Image Processing Reference
In-Depth Information
Figure 8.9
Grayscale erosion by structuring element (-1, 0, -1).
This is important in order to preserve the stacking property of the output signals
y
i
.
In stack filters this ordering is guaranteed by using only positive Boolean functions.
For computational morphology, Dougherty has named this property
consistency
.
In practice, computational morphology is often too general for most applica-
tions and special cases of it are adopted. One practical method is that of aperture fil-
ters described in the previous chapter. Aperture filters are very similar to those
based on computational morphology, but with a much reduced dynamic range. This
is achieved by subtracting a signal similar to a moving average corresponding to the
aperture placement function. This signal is added back onto the aperture filter out-
put following filtering.
An aperture placement signal
P
is calculated as a running function
ρ
of
X
:
P
=
ρ
(
X
)
(8.18)
This signal
P
is subtracted from the input signal
X
giving the aperture filter input. A
representation of this process is given in Fig. 8.10.
