Image Processing Reference
In-Depth Information
Figure 9.3
Standard morphological erosion by a structuring element. The dotted line indi-
cates the signal after filtering (i.e. the eroded signal).
Soft morphology is slightly more subtle than standard grayscale morphology. First,
let us remind ourselves of the operation of grayscale morphology. A brief non-
mathematical overview of standard grayscale morphology is provided here fol-
lowed by an equivalent description of soft morphology in order to allow the reader
to distinguish between them. Readers requiring a more mathematically rigorous ex-
planation should consult the references.
Figure 9.3 shows a sketch of a standard grayscale erosion of a 1D signal, using
a circular structuring (SE). The SE is “pushed up” from below so that it just touches
the signal. The SE then slides along the signal, moving up and down while main-
taining contact from below. The filtered signal is given by the path mapped out by
the reference point of the SE (which is shown as a dotted line in Fig. 9.3). In this
case, the reference point is located at the center of the SE. Note that the whole of the
SE remains below the signal at all times. In general, erosion lowers the overall level
of the signal, and peaks that are too narrow to contain the SE are removed. By con-
trast, valleys remain unchanged.
Similarly, the standard 1D grayscale dilation of the same signal by the same SE
is given in Fig. 9.4. In this case, the SE is lowered onto the surface of the signal and
slides along it, moving up and down as necessary, while remaining in contact from
above. Again, the filtered signal is given by the path mapped out by the reference
point of the SE and the whole of the SE remains above the signal at all times. In the
case of dilation, valleys that are too narrow to contain the SE are filled in, whereas
the peaks remain unchanged.
From the above examples, it has been emphasized that the
whole
of the struc-
turing element must remain below the surface for erosion or above the surface for
