Cryptography Reference
In-Depth Information
Fig. 2.7 shows an example of original 88 DCT coe
cients F (u, v)(from
Fig. 2.6), the JPEG luminance quantization table Q
lum
(u, v), and the quan-
tized coe
cients F
q
(u, v). Note that in Fig. 2.7, for each coe
cient F (u, v),
its value is quantized such that F
q
(u, v)=F (u, v)/Q
lum
(u, v). It is also noted
that the design of the quantization table has incorporated the characteristics
of the HVS, i.e., the lower frequency coe
cients are fine quantized while the
higher frequency coe
cients are coarsely quantized. Sometimes this type of
quantization is called perceptual quantization [9]. Note that it is common that
different quantization tables are used for compressing luminance and chromi-
nance separately.
Obviously, quantization is a process of approximation, and a good quan-
tizer is one which represents the original signal with minimum perceptual
loss or distortion, and thus achieves good tradeoff between the bit rate and
the reconstructed video quality. In video coding, the choice of quantization
value helps to regulate the bit rate such that it meets the constraints of the
transmission channel. This process is usually called rate control [10].
2.2.6 Zigzag Scanning and Run Length Coding
Fig. 2.7(c) shows a very unique data structure, i.e., all the significant values are
concentrated on the top left corner, and the rest are mostly zeros. Therefore
we can code the coe
cients in the order from low frequency coe
cients to
high frequency coe
cients. This process is called zigzag scanning as shown in
Fig. 2.8(a). After zigzag scanning, we will have a sequence of coe
cients with
a few nonzero in the beginning, following by a long strings of zeros. Fig. 2.8(b)
shows the result of zigzag scanning. This sequence is very suitable to be coded
using run length coding.
Run length coding takes advantage of the fact that, in many data streams,
consecutive single tokens are often identical. In run length coding, repeated
occurrence of the same value is called a run, and the number of repetition is
called the length of the run. By scanning through the data stream, run length
coding checks the stream for repeated occurrence of the same value and its
length.
The first value of Fig. 2.8(b), 23, is called the DC coe
cient of the DCT
transform. It represents the average grey level of the 88 image block. This
DC value will be coded together with DC values of the previous blocks using
DPCM coding to achieve the maximum data reduction. This is based on
the assumption that the neighboring blocks in an image will have similar
brightness level.
The rest values in Fig. 2.8(b) are all called the AC coe
cients of the
DCT transform. They are run-length-coded into a number pair (L, R), such
that L presents the number of zeros between the current nonzero AC value
R and the previous nonzero AC value in the sequence. For example, the first
pair in Fig. 2.8(c), (0, 3), indicates that there is no zero between the current
nonzero AC value 3, and its preceding DC value 23. Similarly, the third pair
