Databases Reference
In-Depth Information
O O O
O O O O A
O O X
O O O O
O O O O X
O A
(a)
(b)
F I GU R E 7 . 12
(a) Three-line and (b) two-line neighborhoods.
0 0 0
1 0 0 0 1
1 0 0
0 0 1 1
0 0 0 1 1
1 0
(a)
(b)
F I GU R E 7 . 13
(a) Three-line and (b) two-line contexts.
the pixel being encoded. The
A
pixel can be moved around to capture any structure that might
exist in the image. This is especially useful in halftone images in which the
A
pixels are used
to capture the periodic structure. The location and movement of the
A
pixel are transmitted to
the decoder as side information.
In Figure
7.13
, the symbols in the neighborhoods have been replaced by 0s and 1s. We take
0 to correspond to white pixels, while 1 corresponds to black pixels. The pixel to be encoded
is enclosed by the heavy box. The pattern of 0s and 1s is interpreted as a binary number,
which is used as an index to the set of probabilities. The context in the case of the three-line
neighborhood (reading left to right, top to bottom) is 0001000110, which corresponds to an
index of 70. For the two-line neighborhood, the context is 0011100001, or 225. Since there
are 10 bits in these templates, we will have 1024 different arithmetic coders.
In the JBIG standard, the 1024 arithmetic coders are a variation of the arithmetic coder
known as the QM coder described in Chapter 4. The QM coder is a modification of an adaptive
binary arithmetic coder called the Q coder [51, 52, 53], which in turn is an extension of another
binary adaptive arithmetic coder called the skew coder [
102
].
As the lower-resolution layers are obtained from the higher-resolution images, we can use
them when encoding the higher-resolution images. The JBIG specification makes use of the
lower-resolution images when encoding the higher-resolution images by using the pixels of
the lower-resolution images as part of the context for encoding the higher-resolution images.
The contexts used for coding the lowest-resolution layer are those shown in Figure
7.12
.The
contexts used in coding the higher-resolution layer are shown in Figure
7.14
.
Ten pixels are used in each context. If we include the 2 bits required to indicate which
context template is being used, 12 bits will be used to indicate the context. This means that
we can have 4096 different contexts.
