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In-Depth Information
(2)
n
0
(2)
n
1
(2)
n
8
(2)
n
layer 2
5
(2)
(2)
(2)
n
n
n
2
4
empty
empty
empty
3
(2)
(2)
n
(2)
n
n
9
6
7
(1)
n
2
(1)
n
7
(1)
n
8
(1)
(1)
n
n
0
6
(1)
(1)
n
n
layer 1
4
empty
empty
empty
(1)
3
(1)
(1)
n
n
n
1
5
9
(0)
n
(0)
(0)
5
(0)
n
n
n
0
9
8
(0)
n
3
(0)
(0)
layer 0
n
n
(0)
1
6
n
7
(0)
empty
(0)
empty
n
n
4
2
BBBBBBBBBB
0
1
2
3
4
5
6
7
8
9
F I GU R E 16 . 21
An example of the collection of bits from subblocks
B
k
into quality
levels.
Rate Control
The embedded coding scheme in JPEG 2000 is similar in philosophy to the EZW and SPIHT
algorithms; however, the data structures used are different. The EZW and SPIHT algorithms
use trees of coefficients from the same spatial location across different bands. In the case
of the EBCOT algorithm, each block resides entirely within a subband, and each block is
coded independently of other blocks. This allows JPEG 2000 to organize bits from different
embedded bitstreams from subblocks into what Taubman and Marcellin call a
pack-stream
.
As the construction of the pack-stream occurs after the compression has been performed, the
process has been called a post-compression process. In order to perform the post-compression
process in an optimum manner, the EBCOT algorithm uses the PCRD-opt algorithm.
Let the truncation points for code-block
i
be denoted by
t
(
k
)
i
. A reasonable set of truncation
points are the ends of the various coding passes described above. The EBCOT algorithm
collects bits from different code-blocks into quality layers. The number of bits collected from
various code-blocks are selected from the truncation points that lie on the convex hull of the
operational rate-distortion curve. A conceptual view of the construction of quality layers is
shown in Figure
16.21
. The number of bits from subblock
B
k
in quality level
Q
l
is given
by
n
(
l
)
k
{
}
where the number of bits contributed by the
k
th code-block depends on the truncation
t
(
j
)
k
points
{
}
:
l
−
1
n
(
l
)
k
t
(
j
)
k
n
(
i
)
k
=
−
i
=
0
