1.6 Quantized Images 11
a pixel
8-bit representation
FIGURE 1.9
Illustration of 8-bit representation of a quantized pixel.
individually or collectively (“vector quantization”);for example, a three-component color
image is frequently represented with 24 bits per pixel of color precision.
Unlike sampling, quantization is a difficult topic to analyze since it is nonlinear.
Moreover, most theoretical treatments of signal processing assume that the signals under
study are not quantized, since it tends to greatly complicate the analysis. On the other
hand, quantization is an essential ingredient of any (lossy) signal compression algorithm,
where the goal can be thought of as finding an optimal quantization strategy that simul-
taneously minimizes the volume of data contained in the signal, while disturbing the
fidelity of the signal as little as possible. With simple quantization, such as gray level
rounding, the main concern is that the pixel intensities or gray levels must be quantized
with sufficient precision that excessive information is not lost. Unlike sampling, there is
no simple mathematical measurement of information loss from quantization. However,
while the effects of quantization are difficult to express mathematically, the effects are
visually obvious.
Each of the images depicted in Figs. 1.4 and 1.8 is represented with 8 bits of gray
level resolution—meaning that bits less significant than the 8
th
bit have been rounded or
truncated. This number of bits is quite common for two reasons: first, using more bits
will generally not improve the visual appearance of the image—the adapted human eye
usually is unable to see improvements beyond 6 bits (although the total range that can
be seen under different conditions can exceed 10 bits)—hence using more bits would
be of no use. Secondly, each pixel is then conveniently represented by a by te. There are
exceptions: in certain scientific or medical applications, 12, 16, or even more bits may be
retained for more exhaustive examination by human or by machine.
Figures 1.10 and 1.11 depict two images at various levels of gray level resolution.
Reduced resolution (from 8 bits) was obtained by simply truncating the appropriate
number of less significant bits from each pixel’s gray level. Figure 1.10 depicts the
256 ⫻ 256 digital image “fingerprint” represented at 4, 2, and 1 bits of gray level resolu-
tion. At 4 bits, the fingerprint is nearly indistinguishable from the 8-bit representation
of Fig 1.8. At 2 bits, the image has lost a sig nificant amount of information, making the
print difficult to read. At 1 bit, the binary image that results is likewise hard to read.
In practice, binarization of fingerprints is often used to make the print more distinc-
tive. Using simple truncation-quantization, most of the print is lost since it was inked
insufficiently on the left, and excessively on the rig ht. Generally, bit truncation is a poor
method for creating a binary image from a gray level image. See Chapter 2 for better
methods of image binarization.