ADAPTIVE HISTOGRAM EQUALIZATION

Adaptive histogram equalization is a computer image processing technique used to improve contrast in images. It differs from ordinary histogram equalization inthe respect that the adaptive method computes several histograms, each corresponding to a distinct section of the image, and uses them to redistribute the lightness values of the image. Ordinary histogram equalization simply uses a single histogram for an entire image.

The underlying reason for this technique is that human vision can only detect local brightness changes of about 2-3 percent, depending on the viewing conditions. A typical (8-bit) digitized image has 256 grey scale levels, and  some cameras, scanners and other instruments produce images with much higher range (14 bits from a cooled astronomical camera corresponds to 16,384 grey scale levels). These cannot all be distinguished by the eye, and in fact cannot be displayed or recorded by most output devices (computer displays, printers, etc.) and at the high end even challenge photographic film. Several approaches have been used to perform this type of image processing, some of them very ad-hoc and without any sound scientific or mathematical basis. The most generally accepted and successful are “unsharp masking” (a term borrowed from photographic darkroom technique) and “local histogram equalization”.

The first of these is a linear technique, meaning that it can be carried out using an array of weights that are multiplied by each pixel and its neighbors to produce a summed result that replaces the pixel. The optimum array of weights is a Gaussian filter, and Photoshop and many similar programs include this function (with the ability to add a proportion of the result to the original image). Logically, it is equivalent to making a copy of the image, blurring it enough to remove the desired small details, and then subtracting this image from the original to enhance the visibility of those details. In many cases it is more efficient to actually perform the operation using Fourier transforms, in which case the method may be described as a high pass filter (meaning that it preserves high frequencies). The details of how the unsharp masking method is implemented influence the speed of computation but not the results. One of the drawbacks of this method is that it is sensitive to noise, which is generally high frequency and is amplified in the process. A more elaborate method called the difference-of- Gaussians (D.O.G.) filter can be used to deal with the noise.

The second method mentioned above uses the histogram in a small region around each pixel in the image. The histogram is a graph of the number of pixels having each possible brightness level. Equalization, which is sometimes applied to an entire image, assigns new brightness values to each pixel based on the original brightness level, so that the cumulative histogram becomes a straight line. This means that all brightness levels are used for equal areas in the image. Local equalization applies this same logic to the histogram of each region but keeps the new brightness level only for the central pixel. The result is to make pixels that are slightly brighter (or darker) than their surroundings much brighter (or darker) thus increasing local contrast. For practical reasons of implementation, many systems use a moving square neighborhood