Image Processing Reference
In-Depth Information
Example 2.12
Consider the 4
4 subimage
2
4
3
5
15 15 16 14
16 17 15 13
14 11 12 15
13 12 15 13
f (n, m)
¼
The DCT of this image is
2
4
3
5
56
:
5
0
:
574
0
1
:
3858
3
:
5042
1
:
7071
1
:
5443
0
:
9142
C(k, l)
¼
0
1
:
0031
1
:
5
1
:
4979
1
:
9927
1
:
9142
2
:
8045
0
:
2929
2.5.3 T
WO
-D
IMENSIONAL
H
ADAMARD
T
RANSFORM
The 2-D Hadamard transform (HT) is a real transform where the components of the
basis functions take values from the binary set
{
1
1
}
. The N
N HT of an N
N
image f is de
ned as
F
¼
AfA
(
2
:
74
)
2
m
. The N
N matrix A is called Hadamard trans-
formation matrix and is related to the N
N Hadamard matrix H by
Here, it is assumed that N
¼
1
p
H
N
A
¼
(
2
:
75
)
The 2
2 Hadamard matrix is
11
1
H
2
¼
(
2
:
76
)
1
The 2N
2N Hadamard matrix is related to the N
N Hadamard matrix through the
recursive equation given by
H
N
H
N
H
N
H
N
H
2N
¼
(
2
:
77
)
For example,
2
3
1111
1
4
5
H
2
H
2
H
2
H
2
11
1
H
4
¼
¼
(
2
:
78
)
11
1
1
1
1
11
Search WWH ::
Custom Search