Biomedical Engineering Reference
In-Depth Information
This is because such techniques often rely on minimize/maximize a similarity
measure which has a large number of local minima/maxima due to the corre-
spondence ambiguity. Examples include methods that minimizing/maximizing
similarity measures between features in the source and target images such as
image intensities, object boundaries/surfaces, etc. In theory, the higher the di-
mension of the transformation the more local minima these similarity measures
have. Methods that use specified correspondences for registration will benefit
less or not at all from the invertibility consistency constraint. For example, land-
mark based registration methods implicitly impose an invertibility constraint at
the landmarks because the correspondence defined between landmarks is the
same for estimating the forward and reverse transformations. However, the
drawbacks of specifying correspondences include requiring user interaction to
specify landmarks, unique correspondences can not always be specified, and
such methods usually only provide coarse registration due to the small number
of correspondences specified.
In this chapter, we will restrict our analysis to the class of applications that
can be solved using diffeomorphic transformations. A diffeomorphic transfor-
mation is defined to be continuous, one-to-one, onto, and differentiable. The
diffeomorphic restriction is valid for a large number of problems in which the
two images have the same structures and neighborhood relationships but have
different shapes.
Diffeomorphic transformations maintain the topology and guarantee that
connected subregions of an image remain connected, neighborhood relation-
ships between structures are preserved, and surfaces are mapped to surfaces.
Preserving topology is important for synthesizing individualized electronic at-
lases the knowledge base of the atlas maybe transferred to the target anatomy
through the topology preserving transformation providing automatic labeling
and segmentation. If the total volume of a nucleus, ventricle, or cortical sub-
region are an important statistic it can be generated automatically. Topology
preserving transformations that map the template to the target can also be used
to study the physical properties of the target anatomy such as mean shape
and variation. Likewise, preserving topology allows data from multiple indi-
viduals to be mapped to a standard atlas coordinate space [23]. Registration
to an atlas removes individual anatomical variation and allows information
from many experiments to be combined and associated with a single canonical
anatomy.
