Image Processing Reference
In-Depth Information
Figure 6.5
The detail in image (a) consists of very thin text corrupted by noise. The probabil-
ity estimates are given in (b). Much of the text is preserved using the optimum weighted
median filter (c) with
W=
5 (equivalent to |
x
| = 7). However, it is almost destroyed by the stan-
dard median filter (d).
)
)
(
(
where
N
yX
c
x
'
and
N
yX
c
x
'
are the number of times that the center value
=
≠
switches, i.e.,
y
X
c
or is unchanged (
y=X
c
) for input |
x
'|.
Figure 6.5(a) shows an image containing very thin text corrupted by noise. The
probability estimates are given in Fig. 6.5(b). These show that a value of |
x
'|
opt
=
7
gives the optimum weighted median. This is the minimum value of |
x
'| for which
P
(
d
=
1
|
|
x
'|)
0.5 and corresponds to a filter weight of
W=
5. The result of applying the
optimum weighted filter is shown in Fig. 6.5(c), where it can be seen that most of the
text is preserved. In contrast, applying the standard median destroys most of the text
and results in the image shown in Fig. 6.5(d). The filters with weights on either side
of the optimum, i.e.,
W=
3 and 7, were found to give very poor results, suggesting
that the selection of the optimum weight is critical in this case.
≠
