Image Processing Reference
In-Depth Information
Fig. 2.11.
Composition of image operations: (
a
) Parallel composition; (
b
)serial
composition; (
c
) iterative composition (
n
-th power); (
d
) associative law of serial
compositions; (
e
) distributive law.
Furthermore,
O
−n
is defined as follows:
O
−n
≡
O
−
1
·
O
−
(
n−
1)
,n
≥
2
,
(2.23)
whereweassumethat
O
−
(
n−
1)
exists and its range is included in the domain
of
O
−
1
for all
n
≥
2
(Fig. 2.11 (c)).
To represent iterative application of more than one operator, we use no-
tations similar to those of real numbers. For example,
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