Image Processing Reference
In-Depth Information
Figure 9.4
Standard morphological dilation by a structuring element.
dilation at all times. However, in soft morphology this constraint is relaxed so that
only a certain percentage of the SE is forced to lie below the surface for erosion, or
above it for dilation. In fact, in soft morphology the structuring element is parti-
tioned into two regions, a
hard center
. The hard center be-
haves in a similar way to the structuring element in standard morphology. That is,
for soft erosion the
whole
of the hard center must be “beneath” the signal surface.
On the other hand, only a proportion of the soft surround must lie beneath the signal
surface. The amount of the soft surround that is forced to lie beneath the surface is
controlled by a value
r
, known as the repetition parameter
α
and a
soft surround
β
Conversely, for soft di-
lation a proportion of the soft surround must remain above the signal.
Soft morphological filtering is therefore a function of three parameters:
.
α
,
β
and
r
. The first two,
, specify pixels within the structuring element, and
r
is a
scalar quantity that defines what proportion of
α
and
β
must lie either below or above the
surface for soft erosion and soft dilation, respectively. By adjusting the three pa-
rameters, a more subtle filtering effect is produced. Examples of soft morphologi-
cal erosion and dilation are given in Fig. 9.5(a) and Fig. 9.5(b), respectively.
Notice that this is a less harsh process. By careful design of the structuring ele-
ments, soft morphological filters can by used to remove different types of noise
from images while leaving the important structures intact. The design is carried out
by a training process using representative examples. In this way, the filter models
the inverse process and produces an optimum mapping from noisy to restored im-
age.
β
