Biomedical Engineering Reference
In-Depth Information
Here the influence of the speed function
F
is split into two parts,
F
A
and
F
G
. The
term
F
A
is the advection term, causing the front to uniformly expand or contract
with a speed of
F
A
depending on its sign. The second term
F
G
is the part that
depends on the geometry of the front, such as its local curvature. The affect of this
curvature term was investigated in the previous section. An example is
±
1
−
κ
,
where
is a constant. The constant 1 or
−
1 acts as an advection term (
F
A
), to
expand or contract the front. The diffusive term
κ
(
F
G
) keeps the propagating
front smooth. The curve evolution is coupledwith the image segmentation problem
by multiplying (
F
A
+
F
G
) by a stopping term:
1
1+
|∇
(
G
σ
⊗
g
I
(
x, y
)=
,
(21)
I
(
x, y
))
|
where the expression
G
σ
⊗
I
means that we convolute the image
I
with a Gaussian
smoothing filter
G
σ
with characteristic width of
σ
. When in homogenous regions,
∇
(
G
σ
⊗
I
(
x, y
)) will converge to zero, so that the affect of
g
I
on
F
A
+
F
G
is minor.
In the case when at the boundary the filter
g
I
(
x, y
) drops to zero, it performs as a
halting criteria for the speed function and stops the evolving front at the desired
region.
An example of this speed function on amulti-object image is shown inFigure 5.
The bottom images (Figure 5c,d) show topology adaptability during propagation.
Figure 5.
Shape extraction on multi-object image. See attached CD for color version.