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Journal of Electronic Imaging 16(3), 033005 (Jul–Sep 2007)

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Image contrast enhancement based on the generalizedhistogram

Byoung-Woo YoonWoo-Jin Song

Pohang University of Science and TechnologyDivision of Electrical and Computer Engineering

San 31 Hyoja-Dong, PohangKyungbuk, 790-784 Korea

E-mail: wjsong@postech.ac.kr

bstract. We present an adaptive contrast enhancement methodased on the generalized histogram, which is obtained by relaxing

he restriction of using the integer count. For each pixel, the integerount 1 allocated to a pixel is split into the fractional count and theemainder count. The generalized histogram is generated by accu-ulating the fractional count for each intensity level and distributing

he remainder count uniformly throughout the intensity levels. Thentensity mapping function, which determines the contrast gain forach intensity level, is derived from the generalized histogram.ince only the fractional part of the count allocated to each pixel issed for increasing the contrast gain of its intensity level, themount of contrast enhancement is adjusted by varying the frac-

ional count according to regional characteristics. The proposedcheme produces visually more pleasing results than the conven-ional histogram equalization. © 2007 SPIE and IS&T.DOI: 10.1117/1.2775482�

Introductionhe most common way to enhance image contrast is the

ntensity mapping that reassigns the intensity of the pixelshrough a monotonically increasing function. One of theost popular intensity mapping methods is local histogram

qualization,1–3 in which the mapping function for eachixel is generated by accumulating the histogram of theegion surrounding the target pixel. Although the local his-ogram equalization method is useful in various fields, itften produces unnatural appearances resulting from con-rast overenhancement, especially in homogeneous regions.

Although the desirable contrast gain for human observ-rs is different from pixel to pixel according to its regionalharacteristics and the purpose of the application, the his-ogram includes little information about the pixel character-stics related to the desirable contrast gain and informs onlyhe probabilistic distribution of the intensity levels. Sinceocal histogram equalization generates the mapping func-ion relying on the histogram, it attempts to amplify theontrast for every pixel as much as possible. Therefore,ocal histogram equalization can cause overenhancement inhe regions where contrast preserving rather than contrasttretching is more desirable. To overcome this limitation ofocal histogram equalization, numerous methods have been

aper 06029RR received Feb. 24, 2006; revised manuscript received Feb.3, 2007; accepted for publication Mar. 13, 2007; published online Aug.7, 2007.

017-9909/2007/16�3�/033005/8/$25.00 © 2007 SPIE and IS&T.

ournal of Electronic Imaging 033005-

proposed by modifying the histogram.4–16 Unlike theseconventional methods, which generate the mapping func-tions based on the histogram, we introduce a new contrastenhancement method based on the generalized histogramby relaxing the restriction of using the integer count of thehistogram. In generating the generalized histogram, thecount allocated to each pixel is split into the fractionalcount and the remainder count. Then the generalized histo-gram is obtained by accumulating the fractional count foreach intensity level and distributing the remainder countuniformly over the intensity levels. From the viewpoint ofcontrast enhancement, increasing the occurrence of an in-tensity level means increasing the contrast gain of that in-tensity level. In the generalized histogram, the fractionalcount instead of the whole integer count 1 is used for in-creasing the contrast gain, so that the amount of contrastenhancement can be controlled. By adjusting the value ofthe fractional count according to the regional characteristicsand user’s requirement, the desirable contrast gain can berealized from the generalized histogram. Therefore, the pro-posed method that uses the generalized histogram in gener-ating the mapping function can give visually more pleasingresults than the conventional local histogram equalization.

This paper is organized as follows. In Section 2, theintensity mapping is described using the contrast gain func-tion and the local histogram equalization method is re-viewed in this framework. In Section 3, we introduce thegeneralized histogram, which replaces the conventional his-togram in the procedure of generating the mapping func-tion, and propose a scheme that generates the fractionalcount for each pixel according to its regional characteristicsand user’s requirement. In Section 4, we present the experi-mental results. Finally, Section 5 gives our conclusion.

