Databases Reference
In-Depth Information
The contexts in JPEG-LS also reflect the local variations in pixel values. However, they
are computed differently from CALIC. First, measures of differences
D
1
,
D
2
, and
D
3
are
computed as follows:
D
1
=
NE
−
N
D
2
=
N
−
NW
D
3
=
NW
−
W
.
The values of these differences define a three-component context vector
Q
. The components
of
Q
(
Q
1
,
Q
2
, and
Q
3
) are defined by the following mappings:
D
i
−
T
3
⇒
Q
i
=−
4
−
T
3
<
D
i
−
T
2
⇒
Q
i
=−
3
−
T
2
<
D
i
−
T
1
⇒
Q
i
=−
2
−
T
1
<
D
i
0
⇒
Q
i
=−
1
D
i
=
0
⇒
Q
i
=
0
0
<
D
i
T
1
⇒
Q
i
=
1
T
1
<
D
i
T
2
⇒
Q
i
=
2
T
2
<
D
i
T
3
⇒
Q
i
=
3
T
3
<
D
i
⇒
Q
i
=
4
(9)
where
T
1
,
T
2
, and
T
3
are positive coefficients that can be defined by the user. Given nine
possible values for each component of the context vector, this results in 9
729
possible contexts. In order to simplify the coding process, the number of contexts is reduced
by replacing any context vector
Q
whose first nonzero element is negative by
×
9
×
9
=
−
Q
. Whenever
this happens, a variable
SIGN
is also set to
1; otherwise, it is set to +1. This reduces the
number of contexts to 365. The vector
Q
is then mapped into a number between 0 and 364.
(The standard does not specify the particular mapping to use.)
The variable
SIGN
is used in the prediction refinement step. The correction is first multi-
plied by
SIGN
and then added to the initial prediction.
The prediction error
r
n
is mapped into an interval that is the same size as the range occupied
by the original pixel values. The mapping used in JPEG-LS is as follows:
−
M
2
⇒
r
n
<
−
r
n
←
r
n
+
M
M
2
⇒
r
n
>
r
n
←
r
n
−
M
Finally, the prediction errors are encoded using adaptively selected codes based on Golomb
codes, which have also been shown to be optimal for sequences with a geometric distribution.
In Table
7.3
, we compare the performance of the old and new JPEG standards and CALIC.
The results for the new JPEG scheme were obtained using a software implementation courtesy
of HP.
We can see that for most of the images, the new JPEG standard performs very close to
CALIC and outperforms the old standard by 6% to 18%. The only case where the performance
is not as good is for the Omaha image. While the performance improvement in these examples
