Page 55 - Video Coding for Mobile Communications Efficiency, Complexity, and Resilience

32 Chapter 2. Video Coding: Fundamentals

8 5 5 3 3 2 2 2 16 11 10 16 24 40 51 61
5 5 5 3 3 2 2 0 12 12 14 19 26 58 60 55
5 5 3 3 3 2 0 0 14 13 16 24 40 57 69 56
3 3 3 3 2 2 0 0 14 17 22 29 51 87 80 62
3 3 3 2 2 0 0 0 18 22 37 56 68 109 103 77
2 2 2 2 0 0 0 0 24 35 55 64 81 104 113 92
2 2 0 0 0 0 0 0 49 64 78 87 103 121 120 101
2 0 0 0 0 0 0 0 72 92 95 98 112 100 103 99
(a) Zonal mask with bit (b) Quantization matrix (c) Zigzag scanning
allocation for threshold coding
Figure 2.10: Transform coeGcient bit allocation

use of smaller block sizes reduces computational complexity. 17 However, as
will be discussed later, transform coding su6ers from blocking artefacts at very
low bit rates. Such artefacts are more disturbing with smaller block sizes [15].
As a compromise between computational complexity and blocking artefacts,
most transform coding systems employ a block size of 8 × 8or16 × 16. Note
that both sizes are powers of 2, which simpli es computations.
Another important factor in transform coding is bit allocation. This refers
to the process of determining which coeGcients should be retained for cod-
ing and how coarsely each retained coeGcient should be quantized. There are
two main approaches: zonal coding and threshold coding. In zonal coding the
retained coeGcients are selected on the basis of maximum variance. Thus, the
locations of the retained coeGcients with the largest variances are indicated
by a zonal mask that is the same for all blocks. Once the retained coeGcients
are decided, a number of methods can be used to decide the number of bits
allocated to each. One method is to choose the number of bits to be propor-
tional to the variance of the coeGcient. Figure 2.10(a) shows a zonal mask
with the allocated bits. Once the number of bits allocated for each coeGcient
is determined, a di6erent quantizer can be designed for each coeGcient.
One disadvantage of zonal coding is that the locations of the retained co-
eGcients and the bits allocated to them are xed for all blocks. In threshold
coding, however, the locations and the bit allocation can be adapted to the
characteristics of the block. For this reason, this method is employed by most
video coding standards. In threshold coding, the retained coeGcients are se-
lected on the basis of maximum magnitude. Thus, only those coeGcients whose

17 For example, if a 256 × 256 frame was divided into 256 blocks, each of 16 × 16 pels, then a
4
4
direct implementation of the 2-D DCT will require: blocks × N =256 × 16 =16; 777; 216 mul-
tiplications. If, however, the same frame was divided into 4096 blocks, each of 4 × 4 pels, then
4
4096 × 4 =1; 048; 576 multiplications will be required.