Biomedical Engineering Reference
In-Depth Information
is that it has difficulty dealing with topological adaptation such as splitting or
merging model parts, a useful property for recovering either multiple objects
or objects with unknown topology. This difficulty is caused by the fact that a
new parameterization must be constructed whenever topology change occurs,
which requires sophisticated schemes [5, 6]. Level set deformable models [7,
8], also referred to as geometric deformable models, provide an elegant solu-
tion to address the primary limitations of parametric deformable models. These
methods have drawn a great deal of attention since their introduction in 1988.
Advantages of the contour implicit formulation of the deformable model over
parametric formulation include: (1) no parameterization of the contour, (2) topo-
logical flexibility, (3) good numerical stability, (4) straightforward extension of
the 2D formulation to
n
-D. Recent reviews on the subject include papers from
Suri [9, 10].
In this chapter we give a general overview of the level set segmentation
methods with emphasis on new frameworks recently introduced in the context
of medical imaging problems. We then introduce novel approaches that aim at
combining segmentation and registration in a level set formulation. Finally, we
review a selective set of clinical works with detailed validation of the level set
methods for several clinical applications.
2.2
Level Set Methods for Segmentation
A recent paper from Montagnat, Delingette, and Ayache [11] reviews the gen-
eral family of deformable models and surfaces with a classification based on
their representation. This classification has been reproduced to some extent in
Fig. 2.1. Level set deformable models appear in this classification diagram as
part of continuous deformable models with implicit representation.
2.2.1
Level Set Framework
Segmentation of an image
I
via active contours, also referred to as snakes [2],
operates through an energy functional controlling the deformation of an initial
contour curve
C
(
p
)
,
p
∈
[0
,
1] under the influence of internal and external forces
achieving a minimum energy state at high-gradient locations. The generic energy
