Image Processing Reference
In-Depth Information
Chapter 7
Extension to Grayscale
The chapters of this topic have thus far mainly addressed binary image processing.
While binary image processing is useful in some circumstances, it is very limited in
its applications. The challenge facing nonlinear image processing is to take these
methods and extend them to grayscale. This can be done in a number of different
ways. Current approaches are listed below:
•
Stack filters
•
Grayscale morphology
•
Computational morphology
•
Aperture filters
7.1 Stack Filters
Stack filters were introduced by Wendt, Coyle, and Gallagher
1
at Purdue in the
1980s. They enable the transition between binary and grayscale processing through
a concept known as threshold decomposition.
2
In digital systems where a signal is
represented in a finite number of bits, a grayscale signal
X
consisting of
m
discrete
levels may be thresholded at every level to produce
m
- 1 binary signals
x
t
, i.e.,
x
t
=
[
X
]
t
where [ ]
t
is the thresholding operator, defined as
1
0
if
[]
[]
≥
<
t
t
[]
=
(7.1)
if
t
An example of threshold decomposition is given in Fig. 7.1.
Note: there is usually one less binary signal
x
t
than the number of gray levels in
X
because thresholding at the bottom level 0 results in the trivial binary signal
x
0
for
which every value is equal to 1. This is sometimes omitted.
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