Page 56 - Video Coding for Mobile Communications Efficiency, Complexity, and Resilience

Section 2.6. Intraframe Coding 33

magnitudes are above a threshold are retained. In practice, the thresholding and
the following quantization operations are combined in one operation using a
uniform threshold quantizer as was described in Section 2.5.4 (see Figure 2.5
and Equations (2.8) and (2.10)). In this case, a quantization matrix is used to
de ne the quantizer step size, , for each coeGcient in the block. A typical
quantization matrix is given in Figure 2.10(b). Note that low-frequency coeG-
cients (toward top-left corner) are more nely quantized (i.e., quantized with a
smaller step size) because of two reasons. First, the DCT tends to concentrate
most of the energy in low frequencies. Second, the HVS is more sensitive
to variations in low frequencies. Since in threshold coding the locations of
the retained coeGcients vary from block to block, those locations need to be
encoded. A commonly used strategy is to zigzag scan the transform coeG-
cients, as illustrated in Figure 2.10(c), in an attempt to produce long runs of
zeros, and then RLE is used to encode the resulting array.
Compared to predictive coding, transform coding provides higher compres-
sion with less sensitivity to errors and less dependence on the input data
statistics. Its higher computational complexity and storage requirements have
been o6set by advances in integrated circuit technology. One disadvantage,
however, is that when compression factors are pushed to the limit, three
types of artefacts start to occur: (i) “graininess” due to coarse quantization
of some coeGcients, (ii) “blurring” due to the truncation of high-frequency
coeGcients, and (iii) “blocking artefacts,” which refer to arti cial disconti-
nuities appearing at the borders of neighboring blocks due to independent
processing of each block. Since blocking artefacts are the most disturbing, a
number of methods have been proposed to reduce them. Examples are over-
lapping blocks at the encoder [34], the use of the lapped orthogonal trans-
form (LOT) [35], and postprocessing using ltering and image restoration
techniques [36].

2.6.3 Subband Coding
As already mentioned, rate-distortion theory can provide insights into the de-
sign of eGcient coders. For example, in Ref. 37 it is shown that the math-
ematical form of the rate-distortion function suggests that an eGcient coder
splits the original signal into spectral components of in nitesimal bandwidth
and encodes these spectral components independently. This is the basic idea
behind subband coding. Subband coding was rst introduced by Crochiere
et al. in 1976 in the context of speech coding [38] and was applied to image
coding by Woods and O’Neil in 1986 [39]. In subband coding the input image
is passed through a set of bandpass lters to create a set of bandpass images,
or subbands. Since a bandpass image has a reduced bandwidth compared to
the original image, it can be downsampled (subsampled or decimated). This