Digital Signal Processing Reference
In-Depth Information
strategically around or in areas of interest so that an interpolated deformation field
will provide meaningful correction to regions of interest. For example, deriving
fiducial locations from externally placed markers is an effective way of attaining
surface alignment, but does not in general provide accurate alignment of internal
structures. Internal fiducials are able to align internal structures, but such markers
are invasive and have limited clinical application.
7.2
Intensity-Based
Intensity-based image registration algorithms rely on correlations between voxel
intensities and are known to be robust and computationally intensive. Since
landmarks are not explicitly provided, intensity-based approaches can utilize any
number of approaches to model and apply deformation fields. Construction of the
deformation field can start from just a few parameters in the case of rigid registration
or from a set of points, which capture the non-uniformity of nonrigid registration.
The final transformation contains the information necessary to deform all of the
voxels in the floating image. Once a transformation is constructed, it is applied to
the floating image. This transformed image can be compared to the reference image
using a variety of morphological operations such as mean squared difference (MSD)
or mutual information. For iterative approaches, the similarity value is returned so
that it may guide towards successively better solutions. Problem parameters may
change during runtime to improve speed and accuracy.
7.2.1
Similarity
The foundation of intensity-based image registration is the calculation of how
similar two images are. The similarity calculation guides the transformation of the
floating image and can be part of the convergence criteria. In an iterative intensity-
based algorithm, the similarity calculation tends to dominate the execution time even
for simple similarity metrics, because of the time it takes to traverse and transform
the images.
A common complication of determining if a transformed floating image is similar
to a reference image is the problem of overlap. Since images and regions of interests
have boundaries beyond which we often have no data, similarity measurements must
account for solutions that lead to non-overlapping voxels. Similarity metrics are
often normalized with respect to overlap, by dividing the result by the number of
overlapping voxels. This gives a per voxel account of similarity that mitigates some
of the effects of changing overlap.
One of the simpler similarity metrics is sum of squared differences in which
intensities between images are assumed to be directly correlated, which can work
well for single modality registration. But since intensity values mean different
things in different images, registration engines often apply more flexible (but