2 Intensity MappingIntensity mapping methods generate the output intensity yijby mapping the input intensity level xij through a mappingfunction f ij�·� such that

yij = f ij�xij� . �1�

Intensity mapping methods can be classified into global andlocal methods. Global methods apply just one mapping

function for every pixel, so the mapping function does not

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ary with the pixel location and can be represented as f�·�.n the other hand, local methods apply different mapping

unctions for different pixels. Hence, f ij�·� should be deter-ined for each pixel using the information of the pixelsithin the local region surrounding the target pixel at �i , j�.The slope of the mapping function at an intensity level

ndicates the amount of contrast enhancement for that level.hus, we define the contrast gain function wij�·� using theiscrete derivative, df�k� /dk, such that

ij�k� = � f ij�0� , k = 0,

dfij�k�dk

= f ij�k� − f ij�k − 1� , k = 1, . . . ,Q − 1, ��2�

here Q represents the number of intensity levels. If wij�·�s given, then f ij�·� can be readily obtained by

f ij�k� = �l=0

k

wij�l�, k = 0,1, . . . ,Q − 1. �3�

ince the contrast gain function is more useful in under-tanding the characteristics of an intensity mapping methodhan the mapping function, we deal with wij�·� hereafter.

Local histogram equalization, which is one of the mostell-known local methods, uses the histogram of the local

egion as a contrast gain function. If we assume that theutput intensity range is �0, 1�, the contrast gain function ofocal histogram equalization is obtained by normalizing theistogram of the local region as follows:

ij�k� =1

Nijhij�k�, k = 0,1, . . . ,Q − 1, �4�

here hij�·� denotes the histogram of the local region Aij

nd Nij represents the number of pixels in the local regionij. If the entire image is taken for the local region forvery pixel, hij�·� becomes the global histogram and wij�·�n �4� is equivalent to the contrast gain function of globalistogram equalization.17 Hence, global histogram equal-zation can be regarded as a special case of local histogramqualization. In the basic form of local histogram equaliza-ion, the local region Aij is a square window centered at thearget pixel. The histogram of the local region Aij can beepresented by

ij�k� = ��u,v��Aij

��xuv,k�, k = 0,1, . . . ,Q − 1, �5�

here ��k , l� represents the Kronecker delta function,hich equals 1 if k= l and equals 0 otherwise. As you can

ee in �5�, the histogram is obtained by the procedure inhich each pixel increases the occurrence of its intensity

evel by the allocated count 1. From the viewpoint of con-rast enhancement, this means that each pixel increases theontrast gain for its intensity level by an equal amount,ince the contrast gain is proportional to the histogram ofhe local region as we see in �4�. However, the desirableontrast gain for the human observers is not constant butather varies from pixel to pixel according to many factors

uch as regional characteristics, user’s requirement, and so

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on.18,19 Therefore, the equal increment of the contrast gainfor every pixel causes contrast overenhancement when thenumber of pixels with an intensity level is large and a smallcontrast gain is appropriate for the human observers. Inaddition, the result of local histogram equalization cannotsatisfy various situations where the desirable amount ofcontrast enhancement is different according to the objectiveof applications, a user’s tastes, and so on. A number ofmethods have been proposed to solve these problems bymodifying the histogram such as smoothing thehistogram.4–16 Instead of taking an action on the histogram,however, we generalize the histogram itself to overcomethe drawback of the conventional histogram manipulationfor contrast enhancement.

3 Adaptive Contrast Enhancement Basedon the Generalized Histogram

In the histogram shown in �5�, the pixel at �u ,v� increaseshij�xuv� by one. From �4�, this results in increasing the con-trast gain of the intensity level xuv by the same amount,1 /Nij, as any other pixel. If the pixel requires a small con-trast gain, this increment of the contrast gain function mightbe too much. The excessive increment in the contrast gainis caused by using the integer count 1 for all pixels regard-less of the desirable contrast gain.

