Alternatively, the function ScaleSigma may be used to achieve a similar transformation using an s-shaped transfer function f

_{} of the form

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.

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.