Biomedical Engineering Reference
In-Depth Information
Besides, some polygonal surfaces may contain more than one object of interest
(see Figure 7). Now, we can use upper bounds for the features. These upper bounds
are application dependent (anatomical elements can be used).
The surfaces whose interior has volumes larger than the upper bound will be
processed at a finer resolution. 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 of
computation in regions where the boundaries enclose only one object.
When the T-Surface's grid resolution is increased, we just reparameterize the
model over the finer grid and evolve the corresponding T-Surfaces. For uniform
meshes, as in the Figure 6, this multiresolution scheme can be implemented through
Adaptive Mesh Refinement
data structures [29]. 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
=2and
n
=3in our case). Such a scheme
has also been explored in the context of
Level Sets
methods [30].
Figure 6.
Representation of the multiresolution scheme.
As an example, let us consider Figure 7. In this image, the
outer
scale cor-
responding to the separation between the objects is finer than the object scales.
Hence, the coarsest resolution could not
separate
all the objects. This happens for
the bottom-left cells in Figure 7a. To correct that result, we increase the resolution
only inside the extracted region to account for more details (Figure 7b).
Instead of using a multiresolution method, we could apply mathematical mor-
phology operators before steps (1)-(4) in order to avoid the problems depicted in
Figure 7a. However, even for these approaches, some manual intervention may
be required to split the upper-right cells in Figure 7b. Besides, due to inhomo-
geneities of the image field (supposed graylevel), some objects may be split in step
(4). Sometimes, T-Surfaces model are not able to merge them again.
To correct these problems, the user can manually burn some grid nodes to
force merges or splits.
From the entropy condition, these nodes remain burnt
