Biomedical Engineering Reference
In-Depth Information
functions, which control the fairness of the resulting curve, on one hand, while
attracting it to the object boundaries of the AOI.
However, two main limitations of deformable templates have been noted.
First, snakes are quite sensitive to initial conditions. Deformable models may con-
verge to a wrong boundary if the initial position is not close enough to the desired
boundary. Second, its topological constraint is another disadvantage. Terzopoulos
et al. [14] and Cohen [15] used balloon forces to free the deformable models from
the initial conditions problem. The key is to introduce a constant force, which con-
tinuously expands or shrinks the initial contour. Caselles et al. [16] and Malladi
et al. [9] tackled the variable topology problem by introducing the implicit snakes
models. Many models have difficulties in progressing into boundary concavities.
Addressing these problems, a new class of external forces has been proposed by
deriving from the original image a gradient vector flow field in a variational frame-
work [17]. Sensitivity to initialization has been drastically reduced, and contours
have a more sensible behavior in the regions of concavities.
The level set technique, introduced by Osher and Sethian [4, 18, 19, 20],
is an emerging method to represent shapes and track moving interfaces. Such
techniques have been intensively studied in segmentation and tracking [9]. The
ability of handling local deformations, multicomponent structures, and changes of
topology are its major strengths. In this approach, the initial curve is interpreted
as the zero level curve of a function Φ(
t,
0):Ω
→
R
. The evolution of these
curves is controlled by a Partial Differential Equation (PDE) [4]. The attempts to
evolve interfaces with level set methods has received much attention in the last
few years due to its ability in a boundary-driven approach for image segmentation
[16, 10, 21, 22, 23].
Recently, a general variational framework for
Mumford-Shah
[24] and Geman
[25]-type functionals has been introduced [26]. Edge boundaries are represented
by a continuous function, yielded by minimizing an energy function. Caselles et
al. [27], Kichenassamy et al. [11], and Paragios [28] developed another classi-
cal snake model, the
geodesic active contour
, as the geometric alternative to the
original snake. Its implicit parametrization allows one to handle the topological
changes naturally.
In the level set method, the construction of the speed function is vital to the
final result. The speed function is designed to control the movement of the curve.
In different applications, the key is to determine the appropriate stopping criteria
for the evolution [4]. In case of segmentation, segmentation accuracy depends
on the termination criteria of the evolving surface, which in turn depends on the
speed term. When segmenting or localizing an anatomical structure, having prior
information about the expected shape can significantly help in the segmentation
process. This was recently addressed in various forms [29, 30, 31, 32]. Cootes
et al. [33] and Wang et al. [34] found a set of corresponding points across a
set of training images and constructed the statistical model of shape variation
that is then used in the localization of the boundary. Staib and Duncan [13]
