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IMAGE QUANTIZATION Any analog quantity that is to be processed by a digital computer or digital system must be converted to an integer number proportional to its amplitude. The conversion process between analog samples and discrete-valued samples is called quantization. The following section includes an analytic treatment of the quantization process, which is applicable not only for images but for a wide class of signals encountered in image processing systems. | Digital Image Processing PIKS Inside Third Edition. William K. Pratt Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-37407-5 Hardback 0-471-22132-5 Electronic 6 IMAGE QUANTIZATION Any analog quantity that is to be processed by a digital computer or digital system must be converted to an integer number proportional to its amplitude. The conversion process between analog samples and discrete-valued samples is called quantization. The following section includes an analytic treatment of the quantization process which is applicable not only for images but for a wide class of signals encountered in image processing systems. Section 6.2 considers the processing of quantized variables. The last section discusses the subjective effects of quantizing monochrome and color images. 6.1. SCALAR QUANTIZATION Figure 6.1-1 illustrates a typical example of the quantization of a scalar signal. In the quantization process the amplitude of an analog signal sample is compared to a set of decision levels. If the sample amplitude falls between two decision levels it is quantized to a fixed reconstruction level lying in the quantization band. In a digital system each quantized sample is assigned a binary code. An equal-length binary code is indicated in the example. For the development of quantitative scalar signal quantization techniques let f and f represent the amplitude of a real scalar signal sample and its quantized value respectively. It is assumed that f is a sample of a random process with known probability density p f . Furthermore it is assumed that f is constrained to lie in the range aL - f - aU 6.1-1 141 142 IMAGE QUANTIZATION ----------------- 256 ---------------------------------------------------- 11111111 ------------------ 255 11111110 ------------------ ----------------- 254 ---------------------------------------------------- ----------------- 33 ----------------------------------------------------- 00100000 32 00011111 ------------------- -----------------31 .
