Biomedical Engineering Reference
In-Depth Information
Snake formulation in a region-based scheme
The “region terms” [7] are added to the minimization scheme as follows:
g
(Ω
in
)
dxdy
+
g
(Ω
out
)
dxdy
+
g
(Γ)
ds,
E
(Ω
in
,
Ω
out
,
Γ)=
Ω
in
Ω
out
Γ
where Ω
in
and Ω
out
refer to the inside and outside of the region of interest.
There are two different approaches to determine the region: a “pseudo-
static” approach and a dynamic one. In the first case, the attraction term
that guides the evolution of each point in the curve is previously computed
and kept fixed during the evolution [5, 12]. In the second, measurements
of the region descriptors depend on the evolving curve [13, 14], so that all
parameters must be updated at each iteration.
Region-based approaches usually rely on a pseudo-mask behavior [12],
which can be implemented by considering:
α
if
P
Background
>P
Target
M
(
x, y
)=
,
−
α
otherwise
and evolving the snake using
∂
∂t
= sign(
I
)
·
n.
(3)
We propose to reformulate (2) decoupling the regularity and convergence
terms and embedding the scheme in a region-based framework.
3.
STOP AND GO FORMULATION
The evolution of deformable models is basically guided by a compromise
achieved by balancing an external force and the inner constraints of the model.
The full process of evolution can be decoupled in two stages: a straightforward
advancing front defined outside the regions of interest, and an inside region term
opposed to it. Evolution stops if these two forces cancel along the curve of interest.
Amask defining the object of interest is needed to bound the range of the curvature
term and to perform this decoupling. On the other hand, any standard snake vector
evolution definition serves to build an outer force ensuring convergence.
3.1. Basics of the STOP and GO Formulation
The formulation of the STOP and GO deformable model needs the definition
of two different vector flows: an attractor vector field (GO) moving the curve
toward the target and a repulsive one (STOP) making that evolution stop. In order
