Biomedical Engineering Reference
In-Depth Information
Thus, a method that generates only the connected component being evolved is
interesting, that is, the PL Generation algorithm.
However, what about the seed points? Our implementation of T-Surfaces
uses a hash whose elements are specified by keys composed by two integers:
the first one indicates a simplex and the second the connected component that
cuts the simplex. There is one entry for each simplex of the triangulation. This
structure is simple to implement. There are no additional costs of insertion or
removal operations, and the cost of verifying if a transverse tetrahedron has been
cut is
O
(1). In this structure, seed points are found as follows. Let us take
an intersection point obtained in step (1) of the reparameterization process. If
it belongs to a simplex that is on the hash, the point is stored in a hash entry.
Otherwise, we check if that simplex is a transverse one. If true, the point is stored
and the simplex becomes a new seed to find another connected component through
the PL Generation Algorithm (Section 3). The simplices that are obtained through
this algorithm become new entries on the hash. Following this procedure, when the
queue of projected points is empty, we can be sure that all the transverse simplices
are on the hash. Then, the T-Surfaces components can be obtained by traversing
the hash only once.
The next section presents our segmentation framework, which is the main
contribution of the present work. It is based on application of isosurface techniques
in the context of the T-Surfaces framework. In addition, we take advantage of the
T-Surfaces reparameterization process (Section 2.1) to enable offset generation.
5.
RECONSTRUCTION METHOD AND OFFSET GENERATION
The segmentation/surface reconstruction method that we propose in this chap-
ter is based on the following steps [17]: (1) extract the threshold
T
, or a range
[
T
−
∆
T,T
+∆
T
] that characterizes the objects of interest; (2) coarser image
resolution; (3) define the
Object Characteristic Function
; (4) PL manifold extrac-
tion by the tetra-cubes; (5) if needed, increase the resolution and return to step (3);
(6) apply the T-Surfaces model; (7) user interaction, if needed.
Step (1) can be performed by a simple inspection or any pre-segmentation
step cited in Section 2. It is important to highlight that the T-Surfaces model can
deal naturally with the self-intersections that may occur during the evolution of
the surfaces obtained by step (4). This is an important advantage of T-Surfaces.
Among the surfaces extracted in step (4), there may be open surfaces that start
and end in the image frontiers, small surfaces corresponding to artifacts or noise
in the background. The former is discarded by a simple automatic inspection. To
discard the later, we need a set of predefined features (volume, surface area, etc.),
and corresponding lower bounds. For instance, we can set the volume lower bound
as 8(
r
)
3
, where
r
is the dimension of the grid cells.
