Image Processing Reference
In-Depth Information
Figure 5.3
Minimization and implementation of an increasing function into morphological
structuring elements.
puts. The design of an increasing filter can be reduced to the identification of the
basis inputs that partition the set of all inputs into a lower and upper portion.
If this increasing filter
inc
is represented by the pixels within a 3-point hori-
zontal window, then it may be implemented by determining if any of the basis in-
puts fits within the foreground of the image. This is equivalent to Boolean
reduction where it is not necessary to test for every input of the filter, but it is suffi-
cient to simplify the function and to test only for the reduced set.
Figure 5.3 shows how the increasing function may be reduced using the stan-
dard technique of a K map to produce the minimized function of
ψ
F=X
0
X
1
+X
2
.
(5.6)
This means that a foreground (black) pixel will be produced if either X
2
is black
OR both X
0
AND X
1
are black. If neither of these conditions holds, the pixel will be
white. This function may therefore be implemented by testing if either of the
sub-windows below fits the image.
