Image Processing Reference
In-Depth Information
This comparison is shown in Fig. 7.7. The omission of the minterm
X
0
X
1
X
2
would
result in an error corresponding to 17 pixels whereas the inclusion of the matching
minterm causes an increase in error of only 7 pixels.
Figure 7.6
Ensuring a positive Boolean function. From the above observations (a), the opti-
mum
F
is
F=X
0
X
1
+X
1
X
2
+X
0
X
2
.
From the K MAP (b), it can be seen that
F
reduces to
F=
X
0
X
1
+X
0
X
2
, which is not a PBF. The problem is caused by term
X
0
X
1
X
2
.
Figure 7.7
Identifying the closest PBF. The function F can be transformed to a positive
Boolean function either by omitting term
XXX
012
or adding mirror term
XXX
012
. The latter of
these has the lowest cost.
