Video Compression - Signal Processing Systems - page 54

Fig. 8 Illustration of Discrete Cosine Transform ( a ) The original Lena image; ( b ) After transform,
energy is compacted to low-frequency components (the upper-left side ). White and black pixels are
with high energy. Gray pixels are with low energy

×

(DCT) [ 18 ] is adopted in most of the video coding standards. The N N 2-D DCT

transform is defined as Eq. ( 4 ) .

cos 2 Π ( 2 x + 1 ) u
4 N

cos 2 Π ( 2 y + 1 ) v
4 N

2
N C

N − 1 N − 1

F ( u , v )= ( u ) C ( v ) ∑

0 f

( x , y )

∑

x = y =

0

1
√ 2 , (4)

if u,v = 0

C ( u ) , C ( v )=

1 , otherwise

F is the pixel value at the

location (x,y). The first and the second cosine terms are the vertical/horizontal
cosine basis function. With DCT, energy will be gathered to the low-frequency parts
asshowninFig. 8 . The entropy of a block is reduced and it leads to better coding
efficiency in entropy coding.
Quantization [ 8 ] is performed after transformation. It discards some of the
information in a block and leads to lossy coding. A simple example of uniform
quantization is shown in Fig. 9 . There are several decision boundaries like x 1 and x 2 .
All input value between two decision boundaries are output as the same value. For
example, the output value is y 1 if the input value is inside the interval x 1 <

( u , v ) is the DCT value at the location (u,v) and f ( x , y )

x 2 .
In this example, y 1 is set as the average value of x 1 and x 2 . Quantization step is the
distance between two decision boundaries. In a video coding system, quantization
step is adjusted to control the data rate. Larger quantization step leads to lower data
rate but poorer visual quality, and vice versa. In addition, human visual system is less
sensitive to high-frequency components. High-frequency components are usually
quantized more heavily with less visual quality degradation. This is another example
to remove perceptual redundancy for data compression.

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