Biomedical Engineering Reference
In-Depth Information
good initialization or a balloon force [13]. On the other hand, the region-based
energy has a large realm of attraction and can converge even if explicit edges are
not present. However, it does not as give good localization as the edge-based
energy at image boundaries. The region-based energy defined in [32] attempts to
ensure that in the region having maximum inhomogeneity the region-based force
factor approaches zero to complement the gradient force. Also, the region-based
energy is designed with the property that any control point will want to preserve
the “nearness” to the initial intensity value fromwhere it started. Thus, the defined
force field has two factors — intensity difference from the initial location and local
edge strength — and is equated as follows:
γ
(
τ
(
s
i
)) =
1
.
0
−
ψ
(
f
(
τ
(
s
i
))
−
ψ
(
f
(
τ
(
s
i
))
∗
(1
.
0
−
ψ
(
|∇
G
σ
⊗
f
|
))
.
(17)
In Eq. (18) the term
ψ
(
f
(
τ
(
s
i
))
−
ψ
(
f
(
τ
(
s
i
))
gives the difference of the nor-
malized feature image between the points
τ
(
s
i
)
represent the
i
th point on the contour at the
t
th and 0th iterations, respectively.
f
represents the feature image, which in this case is intensity.
ψ
represents a
normalized feature. The first term in Eq. (18) tends to reduce the force, while
the difference between the two feature values increases, i.e., tends to 1.0. On the
other hand, the second term vanishes as the point approaches a high-gradient re-
gion. This force field thus tends to balance between the region-based homogeneity
information and the local edge information [32]. Figure 16 illustrates the use of
the above-mentioned region-based force field for segmenting ultrasound images.
In both the cases the contour has been initiated outside the region of interest. It
is to be noted that the active contour models that have been discussed so far are
unidirectional in nature. Thus, they have the ability to either expand or contract
depending on how they are set. Thus, the major challenge of this framework is that
once the contour leaks through a boundary to the background, there is no force
to bring it back to the object region. This limitation is due to the fact that the
active contour does not have the knowledge of which region it belongs to. If this
information can be imparted a priori to the snake process, then the deformation
could be more controlled.
τ
(
s
i
) and
τ
(
s
i
), where
τ
(
s
i
) and
4.
A-PRIORI INFORMATION
Use of factors like homogeneity provides better segmentation results com-
pared to the local statistics-based approach; however, as discussed previously,
they are limited by their inability to undertake bidirectional motion. The active
contour model has unidirectional motion because of its lack of knowledge about
object and background in any form of statistical information. If the snake can
distinguish between object class and background class, then once it leaks from
one structure to the other, the snake could go back to the desired interface. Thus,
the active contour needs to be intelligent enough to distinguish between object
