Image Processing Reference
In-Depth Information
The proposed method can be applied without any a priori evaluation of SNR.
It is assumed that image gray levels are composed of 2-D locally constant or
slowly varying regions separated by discontinuities called edges. In locally con-
stant regions, local variations are mainly due to random noise, and the values of
the standard deviations are relatively small. Across edges, the local standard devi-
ations are relatively large because of the large intensity differences across image
structures.
The adaptive filter should be able to distinguish between locally constant
regions and edge regions: the edge regions should be excluded from the filtering
process in order to prevent resolution degradation.
The algorithm proposed in [3] defines multiple templates, each template being
composed of free cells and active cells, i.e., cells made available for the filter
coefficients. The number NT of multiple templates is given according to the
following relationship
N
N
∑∑
0
N
kN k
!
k
(6.7)
NT
=
C
=
!
(
)
!
k
=
k
=
0
where N is the template dimension minus the current pixel (for a 3
×
3 template,
N
k) the number of active
cells. The number of active cells defines the filter size. Equation 6.7 defines the
number of templates for any filter size, i.e., the possible combinations of (N
=
8), k the number of free cells in the template, and (N
k)
active cells in a template.
In Figure 6.1, an example is reported for a 3
×
3 template (N
=
8): when k
=
0
we have NT
=
1 possible combinations, whereas for k
=
4, the number of templates
is NT
70. In the figure, “1” denotes active cells, “0” corresponds to free cells,
and the reference cell is drawn in black.
=
111
1 1
111
N = 8
110
1 1
111
101
1 1
111
011
1 1
111
111
0 1
111
N = 7
100
1 1
111
010
1 1
111
110
0 1
111
110
1 1
011
110
1 1
101
N = 6
FIGURE 6.1
×
Example of the number of template configurations for a 3
3 template.
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