DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

In the JPEG and MPEG standards,
and in most JPEG-like schemes,
each entry in the quantizer matrix
takes a value between 1 and 255.
Figure 38.7 DCT coefficients
after quantization are
shown. Most of the highfrequency
information in this
block – DCT entries at the
right and the bottom of the
matrix – are quantized to
zero. The nonzero coefficients
have small magnitudes.
Q
=
16 11 10 16 24 40 51 61
12 12 14 19 26 58 60 55
14 13 16 24 40 57 69 56
14 17 22 29 51 87 80 62
18 22 37 56 68 109 103 77
24 35 55 64 81 104 113 92
49 64 78 87 103 121 120 101
72 92 95 98 112 100 103 99
Figure 38.6 Typical JPEG quantizer matrix reflects the visual
system’s poor sensitivity to high spatial frequencies. Transform
coefficients can be approximated, to some degree,
without introducing noticeable impairments. The quantizer
matrix codes a step size for each spatial frequency. Each transform
coefficient is divided by the corresponding quantizer
value; the remainder (or fraction) is discarded. Discarding the
fraction is what makes JPEG lossy.
At first glance, the large step size associated with the
DC coefficient (here, Q 0,0 = 16) looks worrisome: With
8-bit data ranging from -127 to +128, owing to the
divisor of 16, you might expect this quantized coefficient
to be be represented with just 4 bits. However, as
I mentioned earlier, the arithmetic of Equation 38.1
scales the coefficients by 8 with respect to the sample
values, so a quantizer value of 16 corresponds to 7 bits
of precision when referenced to the sample values.
DCT coefficients after quantization, and after discarding
the quotient fractions, are shown in Figure 38.7:
F*
=
79 0 -1 0 0 0 0 0
-2 -1 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
454 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES