Histogram equalization: Difference between revisions

Revision as of 11:49, 7 April 2025

Revision as of 15:01, 12 April 2025

Line 3:

{{Use American English|date=March 2021}}

{{Use mdy dates|date=March 2021}}

[[Image:Histogrammeinebnung.png|thumb|right|300px|alt=A histogram which is zero apart from a central area containing strong peaks is transformed by stretching the peaked area to fill the entire x-axis.|Histograms of an image before and after equalization.]]

'''Histogram equalization''' is a method in [[image processing]] of [[contrast (vision)|contrast]] adjustment using the [[image]]'s [[Image histogram|image's histogram]].

Histogram equalization is a specific case of the more general class of histogram remapping methods. These methods seek to adjust the image to make it easier to analyze or improve visual quality (e.g., [[retinex]])

[[Image:Histogrammeinebnung.png|thumb|right|300px|alt=A histogram which is zero apart from a central area containing strong peaks is transformed by stretching the peaked area to fill the entire x-axis.|Histograms of an image before and after equalization.]]

==Overview==

This method usually increases the global [[contrast (vision)|contrast]] of many images, especially when the image is represented by a narrow range of intensity values. Through this adjustment, the [[luminous intensity|intensities]] can be better distributed on the histogram utilizing the full range of intensities evenly. This allows for areas of lower local contrast to gain a higher contrast. Histogram equalization accomplishes this by effectively spreading out the highly populated intensity values, which are usedtend to degrade image contrast.

The method is useful in images with backgrounds and foregrounds that are both bright or both dark. In particular, the method can lead to better views of [[bone]] structure in [[x-ray]] images, and to better detail in [[photographs]] that are either over or under-exposed. A key advantage of the method is that it is a fairly straightforward technique adaptive to the input image and an [[invertible]] [[Operator (mathematics)|operatoroperation]]. So, in theory, if the histogram equalization [[function (mathematics)|function]] is known, then the original histogram can be recovered. The calculation is not [[computation]]ally intensive. A disadvantage of the method is that it is indiscriminate. It may increase the contrast of background [[signal noise|noise]], while decreasing the usable [[signal]]. In scientific imaging where spatial correlation is more important than intensity of signal (such as separating [[DNA]] fragments of quantized length), the small [[signal-to-noise ratio]] usually hampers visual detections.

In scientific imaging where spatial correlation is more important than intensity of signal (such as separating [[DNA]] fragments of quantized length), the small [[signal-to-noise ratio]] usually hampers visual detections.

Histogram equalization often produces unrealistic effects in photographs; however it is very useful for scientific images like [[Thermography|thermal]], [[satellite]] or [[x-ray]] images, often the same class of images to which one would apply [[false-color]]. Also histogram equalization can produce undesirable effects (like visible [[image gradient]]) when applied to images with low [[color depth]]. For example, if applied to 8-bit image displayed with [[List of 8-bit computer hardware palettes|8-bit gray-scale palette]] it will further reduce [[color depth]] (number of unique shades of gray) of the image. Histogram equalization will work the best when applied to images with much higher [[color depth]] than [[Palette (computing)|palette]] size, like [[Continuous function|continuous]] data or 16-bit gray-scale images.

There are two ways to think about and implement histogram equalization, either as image change or as [[Palette (computing)|palette]] change. The operation can be expressed as ''P(M(I))'' where ''I'' is the original image, ''M'' is histogram equalization mapping operation and ''P'' is a palette. If we define a new palette as ''P'=P(M)'' and leave image ''I'' unchanged then histogram equalization is implemented as [[Palette (computing)|palette]] change or mapping change. On the other hand, if palette P remains unchanged and image is modified to ''I'=M(I)'' then the implementation is accomplished by image change. In most cases palette change is betterpreferred as it preserves the original data.

Modifications of this method use multiple histograms, called subhistograms, to emphasize local contrast, rather than overall global contrast. Examples of such methods include [[adaptive histogram equalization]] and variations including, ''contrast limitinglimited adaptive histogram equalization'' or [[CLAHE]], multipeak histogram equalization (MPHE), and multipurpose beta -optimized bihistogram equalization (MBOBHE). The goal of these methods, especially MBOBHE, is to modifying the algorithm to improve the contrast without producing brightness mean-shift and detail loss artifacts by modifying the HE algorithm.<ref>{{cite journal|last1=Hum|first1=Yan Chai|last2=Lai|first2=Khin Wee|last3=Mohamad Salim|first3=Maheza Irna|title=Multiobjectives bihistogram equalization for image contrast enhancement|journal=Complexity|date=11 October 2014|volume=20|issue=2|pages=22–36|doi=10.1002/cplx.21499|bibcode=2014Cmplx..20b..22H}}</ref>

A signal transform equivalent to histogram equalization also seems to happen in [[biological neural networks]] so as to maximize the output firing rate of the neuron as a function of the input statistics. This has been proved in particular in the [[fly]] [[retina]].<ref>{{cite journal|last=Laughlin|first=S.B|year=1981|title=A simple coding procedure enhances a neuron's information capacity|journal=Z. Naturforsch.|volume=9–10(36):910–2}}</ref><!--[[User:Kvng/RTH]]-->

Histogram equalization is a specific case of the more general class of histogram remapping methods. These methods seek to adjust the image to make it easier to analyze or improve visual quality (e.g., [[retinex]])

===Back projection===