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.
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