Lecture 4
Digital image fundamentals:
Mathematical tools (array and matrix operations,
linear and nonlinear operations, arithmetic
operation, sets and logic operation)
Mathematic operations on images
Array or matrix operations?
•
Array operation (default) : each pixel is
operated with its corresponding pixel
in the second image
•
Matrix operation (if stated): standard
matrix operations
Linear and nonlinear operations
•
An operation is linear if homogeneity
and additively are applicable
•
An operation is nonlinear if it’s not
linear
)
(additvety
,
(
)
,
(
)
,
(
)
,
(
and
ty),
(homogenei
)
,
(
)
,
(
applicable
are
conditions
two
followinh
the
if
linear
is
H
y)
g(x,
image
the
produce
to
y)
f(x,
image
an
on
H
operation
an
Consider
y
x
f
H
a
y
x
f
H
a
y
x
f
a
y
x
f
a
H
y
x
f
aH
y
x
af
H
j
j
i
i
j
j
i
i
Linear and nonlinear operation: examples
The sum of all pixel values in an
image
The maximum pixel value in an
image
linear
is
operation
Sum
the
Hence
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
y
x
f
a
y
x
f
a
y
x
f
a
y
x
f
a
y
x
f
a
y
x
f
a
j
j
i
i
j
j
i
i
j
j
i
i
nonlinear
is
operation
the
general
in
Hence,
4
7

3
7
4
5
6
)
1
(
3
2
2
0
)
1
(
while
2
4
2
3
6
7
4
5
6
)
1
(
3
2
2
0
)
1
(
Max
Max
Max
Max
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 Fall '15
 Hamed Hemeda
 Image processing, Addition