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In-Depth Information
in context
k
, then the first number that is transmitted is coded with respect to context
k
;if
further recursion is needed, we use the
k
1 context.
We can summarize the CALIC algorithm as follows:
+
1.
Find the initial prediction
X
.
2.
Compute the prediction context.
3.
Refine the prediction by removing the estimate of the bias in that context.
4.
Update the bias estimate.
5.
Obtain the residual and remap it so the residual values lie between 0 and
M
−
1, where
M
is the size of the initial alphabet.
6.
Find the coding context
k
.
7.
Code the residual using the coding context.
All these components working together have kept CALIC as the state of the art in lossless
image compression. However, we can get almost as good a performance if we simplify some
of the more involved aspects of CALIC. We study such a scheme in the next section.
7.4 JPEG-LS
The JPEG-LS standard looks more like CALIC than the old JPEG standard. When the initial
proposals for the new lossless compression standard were compared, CALIC was rated first in
six of the seven categories of images tested. Motivated by some aspects of CALIC, a team from
Hewlett-Packard (HP) proposed a much simpler predictive coder, under the name LOCO-I (for
low complexity), that still performed close to CALIC [
87
].
As in CALIC, the standard has both a lossless and a lossy mode. We will not describe the
lossy coding procedures.
The initial prediction is obtained using the following algorithm:
if
NW
max
(
W
,
N
)
X
=
max
(
W
,
N
)
else
{
if
NW
min
(
W
,
N
)
X
=
min
(
W
,
N
)
else
X
=
W
+
N
−
NW
}
This prediction approach is a variation of Median Adaptive Prediction [
88
], in which the
predicted value is the median of the
N
W
, and
NW
pixels. The initial prediction is then
refined using the average value of the prediction error in that particular context.
,
