Image Processing Reference
In-Depth Information
Various algorithms for efficient stack filter implementation especially in
FPGA hardware are presented in Woolfries.
20
8.4 Grayscale Morphology
Grayscale morphology may be implemented as a special case of the more general
computational morphology (CM). The overall CM structure is simplified so that
the processing function
. This re-
mains more general than the stack filter configuration, however, since the individ-
ual threshold output values
y
i
may be formed as a function of input values derived
from any threshold level.
ψ
i
is the same at every threshold level, i.e.,
ψ
i
=
ψ
)
(
i
0
1
1
2
L
−
1
y
=
ψ
x
,
x
,
x
,
x
,
x
(8.11)
i
0
0
1
1
T
−
1
Consider the example of the grayscale erosion of the signal
X
by a grayscale struc-
turing element
B
= (-1, 0, -1) to give the output signal
Y
:
Y=X
Θ
B
(8.12)
This may be calculated by evaluating a stack of threshold values
y
i
as
y
i
=X
e
B
i
,
(8.13)
where
is the elemental erosion operator and
B
i
are structuring elements in the ker-
nel derived from the grayscale structuring element
e
.
The kernel of structuring elements
B
i
correspond to versions of the grayscale
structuring element
B
B
translated vertically by the scalar value
i
, i.e.,
B
i
=
B
+
i
(8.14)
In this case,
B
= (-1, 0, -1); therefore,
B
3
= (2, 3, 2),
B
2
= (1, 2, 1),
B
1
= (0, 1, 0),
and
B
0
= (-1, 0, -1).
