Databases Reference
In-Depth Information
certain high rate points on the convex hull are no longer allowed. In such situations one could
use the points on the convex hull to initiate a search for a point on the operational rate-distortion
curve interior to the convex hull that would satisfy the operational constraint.
13.6 Application to Image Compression
__
JPEG
The JPEG standard is one of the most widely known standards for lossy image compression.
It is a result of the collaboration of the International Standards Organization (ISO), which is a
private organization, and what was the CCITT (now ITU-T), a part of the United Nations. The
approach recommended by JPEG is a transform coding approach using the DCT. The approach
is a modification of the scheme proposed by Chen and Pratt [
196
]. In this section, we will
briefly describe the baseline JPEG algorithm. In order to illustrate the various components of
the algorithm, we will use an 8
×
8 block of the Sena image, shown in Table
13.5
.Formore
details, see [
6
].
13.6.1 The Transform
The transform used in the JPEG scheme is the DCT transform described earlier. The input
image is first “level shifted” by 2
P
−
1
; that is, we subtract 2
P
−
1
from each pixel value, where
P
is the number of bits used to represent each pixel. Thus, if we are dealing with 8-bit images
whose pixels take on values between 0 and 255, we would subtract 128 from each pixel so that
the value of the pixel varies between
−
128 and 127. The image is divided into blocks of size
8
8 forward DCT. If any dimension of the image
is not a multiple of eight, the encoder replicates the last column or row until the final size is a
multiple of eight. These additional rows or columns are removed during the decoding process.
If we take the 8
×
8, which are then transformed using an 8
×
8 block of pixels shown in Table
13.5
, subtract 128 from it, and take the
DCT of this level-shifted block, we obtain the DCT coefficients shown in Table
13.6
. Notice
that the lower-frequency coefficients in the top-left corner of the table have larger values than
the higher-frequency coefficients. This is generally the case, except for situations in which
there is substantial activity in the image block.
×
13.6.2 Quantization
The JPEG algorithm uses uniform midtread quantization to quantize the various coefficients.
The quantizer step sizes are organized in a table called the
quantization table
and can be
viewed as the fixed part of the quantization. An example of a quantization table from the JPEG
recommendation [
6
] is shown in Table
13.7
. Each quantized value is represented by a label.
The label corresponding to the quantized value of the transform coefficient
θ
ij
is obtained as
θ
ij
Q
ij
+
5
l
ij
=
0
.
(61)
