Fundamentals of Digital Image Processing - Control of Color Imaging Systems: Analysis and Design - page 34

(a)

(b)

FIGURE 2.12 (a) Original LENA Image (b) aliased LENA Image.

2.4.2 I MAGE Q UANTIZATION
Once the signal has been sampled (discretized), the amplitude of the sampled values
is quantized (digitized). A quantizer is a many-to-one mapping that maps a range of
input values into a single output value. There are two ways to quantize a signal:
scalar quantization (SQ), where each signal sample is individually quantized,
and vector quantization (VQ), where a block of signal samples is jointly quantized.
The concept of SQ for 1-D signals is shown in Figure 2.13. A typical B -bit scalar
quantizer for a signal with a dynamic range of x min to x max is de ned as

2 B

Q ( x ) ¼ r i if d i 1 < x < d i i ¼ 1, 2, ... , L where L ¼ ( 2 : 40 )

d i ' s are called decision levels and r i ' s are reconstruction levels.

The function Q ( x ) is shown in Figure 2.14.

2.4.2.1 Uniform Quantization

In uniform SQ, the quantization decision levels are of equal length , referred to as

the quantization step size. The quantization step size is related to the signal dynamic
range

D

[ x min x max ] and number of quantization bits B by

f ( n )

f ( x )

f Q ( n )

x x

FIGURE 2.13 SQ for 1-D signals.