Information Technology Reference
In-Depth Information
Fig. 1
Simplified Block-
Diagram of JPEG2000
frame encoding without
ROI
Pre-processing :
Level offset, color
transformation
DWT
Quantization
EBCOT
Code stream
Tier 1
Context
modeling
Tier 2
Bit
allocation
Visual System (Part 2 of the standard). Hence the degradations on decoded HD
video frames could not be perceived.
As most of digital HD content is now available in compressed form, the com-
pressed data are very much attractive to use directly for analysis and indexing pur-
poses. This was the case for instance in [11], where the Rough Indexing paradigm
was proposed to fulfill all mid-level indexing tasks such as camera motion identi-
fication, scene boundary detection and meaningful object extraction from MPEG2
compressed streams. The motivation of the earlier work in compressed domain was
mainly in saving computational power and re-using already available low-resolution
information. In the case of JPEG2000, this is the hierarchical nature of DWT which
is in the focus, as it can allow analysis and indexing of image content at various
spatial resolutions. Hence in order to give understanding of the data in the com-
pressed domain to be used for this purpose we will briefly introduce the DWT used
in JPEG2000 standard.
2.1.2
DWT in JPEG2000
We will first limit ourselves to the presentation of Wavelet Transform in the 1D
continuous case. A wavelet is a waveform function localized and sufficiently regular.
These properties are expressed by the following
and
+∞
0
=
0
−
∞
2
2
|
FT
[
ψ
](
ω
)
|
|
FT
[
ψ
](
ω
)
|
L
1
L
2
ψ
∈
∩
d
d
<
+
ω
ω
∞
(1)
|
ω
|
|
ω
|
Where
L
1
is the space of integrable functions on
R
and
L
2
is the space of square-
integrable functions on
is the fre-
quency. From this unique function called “mother wavelet” it is possible to build
a basis for analysis of a function
f
from inner product space
L
2
by translation and
scaling of the mother wavelet:
R
,
FT
[
ψ
] is the Fourier transform of
ψ
and
ω
t
,
h
1
√
h
ψ
−
τ
h
+
,
ψ
h
,
τ
(
t
)=
∈
R
τ
∈
R
(2)
The analysis of
f
consists in computing the coefficients
w
f
(
h
,
τ
) of the projection
of
f
:
