Image Processing Reference
In-Depth Information
Figure 7.14
Stack filter example showing erosion by a “flat” structuring element.
So the grayscale morphological filter represents a constraint on the general filter as
the contents of the kernels at each level are forced to be the same shape related
through a simple offset.
Stack filters may also be put in the context of computational morphology and in
this case the structuring elements are not only related by an offset but are con-
strained to be “flat” with vertical sides. Figure 7.14 shows an example of an erosion
of a grayscale signal by a flat structuring element.
Notice that the flat structuring element is drawn with the bottom edge jagged.
The only points that matter are the top surface so the SE could just as easily have
been drawn as a horizontal line three points wide.
The kernel for each output level
K
k
[
ψ
] consists of
k
=1
x
= (1, 1, 1)
k
=2
x
= (2, 2, 2)
i.e.,
x
=(
k
,
k
,
k
)
(7.15)
