Biomedical Engineering Reference
In-Depth Information
where
h
and
r
h
are, respectively, the discrete second order laplacian and gradient
operators, t is the step in time, l , j and m are the indexes for the voxels of I and
D is given by
6D
.n/
D
.n/
l
D
.n/
l;j
D
.n/
l;j;m
l;j;m
C
1;j;m
C
1;m
C
˙
˙
˙
1
D
.n/
l;j;m
D
.
(6)
12
As shown in [
2
] this explicit method is stable if
1
2
!
,
Im.I /
k
1
˛
cos min
C
t
(7)
l;j;m
where ˛
D
4 in 2D and ˛
D
6 in 3D.
2.3
Improved Adaptive 3D NCDF
In the previous analysis, the parameter k is left constant. However, it can be
adaptively used to improve the despeckling method's performance in the case of
OCT data. The diffusion coefficient can be approximated by
1
D
.I =k/
2
:
(8)
C
1
As motivation for these kind of functions, this expression can be seen as a
Lorentzian function (
9
) modified to have its maximum equal to 1 and
w
D
k=2.
2A
w
L.x/
D
x
c
/
2
/
:
(9)
.
w
2
C
4.x
In this way, a family of curves can be generated from (
8
) as shown in Fig.
3
,simply
by modifying the value of k.
The choice for the k parameter (
3
) is therefore important, as it modulates the
spread of the diffusion coefficient in the vicinity of its maximum, that is, at edges
and homogeneous areas, where the image laplacian vanishes. From the plot, it
becomes clear the difference in D for I constant from low- (higher k) to high-
intensity areas (lower k), thus increasing the diffusion for low-intensity areas and
decreasing it for higher-intensity ones.
