Biomedical Engineering Reference
In-Depth Information
Figure 7.10:
Representation of the multiresolution scheme.
The surfaces whose interior have volumes larger than the upper bound will be
processed in a finer resolution. By doing this, we adopted the basic philosophy
of some nonparametric multiresolution methods used in image segmentation
based on pyramid and quadtree approaches [3, 8, 41]. The basic idea of these
approaches is that as the resolution is decreasing, small background artifacts
become less significant relative to the object(s) of interest. So, it can be easier
to
detect
the objects in the lowest level and then propagate them back down the
structure. In this process, it is possible to
delineate
the boundaries in a coarser
resolution (step (4)) and to re-estimate them after increasing the resolution in
step (5).
It is important to stress that the upper bound(s) is not an essential point
for the method. Its role is only to avoid expending time computation in regions
where the boundaries enclose only one object.
When the grid resolution of T-surfaces is increased, we just reparameterize
the model over the finer grid and evolve the corresponding T-surfaces.
For uniform meshes, such as the one in Fig. 7.10, this multiresolution scheme
can be implemented through
adaptive mesh refinement
data structures [5]. In
these structures each node in the refinement level
l
splits into
η
n
nodes in level
l
+
1, where
η
is the refinement factor and
n
is the space dimension (
η
=
2 and
n
=
3 in our case). Such a scheme has also been explored in the context of
level
sets
methods [61].
As an example, let us consider Fig. 7.9. In this image, the
outer
scale corre-
sponding to the separation between the objects is finer than the object scales.
Hence, the coarsest resolution could not
separate
all the objects. This hap-
pens for the bottom-left cells in Fig. 7.9(a). To correct this result, we increase
the resolution only inside the extracted region to account for more details
(Figure 7.9( b)).
We shall observe that T-surfaces makes use of only the data information along
the surface when evolving the model toward the object boundary. Thus, we can
