Biomedical Engineering Reference
In-Depth Information
regions, so it is recommended that both feature spaces be used for definition of
the force equation.
Many other investigators have used the a-priori Gaussian distribution model
(see, e.g., [24, 49-51]). With all these approaches, the main intention is to capture
the confidence level of a pixel belonging to some region. Das et al. [24] developed
an active contour model using the a-priori information within a class uncertainty
[52] framework.
Given a priori knowledge of object/background intensity probability distribu-
tions, the object/background class of any location can be determined based on its
intensity value and establish the confidence level of the classification [52]. The
pixels with a higher confidence of belonging to the object class exert a high ex-
panding force on the contour, while those with a high confidence of belonging to
the background generate a high contracting force. It can be conjectured that the
pixels near the object-background interface will have the lowest confidence of be-
longing to either of the classes and will represent the region of highest uncertainty.
This is based on the assumption that there is a certain amount of mixing between
the two intensities at the interface, which is true for most practical images due to
effects like blurring, partial voluming effect, etc.
Given the probabilities for any pixel with intensity
f
belonging to object and
background as
p
O
(
f
) and
p
B
(
f
), respectively, and
p
(
f
) being the total probability
given by
p
(
f
)=
p
O
(
f
)+
p
B
(
f
), the class uncertainty of a pixel with intensity
f
is expressed as
p
O
(
f
)
2
p
(
f
)
log
p
O
(
f
)
2
p
(
f
)
p
B
(
f
)
2
p
(
f
)
log
p
B
(
f
)
2
p
(
f
)
h
(
f
)=
−
−
.
(25)
The class uncertainty is highest at the object-background interface, where the
pixel intensities are in the most un-deterministic state. The force field is defined
as follows:
1
−
h
(
f
(
τ
(
s
i
))
if
f
(
τ
(
s
i
)
∈
object
,
F
region
(
τ
(
s
i
)) =
(26)
−
(1
−
h
(
f
(
τ
(
s
i
)))
if
f
(
τ
(
s
i
)
∈
background.
Thus, the force field will assist faster movement of the contour in the homogeneous
region and will slow down as it approaches the boundary. Other conventional force
fields have been used with this contour model [49]. The performance of a class
uncertainty-induced snake on medical phantoms and MR images of carotid artery
is depicted in Figure 21.
Other deformable model classes like the level sets also use a-priori classifica-
tion information. Many significant works have been published using this technique
[53-57]. However, active shape models and level sets are not within the purview
of this chapter, and so interested readers are encouraged to refer to the above-
mentioned references.
