Information Technology Reference
In-Depth Information
Fig. 5.8 Image processing using the technique of mathematical morphology
Dilation
A
M
B ¼
B
x
\ A 6¼
0
x
:
magnifies the image, while the operation of erosion
Erosion
A B ¼
x
:
ðÞ
x
A
diminishes it.
Two fundamental operations of mathematical morphology are built on these
elementary operations: opening
Þ
M
B
Opening
A
B ¼ A B
ð
∘
and closing
B
A
M
B
Closing
A B ¼
:
A detailed examination shows that the totality of operations “open” and “close”
allows to perform all basic operations of image processing—selection of image
contour, its skeleton, dividing the image into its simplest parts, etc. As an example,
shows some of the operations performed by the technique of mathematical mor-
phology: image smoothing (Fig.
5.8
) and the selection of its individual regions and
the boundaries between them (Fig.
5.9
).
