Image Processing Reference
In-Depth Information
Table 2.3.
Examples of point operations.
Definition
ψ
(
x
)
Notation
(1) Multiplication by constant
ψ
(
x
)=
cx
M
[
c
]
(2) Substitution of constant
ψ
(
x
)=
c
S
[
c
]
(3) Addition and subtraction by constant
ψ
(
x
)=
x
+
c
A
[
c
]
ψ
(
x
)=
x
c
P
[
c
]
(4) Power by constant
ψ
(
x
)=
e
x
(5) Exponential
EXP
(6) Logarithmic
ψ
(
x
)=log(
x
)
LOG
(7) Absolute value
ψ
(
x
)=
|x|
ABS
ψ
(
x
)=
x,
if
x ≥ t
0
(8) Thresholding (1)
,
if
x<t
U1
[
t
]
ψ
(
x
)=
x,
if
x>t
(9) Thresholding (2)
0
,
if
x ≤ t
U2
[
t
]
ψ
(
x
)=
1
,
if
x ≥ t
(10) Thresholding (3)
0
,
if
x<t
U3
[
t
]
ψ
(
x
)=
1
,
if
x>t
(11) Thresholding (4)
0
,
if
x ≤ t
U4
[
t
]
(12) Idempotent
ψ
(
x
)=
x
I
(13) Negation
ψ
(
x
)=
1
− x
N
(d) Shift-invariant operator
Definition 2.14 (Shift invariance).
An operator
O
is said to be
shift in-
variant
(or
position invariant
) if it is commutative with a shift operator
T
,
that is, if the following equation holds:
·
·
O
,
∀
∈O
T
O
T
=
T
T
(2.36)
where
O
T
is the set of all shift operators.
Both the serial and the parallel compositions of shift invariant operators
are again shift invariant. A point operator and a shift operator itself are always
shift invariant.
2.4 Algorithm of image operations
In the last section, an image operator was defined as a mapping on an image
set or an algebraic operation applied to a set of images. It is another problem,
however, to perform such an operation with a general purpose computer or
a special purpose image processor. In this section, we will examine in more
detail concrete algorithms to perform unary operators of images. After giving
a formal expression as a general image operation, we will introduce several
important types of algorithms including a sequential type, a parallel type, and
local parallel operations.
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