Fundamentals of Digital Image Processing - Control of Color Imaging Systems: Analysis and Design - page 41

P ( x )

x

FIGURE 2.17 Laplacian distribution with a 3 bit optimum quantizer.

uncommon in medical imaging systems. It is well known that uniform quantization of
the intensity values (photon counts) usually creates visual artifacts. This is because
equal changes in the number of photons do not correspond to equal changes in the
perceived brightness. For example, a small change in the photon count at low inten-
sities would be visible, while a large change in the photon count at high intensities may
not be visible. Consequently, to take full advantage of the available quantization
levels, in many imaging systems the quantization is performed in a perceptual domain
as opposed to an intensity domain. It has been argued that the HVS responds almost to
the percentage changes in the intensity. This suggests an approximate logarithmic
relationship between the light intensity and the perceived brightness. There are two
methods for implementing the perceptual quantization in imaging systems: In the rst

technique, the intensity of the pixel value is first quantized to a large number of levels

(e.g., 10 14 bits) during the image digitization stage. Subsequently, the pixel value is

requantized to 8 bits through a nonlinear digital lookup table (LUT) that simulates a
logarithmic or a cube-root transformation. For example, a high-resolution scanner
measures the transmittance of each pixel in roughly 13 bits and uses a cube-root LUT
to convert them into 8 bit values. Similarly, some digital cameras initially digitize the
pixel intensity to 10 bits and subsequently requantize it to 8 bits using LUTs based on
piecewise linear curves simulating a cube-root nonlinearity. In the second approach,
the analog signal is

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first converted to a perceptual domain through an analog non-
linearity (such as a log ampli er) and the output of the ampli er is quantized to 8 bits.

This approach, although less costly, is also less accurate.

2.4.2.5 Vector Quantization

In VQ, the concept of a reconstruction level is generalized to a reconstruction vector
and the decision levels are generalized to decision regions. In general, VQ introduces
less quantization error than SQ for the same number of bits [5,7,8]. As an example,
let is assume that each signal value is scalar quantized to 4 bits (16 levels). To achieve

the same number of bits, the joint vector should be quantized to 8 bits, which

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