Image Processing Reference
In-Depth Information
Figure 7.15
Stack filter within the computational morphology model.
This means that the output at level
k
is 1 if the signal at that level is more than three
points wide or 0 otherwise. It effectively thresholds the input signal leading to the
stack filter as already described. It can be expressed as a simplification of the com-
putational morphology model with thresholding of the input signal and binary fil-
tering of the different levels (Fig. 7.15).
7.5 Aperture Filters
As mentioned earlier, computational morphology is such a general framework that
it can be difficult to design, i.e., it can be difficult to determine the filter kernel. This
is because the number of possible input combinations is huge. For an 8-bit 1D sig-
nal, a 5-point window would have 2
5×8
10
12
inputs and so constraints are
needed. One recently introduced constraint is the aperture constraint. In the same
way that the window constraint limits the inputs to those falling within a finite spa-
tial interval, the aperture constraint limits the inputs to a finite interval in amplitude.
The signal is viewed through a rectangular window known as an aperture. The prin-
ciple will be described in terms of 1D signals, but the concept extends readily to im-
ages where the aperture becomes a rectangular “box”. The aperture slides along the
signal and moves up and down to track the signal level. An example of a signal and
aperture is shown in Fig. 7.16(a).
Aperture placement is an interesting topic and will be discussed in more detail
later. Where a point of the signal lies beyond the top (or bottom) of the aperture, it is
clipped to the highest (or lowest) value within the aperture window. Figure 7.16(b)
shows the quantized samples in an aperture with five spatial points and seven
quantization levels. Without further constraint, the aperture has 7
5
= 16807 input
=2
40
≈
