Histogram equalization

Histogram equalization is a method in image processing of contrast adjustment using the image's histogram.This method usually increases the global contrast of many images, especially when the usable data of the image is represented by close contrast values. Through this adjustment, the intensities can be better distributed on the histogram. This allows for areas of lower local contrast to gain a higher contrast. Histogram equalization accomplishes this by effectively spreading out the most frequent intensity values.Consider a discrete grayscale image {x} and let ni be the number of occurrences of gray level i. The probability of an occurrence of a pixel of level i in the image is The above describes histogram equalization on a grayscale image. However it can also be used on color images by applying the same method separately to the Red, Green and Blue components of the RGB color values of the image. However, applying the same method on the Red, Green, and Blue components of an RGB image may yield dramatic changes in the image's color balance since the relative distributions of the color channels change as a result of applying the algorithm. However, if the image is first converted to another color space, Lab color space, or HSL/HSV color space in particular, then the algorithm can be applied to the luminance or value channel without resulting in changes to the hue and saturation of the image.There are several histogram equalization methods in 3D space. Trahanias and Venetsanopoulos applied histogram equalization in 3D color space However, it results in 'whitening' where the probability of bright pixels are higher than that of dark ones. Han et al. proposed to use a new cdf defined by the iso-luminance plane, which results in uniform gray distribution.For consistency with statistical usage, 'CDF' (i.e. Cumulative distribution function) should be replaced by 'cumulative histogram', especially since the article links to cumulative distribution function which is derived by dividing values in the cumulative histogram by the overall amount of pixels. The equalized CDF is defined in terms of rank as r a n k / p i x e l c o u n t {displaystyle rank/pixelcount}  .