Biomedical Engineering Reference
In-Depth Information
(a)
(b)
Figure 7.
(a) PL manifolds for resolution
3
×
3
.
(b) Result with the highest (image)
resolution.
until the end of the process. This functionality can be implemented by selecting
grid nodes with a pointer (e.g., a mouse), through implicitly defined surfaces (see
Section 6 below), or through a
virtual
scalpel.
We next we present our offset generation approach. Its background is also the
T-Surfaces framework.
5.1. Offset Generation
Offsets have been used for computing levels of detail of a given polygonal
object [31], as well as for initialization of Dual Snakes approaches [18]. Offset
surfaces can self-intersect, and procedures to address this problem may be compu-
tational expensive. The efficiency of T-Surfaces to avoid self-intersections is the
main point of using this model for offsets generation.
To describe our approach, let us first assume that we have an oriented and
connected PL Manifold
S
. In this chapter we call an
n
-offset of
S
the polygonal
surface obtained after
n
iterations of the T-Surfaces model initialized through
S
with
γ
=0in Eq. (5).
Before applying T-Surfaces, we should initialize the Characteristic Function.
As the PL Generation Algorithm attempts to trace the surface into neighboring
simplices, we do not need to visit all grid nodes to perform this task. In fact,
we need only trace the combinatorial manifold whose dual is
S
. This can be
implemented by considering that
S
is oriented. Thus, given a simplex cut by the
surface, we can distinguish the vertices that lie inside from the ones that lie outside
S
. Henceforth, we reduce the complexity of the initialization step.
