Image Processing Reference
In-Depth Information
x
2
1
a
d
-1
x
1
1
r
2
c
b
-1
FIGURE 2.18
VQ and SQ.
x
N
]
T
be an N-dimensional vector con-
De
nition:
VQ. Let X
¼ [
x
1
x
2
...
sisting of N scalars x
i
,1
i
N. One approach to quantize X is to quantize each
component of vector X separately (SQ). An alternative approach is joint quantization
of scalars x
i
'
is This is called VQ.
Quantization Rule:
X
Q
¼
r
i
if
X
is in cell
D
i
i
¼
1, 2,
...
, L
(
2
:
57
)
where r
i
, i
¼
, L are N-dimensional reconstruction vectors and L is the
number of levels. The concept of VQ for N
¼
1, 2,
...
4 is shown in Figure
2.19. The reconstruction vectors ri
i
and the cells Di
i
are determined by minimizing the
total distortion de
2 and L
¼
ned by mean square quantization error, that is,
D
¼
E
(
X
X
Q
)
T
(
X
X
Q
)
(
2
:
58
)
x
2
r
4
D
1
D
4
D
3
r
3
r
1
x
1
r
2
D
2
FIGURE 2.19
VQ concept when the number of scalars in the vector is 2 and the number of
reconstruction vectors is 4.
Search WWH ::
Custom Search