Image Processing Reference
In-Depth Information
Chapter 8
Grayscale Implementation
This chapter considers some of the implementation issues that are encountered in
processing grayscale images. These issues fall into two main areas: grayscale train-
ing issues and grayscale hardware implementation.
8.1 Grayscale Training Issues
8.1.1 Envelope filtering
It was seen in Chapter 4 that training of filters to deal with real-world problems is a
difficult task. A balance must be struck between the dimensionality of the training
set and the size of the search space. The training task may be simplified by limiting
the complexity of the problem through the application of a constraint. This leads to
an increase in error due to the addition of a constraint error term. However, this may
be more than offset by the reduction in estimation error. Estimation error resulting
from inadequate training of filters can be very severe and can even result in filters
that actually increase the error.
Equation 4.2 illustrated the trade-off involved when a filter is constrained by
reducing its window size. A similar trade-off applies to other types of constraints. A
recently introduced constraint that has been shown to be very valuable for the type
of nonlinear filters described in this topic is the use of envelopes. The concept of
envelopes is not new in itself, and it has been used in other areas of signal and image
processing.
1,2,3,4
However, an example of its application to grayscale filter design
was introduced by Brun et al.
5
While other constraints such as the window constraint have limited the input to
the filter, and constraints on the class of functions have limited the processing of the
input, envelope constraints directly constrain the output of the filters. The designed
filter processes the data and produces an output that is then constrained to lie be-
tween a lower and upper bound,
α
and
β
, respectively. Figure 8.1 shows an exam-
ple of a signal
ψ
constrained to an envelope resulting in the signal
ψ
con
. Where
ψ
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