Biomedical Engineering Reference
In-Depth Information
typically extracted from the images via an image analysis algorithm, or simply
drawn manually, and are then used to drive a 3D deformable registration method,
which effectively interpolates feature correspondence in the remainder of the brain.
Related are medialness models [30], which use the medial axes of anatomical
shapes as features, instead of boundaries themselves. Feature-based methods pay
more attention to the biological relevance of the shape matching procedure, since
they only use anatomically distinct features to find the transformation, whereas
image matching methods seek transformations that produce images that look alike,
with little warranty that the implied correspondences have anatomical meaning.
However, the latter approaches take advantage of the full dataset, and not only of
a relatively sparse subset of features.
A method that has been previously developed by our group attempts to bridge
between these two extremes by developing attribute vectors that aimat making each
voxel a feature [52, 61, 62], and it was called the Hierarchical Attribute Matching
Mechanism for Elastic Registration (HAMMER). HAMMER is a hierarchical
warping mechanism that has two key characteristics. First, it places emphasis
on determining anatomical correspondences, which in turn drive the 3D warping
procedure. In particular, we have used feature extraction methods whose goal is
to determine a number of parameters from the images, which can characterize at
least some key anatomical features as distinctively as possible. In [52], we used
geometric moment invariants (GMIs) as a means for achieving this goal. GMIs
are quantities constructed from images that are first segmented into GM, WM,
and CSF, or any other set of tissues of interest. They are determined from the
image content around each voxel, and they quantify the anatomy in the vicinity
of that voxel. GMIs of different tissues and different orders are collected into
an attribute vector, for each voxel in an image. Ideally, we would like for each
voxel to have a distinctive attribute vector; of course, this is not possible in reality.
Figure 2 shows a color-coded image of the degree of similarity between the GMI-
based attribute vector of a point on the anterior horn of the left ventricle and the
attribute vectors of every other point in the image. The GMI attribute vector of
this point, as well as of many other points in the brain, is reasonably distinctive, as
Figure 2 shows. HAMMER was constructed to solve an optimization problem that
involves finding a shape transformation that maximizes the similarity of respective
attribute vectors, while being smoothed by a standard Laplacian regularization
term (a detailed description can be found in [52]). We have recently explored
more distinctive attribute vectors, aiming at constructing even more distinctive
morphological signatures for every image voxel. Toward this goal we usedwavelet-
based hierarchical image descriptions of large neighborhoods centered on each
image voxel [63, 64].
A second key characteristic of HAMMER addresses a fundamental problem
encountered in high-dimensional image matching. In particular, the cost func-
tion being optimized typically has many local minima, which trap an iterative
optimization procedure into solutions that correspond to poor matches between
