at each step, until the desired model is reached. The model can
be augmented qualitatively, such as going from translation-only to general affine
transform, or quantitatively, for example, by decreasing the control node spacing
in semi-local models.
Related to multiresolution are
multigrid
optimization methods, where oc-
casional backward transitions from finer to coarser levels are used besides the
coarse-to-fine refinement used in the multiresolution [63].
9.2.5
Other Attributes and Features
The
dimensionality
refers to the number of dimensions of the images being
registered. The warping function normally works in the space of the same di-
mensionality, transforming one coordinate vector into another.
Interactive algorithms
need human supervision and interaction, as opposed
to fully autonomous ones. Interactive methods often perform well, taking ad-
vantage of the human expert, but are unsuitable for treating high volumes of
data. Good compromise might be to use hybrid methods, requiring manual in-
tervention or approval only in difficult cases.
In some cases there is no inherent reference and test image, both can play
the same role. Then we would like the registration process to be
consistent
with respect to this choice [69, 70]. Consistency is one of the ways to enforce
invertibility
and preservation of the topology of the transformation, other possi-
bilities involve constraining the Jacobian [71] and composition of diffeomorphic
mappings [32].
9.2.6
Complementary Surveys
There is a wide choice of sources of information on registration algorithms. The
surveys by Brown [5] and a newer one by Zitov a [72] are rather general. Warfield
et al.
[73] concentrate on nonlinear registration for brain warping applications.
