Biomedical Engineering Reference
In-Depth Information
There has been a number of works based on the geometric snake and level
set framework. Siddiqi
et al.
[14] augmented the performance of the standard ge-
ometric snake that minimizes a modified length functional by combining it with
a weighted area functional. Xu
et al.
extended their parametric GVF snake [7]
into the generalized GVF snake, the GGVF, in [9]. Later, they also established
an equivalence model between parametric and geometric active contours [10]
using the GGVF. A geometric GGVF snake enhanced with simple region-based
information was presented in [10]. Paragios
et al.
[28, 29] presented a boundary
and region unifying geometric snake framework which integrates a region seg-
mentation technique with the geometric snake. In [30], Yezzi
et al.
developed
coupled curve evolution equations and combined them with image statistics for
images of a known number of region types, with every pixel contributing to the
statistics of the regions inside and outside an evolving curve. Using color edge
gradients, Sapiro [6] extended the standard geometric snake for use with color
images (also see Fig. 10.6). In [11], Chan
et al.
described a region-segmentation-
based active contour that does not use the geometric snake's gradient flow to
halt the curve at object boundaries. Instead, this was modeled as an energy
minimization of a Mumford-Shah-based minimal partition problem and imple-
mented via level sets. Their use of a segmented region map is similar to the
concept we have explored here.
Level set methods can be computationally expensive. A number of fast im-
plementations for geometric snakes have been proposed. The
narrow band
technique, initially proposed by Chop [31], only deals with pixels that are close
to the evolving zero level set to save computation. Later, Adalsterinsson
et al.
[32]
analyzed and optimized this approach. Sethian [33, 34] also proposed the fast
marching method to reduce the computations, but it requires the contours to
monotonically shrink or expand. Some effort has been expended in combin-
ing these two methods. In [35], Paragios
et al.
showed this combination could
be efficient in application to motion tracking. Adaptive mesh techniques [36]
can also be used to speed up the convergence of PDEs. More recently, addi-
tive operative splitting (AOS) schemes were introduced by Weickert
et al.
[37]
as an unconditionally stable numerical scheme for nonlinear diffusion in im-
age processing. The basic idea is to decompose a multidimensional problem
into one-dimensional ones. AOS schemes can be easily applied in implementing
level set propagation [38].
