Biomedical Engineering Reference
In-Depth Information
The resulting force can pull the model towards distant image features. Nonethe-
less, the search is very time consuming and has to be repeated in every step. Lowering
the threshold can shorten the runtime but also reduces the attraction range for image
features.
4.7.2.5 Gradient Vector Flow
In 1998, Xu and Prince [
27
] have proposed a newexternal forcemodel. Their Gradient
Vector Flow (GVF) field is calculated as the diffusion of an intensity image. It allows a
more flexible initialization and supports a more efficient convergence to concavities.
Ng et al. [
105
] present a medical image segmentation that uses a feature-based
GVF snake. The iteration is stopped once the accuracy is sufficient by exploiting
image features. Zhao et al. [
106
] have improved the dynamic GVF force field and
introduced a strategy of deformable contour knots for a B-spline based model.
4.7.2.6 Omnidirectional Displacements
When working with deformable surfaces, forces are commonly directed along a line,
usually the surfaces local normal. Kainmueller et al. [
107
] have proposed omnidirec-
tional displacements for deformable surfaces (ODDS) that consider a sphere around
each vertex. By doing so, a global optimization can be performed. This technique
has been proven to be useful in regions of high curvature, e.g. tips. They have also
proposed a hybrid approach, fast ODDS to overcome the high memory and runtime
requirements.
4.7.3 Interactive Forces
Image artifacts, different protocols and implants can cause problems in automated
segmentation of medical images. In a clinical environment, operators can provide
guidance to the deformable model to overcome these problems. The so called inter-
active forces provide a link between real-time user input and model iteration.
Kass et al. [
20
] have proposed two interactive forces. Spring forces are designed
to pull the model in the direction of a point
p
. Their strength is proportional to the
distance from
p
:
F
spring
(
x
)
=
α
s
(
p
−
x
)
(4.21)
The opposite effect can be achieved using volcano forces. They push a model
away from a point
p
:
r
F
volcano
(
x
)
=
α
v
(4.22)
|
r
|
3
