Cuantizacion

Chapter 14 Review of Quantization
14.1 Tone-Transfer Curve

The second operation of the digitization process converts the continuously valued irradiance of each sample at the detector (i.e., the brightness) to an integer, i.e., the sampled image is quantized. The entire process of measuring and quantizing the brightnesses is significantly affected by detector characteristics such as dynamicrange and linearity. The dynamic range of a detector image is the range of brightness (irradiance) over which a change in the input signal produces a detectable change in the output. The input and output quantities need not be identical; the input may W be measured in mm2 and the output in optical density. The effect of the detector on the measurement may be described by a transfer characteristic ortone-transfer curve (TTC), i.e., a plot of the output vs. input for the detector. The shape of the transfer characteristic may be used as a figure of merit for the measurement process. A detector is linear if the TTC is a straight line, i.e., if an incremental change in input from any level produces a fixed incremental change in the output. Of course, all real detectors have a limited dynamic range,i.e., they will not respond at all to light intensity below some minimum value and their response will not change for intensities above some maximum. All realistic detectors are therefore nonlinear, but there may be some regions over which they are more-or-less linear, with nonlinear regions at either end. A common such example is photographic film; the TTC is the H-D curve which plots recordedoptical density of the emulsion vs. the logarithm of W the input irradiance [ mm2 ]. Another very important example in digital imaging is the video camera, whose TTC maps input light intensity to output voltage. The transfer characteristic of a video camera is approximately a power law:
γ Vout = c1 Bin + V0

where V0 is the threshold voltage for a dark input and γ (gamma) is the exponent of thepower law. The value of γ depends on the specific detector: typical values are γ ∼ 1.7 for a vidicon camera and γ ∼ 1 for an image orthicon. = = 281

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CHAPTER 14 REVIEW OF QUANTIZATION

Nonlinear tone-transfer curve of quantizer, showing a linear region.

14.2

Quantization

Quantization converts continuously valued measured irradiance at a sample to a member of a discrete set of graylevels or digital counts, e.g.,the sample f [x, y] e.g., W f [0, 0] = 1.234567890 · · · mm2 , is converted to an integer between 0 and some maximum value (e.g., 255) by an analog-to-digital conversion (A/D converter or ADC). The number of levels is determined by number of bits available for quantization in the ADC. A quantizer with m bits defines M = 2m levels. The most common quantizers have m =8 bits (one byte); such systems can specify 256 different gray levels (usually numbered from [0, 255], where 0 is usually assigned to “black” and 255 to “white”. Images digitized to 12 or even 16 bits are becoming more common, and have 4096 and 65536 levels, respectively. The resolution, or step size b, of the quantizer is the difference in brightness between adjacent gray levels. It makes littlesense to quantize with a resolution b which is less than the uncertainty in gray level due to noise in the detector system. Thus the effective number of levels is often less than the maximum possible. Conversion from a continuous range to discrete levels requires a thresholding operation (e.g.,truncation or rounding). Some range of input brightnesses will map to W a single output level, e.g., allmeasured irradiances between 0.76 and 0.77 mm2 might map to gray level 59. Threshold conversion is a nonlinear operation, i.e., the threshold of a sum of two inputs is not necessarily the sum of the thresholded outputs. The concept of linear operators will be discussed extensively later, but we should say at this point that the nonlinearity due to quantization makes it inappropriate to analyze the...