Biomedical Engineering Reference
In-Depth Information
which expands from inside the target feature, and another one which contracts
from the outside. The two contours are interlinked to provide a driving force to
carry the contours out of local minima, which makes the solution less sensitive
to the initial position.
The sensitivity to initialization of snakes can also be addressed by a two-stage
approach: (1) The region of interest is limited; and (2) a global minimization tech-
nique is used to find the object boundary. Bamford and Lovell [4] describe such
a method to segment cell nucleus based on a dynamic programming algorithm
( Viterbi algorithm) to find the solution.
The use of dynamic programming (DP) for solving variational problems is
discussed by Amini
et al.
[2]. Unlike the variational approach, DP ensures global
optimality of the solution and does not require estimates of higher order deriva-
tives, which improves the numerical stability. However, these techniques are
limited by their storage requirements of
O
(
NM
2
) and computational complexity
of
O
(
NM
3
), where
N
is the number of snaxels and
M
is the size of the neigh-
borhood around each snaxel (given a
discrete search space
with
NM
points).
These performance difficulties can be lowered with a method to reduce the
search space. That is the main point addressed in [32, 34].
In those works, we propose to reduce the search space through the dual-
T-snakes model [30] by its ability to get closer to the desired boundaries. The
result is two contours close to the border bounding the search space. Hence, a
DP algorithm [2, 4, 38] can be used more efficiently.
The sensitivity to the initial contour position can also be addressed by a
method which initializes automatically the snake closer to the boundaries [43].
An efficient methodology in this field would be worthwhile, not only to save
time/calculation, but also to facilitate the specification of parameters, a known
problem for snake models [31].
In [29, 33] we propose a method to initialize deformable models, which is
based on properties related to the topology and spatial scale of the objects
in 2D or 3D scenes. We assume some topological and scale properties for the
objects of interest. From these constraints we propose a method which first
defines a triangulation of the image domain. After that, we take a subsampling
of the image field over the grid nodes. This field is thresholded, generating a
binary one, an “object characteristic function,” from which a rough approxima-
tion of the boundary geometry is extracted. This method was extended to 3D
in [63].
