Biomedical Engineering Reference
In-Depth Information
Figure 10.3: Motion under constant flow: It causes a smooth curve to evolve
to a singular one.
its own can cause a smooth curve to evolve to a singular one (see Fig. 10.3).
However, integrating it into the geometric snake model lets the curvature flow
(10.1) remain regular:
C
t
=
g
(
|∇
I
|
)(
κ
+
c
)
N
−
(
∇
g
(
|∇
I
|
)
·
N
)
N,
(10.8)
where
c
is a real constant making the contour shrink or expand to the object
boundaries at a constant speed in the normal direction.
The second term of (10.7) or (10.8) depends on the gradient of the conformal
factor and acts like a doublet (Fig. 10.4), which attracts the active contour further
to the feature of interest since the vectors of
−∇
g
point toward the valley of
g
(
·
),
the middle of the boundaries. This
−∇
g
increases the attraction of the active
contour toward the boundaries. For an ideal edge,
g
(
·
) tends to zero. Thus, it
Figure 10.4:
The doublet effect of the second term of Eq. 10.7. The gradient
vectors are all directed toward the middle of the boundary, which forces the
snake into the valley of
g
(
·
).
