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Digital Image Processing (2000)

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3.4 Contrast Modification and Equalization

In this section we present point-based contrast modifying operations that clip, stretch, compress, or selectively modify the image intensity range. Examples include grayscale negation, linear contrast stretching and compression, contrast modification using the power law, and level slicing. In digital image processing hardware, all of these operations are usually performed by dedicated hardware called look-up tables (LUTs). These are memories that function as mapping tables.

Contrast manipulation functions.

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This gets an example image.
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Here we show the full-color image and its monochrome copy (note the use of ToGrayLevel, which is discussed in Section 3.5).
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Negating an image is the simplest image modification operation. This operation changes large values to small and vice versa, according to
where x is a pixel value and 255 is the maximum integer value for the typical 8 bpp monochrome image.
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In the case of color images, the point transformation is applied to each color component of each pixel in the image. Here we show the effect of negation on both the color and grayscale images.
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A simple, but useful, contrast manipulation technique is to define a piecewise linear transformation to selectively stretch and/or compress a range of luminance values. The slope of the transformation is chosen greater than 1 in the region of stretch and less than 1 in the region of compression. The function ScalePiecewiseLinear accepts a list of vertices of the piecewise linear transformation, where the first number of each pair is the input (original) pixel value, and the second is the desired output value.
Alternatively, the function ScaleSigma may be used to achieve a similar transformation using an s-shaped transfer function f of the form
where xmin and xmax are the desired minimum and maximum output values, while the parameters (mean) and (variance) control the mid-level and slope of the transformation, respectively.
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A common approach to contrast modification is to use a power-law point transformation, where each pixel of the original image is raised to some common exponent value. Power-law transformations are ubiquitous in photo and video equipment. This is mainly due to the nonlinear nature of the human perceptual response to light and to the inherently nonlinear capture and reproduction of luminance in image acquisition and display devices. Manufacturers of photo and video equipment typically compensate for these nonlinearities; this is commonly known as gamma correction. Four specific, widely recognized transformations are available in function ScaleGamma.
This plots the transfer functions of the four built-in gamma transformations.
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Traditionally, a lookup table is a hardware unit, a memory buffer, found in most signal and image processing hardware devices to allow for fast point-wise transformations of a digital signal. The original signal value is used to address the memory while the value stored in the lookup table is the result of the transformation. The lookup table may therefore be considered conceptually similar to a list of rules in Mathematica. The function LookupTable provides a convenient method of constructing a list of rules. Using the Mathematica ReplaceAll command this list of rules may be applied to an image to transform its values according to any desired point transformation. For complex point transformations the lookup table may provide a fast method of applying the transformation to an image. The following result shows the speedup obtained from using the lookup table approach as compared to the direct, pointwise evaluation of the ScaleGamma function.
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We conclude with a graphical demonstration of the effects of the various contrast modification operations on the example image.
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Image enhancement by histogram modeling is a useful and powerful technique [Cas96, Gon92, Jai89, Pra91]. Histogram modeling techniques modify an image histogram so that it has some desired shape. Histogram equalization, also known as linearization, is the most widely used method of enhancing low-contrast images. Histogram equalization is typically implemented as a point transformation for which the input/output mapping is defined by the cumulative histogram function of the original image. Here is an example of histogram equalization.
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The histogram of the equalized image is strikingly different. Particularly, note that the histogram is stretched, rather than equalized. The latter is not possible, in the strict sense, given the discrete density and distribution functions of digital images.
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