Biomedical Engineering Reference
In-Depth Information
main motivation was to use global features and reduce reliance on local features.
The rationale behind this approach was the fact that the features derived from local
statistics are prone to errors due to noise and other artifacts that arise during
the imaging process. Thus, a more global statistics would be helpful in detecting
the region of interest. In fact, the basic definition of a structure can be stated as the
region with similar attributes. If the features of interest can be isolated, the region
connected by the similar features can be defined as the same structure. This gives
rise to an entirely new approach toward the deformable model and has been studied
in various forms by different researchers [29-32].
Region-based information is in general incorporated into the snake structure
through a probabilisticmodel. As mentioned earlier, regional information attempts
to capture the likelihood of a pixel (or point) belonging to any specified region. In
general, the “region” is defined using some feature parameter, namely intensity,
texture, etc. Based on the feature value, a pixel has a finite probability of belonging
to a region defined in the feature space. The most widely used measures for feature
space definition in snake-based segmentation is intensity. In some approaches,
spatial intensity correlation and connectivity are used. The homogeneity of a
space is normally defined as the cost function for traveling from a seed pixel to
another location in the spatial domain based on a feature value.
Poon et al. [29] introduced the concept of region-based energy, where the
homogeneity of a region is computed based on the intensity of a scalar image.
For a vector image like that obtained with multispectral MRI (i.e., homogeneity,
T1, T2, PD images), vector information from all the channels has been used for
computing regional features. Figure 14 shows the results at different stages of
snake deformation in delineation of the left ventricle from an MR image sequence
using regional information. Other researchers [33-37] have also integrated region-
based information into deformable contour models.
Region-based information is integrated along with the gradient into the snake
model using a probabilistic approach [35]. A parametric curve is defined using
a Fourier-based approach, where the idea is to use the number of harmonics de-
pending on the required smoothness of the resulting contour. Thus, if the desired
shape has more convexities, then higher Fourier harmonics are used, since the high
frequency is encouraged by the geometry. Thus, the contour is expressed as
x
(
t
)
y
(
t
)
a
0
c
0
a
k
cos(
kt
)
sin(
kt
)
,
∞
b
k
v
(
t
)=
=
+
(14)
c
k
d
k
k
=1
where
v
(
t
) is the contour and
a
k
,
b
k
,
c
k
, and
d
k
are the Fourier coefficients, with
k
ranging from 1 to
. The smoothness of the desired contour determines the
number of harmonics to be used to define the geometry of the contour.
The contour can be deformed by changing the coefficients in the Fourier ex-
pression in Eq. (15). This is analogous to the internal energy of conventional
snakes. The external features that guide the final destiny of the contour are defined
∞
