Image Processing Reference
In-Depth Information
Figure 8.10
Aperture filter placement.
X'
=
X
-
P
(8.19)
The aperture filter is applied to
X'
to give the output
I'
:
Y'
=
ψ
(
X'
)
(8.20)
The offset signal
P
is added back to the aperture output to get the overall output sig-
nal
Y
:
YY P
=+
'
(8.21)
Y
=
ρ
(
X
)+
ψ
[
X
-
ρ
(
X
)]
The reduced dynamic range of aperture filters makes them much easier to design.
Unlike the earlier filters described in this chapter, the amplitude values are both
positive and negative but there are no conceptual problems with this extension.
Further constraints may be applied within the aperture filter if necessary.
8.6 Efficient Architecture for Computational Morphology and
Aperture Filters
As relatively new concepts, hardware implementations of computational morphol-
ogy and aperture filters are still emerging. While in theory the translation from al-
gorithm to logic is straightforward for many practical problems, the complexity can
increase very rapidly. One recent novel approach to implementation involving bit
vector architecture was proposed by Handley.
21
Computational morphology parti-
tions all possible combinations of inputs into a series of intervals with a specific
output associated with that interval. Its implementation reduces to a search problem
in order to determine in which interval a set of windowed observations lie. Com-
parator-based architectures perform this task in parallel
22,23
and the amount of hard-
