Biomedical Engineering Reference
In-Depth Information
Fig. 4
Typical evolution of
the step in time (t )forthe
proposed adaptive process
in 2D
Additionally, using a gaussian filter for D is beneficial to increase speckle
removal. While in edges, filtering D does not change D significantly as long as is
small since Im(I ) is smooth [
13
]. However, at isolated spiky D points, filtering D
turns diffusion less conservative and therefore increases speckle reduction without
compromising edge preservation.
2.3.2
Adaptive Time Step
As opposed to the majority of nonlinear complex diffusion processes that adopt a
constant time step (t ) close to the time step limit of the convergence of the iterative
update process, we opted for an adaptive time step (
12
). The rational behind this
decision is based on the fact that the coefficient of diffusion depends on the gradient
of the image (
3
) and, due to noise, this gradient is much higher in the initial steps of
the diffusion process. Therefore we choose iteratively
h
a
/
i
,
1
˛
be
max
.
j
Re.
@I
.n/
=@t
/
=
Re
.I
.n/
/
j
t
.n/
D
C
(12)
where
ˇ
ˇ
Re
@I
.n/
=@t
=Re.I
.n/
/
ˇ
ˇ
is the fraction of change of the image/volume at
iteration n, ˛ as in (
7
) and parameters a and b control the time step (with a
C
b
1).
The typical evolution of t
.n/
over the iterative process in 2D is shown in Fig.
4
.
As expected, a small step size is used at the initial iterations in which higher
values of D can be found due to the speckle noise. This is, at steady conditions in
which changes over time are small (fraction-wise), the time step can be made larger,
while at fast changes in time the time step can be made smaller.
