DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

In MPEG-2, DC terms can be
coded with 8, 9, or 10 bits – or, in
4:2:2 profile, 11 bits – of precision.
In MPEG, default quantizer
matrices are standardized, but they
can be overridden by matrices
conveyed in the bitstream.
This example shows that image power is concentrated
into low-frequency transform coefficients – that is,
those coefficients in the upper left-hand corner of the
DCT matrix. No information is lost at this stage. The
DCT is its own inverse, so performing the DCT a second
time would perfectly reconstruct the original samples,
subject only to the roundoff error in the DCT and IDCT.
As expressed in Equation 38.1, the arithmetic of an
8×8 DCT effectively causes the coefficient values to
be multiplied by a factor of 8 relative to the original
sample values. The value 1260 in the [0, 0] entry –
the DC coefficient, or term – is 1 ⁄8 of the sum of the
original sample values. (All of the other coefficients
are referred to as AC.)
The human visual system is not very sensitive to information
at high spatial frequencies. Information at high
spatial frequencies can be discarded, to some degree,
without introducing noticeable impairments. JPEG uses
a quantizer matrix (Q), which codes a step size for each
of the 64 spatial frequencies. In the quantization step of
compression, each transform coefficient is divided by
the corresponding quantizer value (step size) entry in
the Q matrix. The remainder (fraction) after division is
discarded.
It is not the DCT itself, but the discarding of the fraction
after quantization of the transform coefficients,
that makes JPEG lossy!
JPEG has no standard or default quantizer matrix;
however, sample matrices given in a nonnormative
appendix are often used. Typically, there are two
matrices, one for luma and one for color differences.
An example Q matrix is shown in Figure 38.6 overleaf.
Its entries form a radially symmetric version of
Figure 19.5, on page 201. The [0, 0] entry in the quantizer
matrix is relatively small (here, 16), so the DC term
is finely quantized. Further from [0, 0], the entries get
larger, and the quantization becomes more coarse.
Owing to the large step sizes associated with the highorder
coefficients, they can be represented fewer bits.
CHAPTER 38 JPEG AND MOTION-JPEG (M-JPEG) COMPRESSION 453