Biomedical Engineering Reference
In-Depth Information
Fig. 4.4
The combination of pressure force and smoothing transforms a cube into a sphere
4.7.1.3 Simple Image Force
A simple approach to include image features is the use of normalized intensity
gradients that, for example, can be calculated using central differences. Along the
vertex normal, several gradients are being calculated and the force will be directed
towards the higher gradients:
)
=−
α
i
n
x
δ
max
F
image
(
x
k
(δ)
∗
Φ(
x
+
δ
·
n
x
)
(4.18)
δ
min
where
k
(δ)
is a weighting factor with respect to the distance
δ
and
∗
is the convolution
operator. An image interpretation factor
Φ
can be calculated, in this case the gradient.
4.7.2 Advanced Forces
The basic forces can be extended by more advanced approaches to improve results
and runtime.
4.7.2.1 Image Intensity Profiles
Instead of simply using the image gradient, intensity profiles can be used to compare
the intensity curve along the normals. By doing so, the desired structure can be
described more powerful and it allows a distinction between noise-induced gradients
and targeted edges. This approach is commonly used [
70
,
97
,
98
]. To reduce the
complexity of the high number of intensity profiles, clustering has been proposed. For
instance, Chung and Delingette [
99
] have proposed an Expectation-Maximization-
based algorithm for clustering and classification. An example of image intensity
profiles in a magnetic resonance (MR) image of the femur is shown in Fig.
4.5
.
