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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 considers the processing of quantized variables. The last section discusses the subjective effects of quantizing monochrome and color images. . SCALAR QUANTIZATION Figure 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 141 142 IMAGE QUANTIZATION ----------------- 256 ---------------------------------------------------- 11111111 ------------------ 255 11111110 ------------------ ----------------- 254 ---------------------------------------------------- ----------------- 33 ----------------------------------------------------- 00100000 32 00011111 ------------------- -----------------31 .