Preliminaries and Definitions

We define a digital image as a two-dimensional array of numbers that represents the real, continuous intensity distribution of a spatial signal. The continuous spatial signal is

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sampled at regular intervals and the intensity is quantized to a finite number of levels. Each element of the array is referred to as a picture element or pixel. The digital image is defined as a spatially distributed intensity signal /(m, n), where / is the intensity of the pixel, and m and n define the position of the pixel along a pair of orthogonal axes usually defined as horizontal and vertical. We shall assume that the image has M rows and N columns and that the digital image has P quantized levels of intensity (gray levels) with values ranging from 0 to P - 1.

The histogram of an image, commonly used in image enhancement and image characterization, is defined as a vector that contains the count of the number of pixels in the image at each gray level. The histogram, can be defined as

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