3.1 Generalized HistogramWe introduce the generalized histogram gij�k� to replace thehistogram hij�k� in �4�. In generating gij�k�, we split theinteger count, 1, allocated to the pixel at �u ,v� within thelocal region Aij and use the fractional count for increasinggij�xuv�. Since the contrast gain function of the proposedmethod is proportional to the generalized histogram, usingthe fractional count instead of the integer count 1 can adap-tively reduce the excessive increment of the contrast gain.However, using the fractional count results in the reductionof the total count, which is related to the total output inten-sity range. In order to maintain the total output intensityrange, the remainder count, that is, one minus the fractionalcount, should be distributed. Since the purpose of splittingthe count is to alleviate contrast overenhancement, the re-mainder count should be distributed in the manner that pre-serves the image contrast. We uniformly distribute the re-mainder count, since the uniform distribution implies acontrast gain function that generates the same contrast gainfor all intensity levels and thus produces contrast preserva-tion. As a result, the generalized histogram gij�k� of thelocal region Aij can be represented by

gij�k� = ��u,v��Aij

�ruv · ��xuv,k� + �1 − ruv� ·1

Q,

k = 0,1, . . . ,Q − 1, �6�

where ruv denotes the fractional count for a pixel at �u ,v�.The range of the fractional count is �0, 1�, because thecount allocated to the pixel is 1 and the fractional countshould be a part of that count. If ruv=1 for every pixel inthe image, i.e., the count is not split, �6� is reduced to �5�.Therefore, the conventional histogram can be regarded asthe special case of the generalized histogram. Let us see �6�

from the viewpoint of contrast enhancement. With �4� and

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6�, it should be noted that from the count allocated to theixel at �u ,v�, the fractional count ruv is assigned for con-rast enhancement by increasing the contrast gain of its in-ensity level and the remainder count �1−ruv� is uniformlyistributed for the contrast preservation. Therefore, the pro-ortion of contrast enhancing to contrast preserving can beontrolled by adjusting the value of ruv.

.2 Generating the Fractional Counts shown in �6�, the fractional count for each pixel should

Fig. 1 Contrast enhancement results with the 5of global histogram equalization; �c� result of lomethod.

e calculated previously to generate the generalized histo-

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gram. In this section, we will explain a method of obtainingan appropriate fractional count for visually pleasing resultsdepending on the regional characteristics of the pixel andthe purpose of applications.

To obtain desirable contrast enhancement results in agiven situation, the contrast gain should be adjusted accord-ing to the purpose of the application, since the appropriateamount of contrast enhancement varies according to thepurpose of applications. For example, relatively large con-trast gains over the whole image are suitable for inspecting

2 building image. �a� Original image; �b� resulttogram equalization; �d� result of the proposed

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cientific images, while relatively small contrast gains areppropriate for enhancing photographic images. In addi-ion, the contrast gain should be adjusted pixel by pixelccording to its spatial activity, which represents the rate ofntensity changes. For the pixel whose intensity level isimilar to those of the neighborhood pixels, strong contrastnhancement causes an excessive intensity change, result-ng in a loss of natural impression. Therefore, the smallerpatial activity a pixel has, the less contrast gain is desir-ble for visually pleasing results. In the proposed method,he degree of relaxation in the contrast gain depends on thealue of ruv. Therefore, ruv should be adjusted according tooth the purpose of applications and the spatial activity ofhe pixel at �u ,v�. Then ruv can be formulated as

uv = � · �uv, �7�

here � and �uv reflect the user’s requirement dependingn the application and the spatial activity of the pixel atu ,v�, respectively. Since ruv should have a value within �0,�, the ranges of both � and �uv should be �0, 1�. In �7�, weall the first term, �, the user control parameter. By varying

from 0 to 1, the user can control the amount of contrastnhancement over the whole image depending on the ap-lication and user’s tastes. As � increases, the fractionalounts for every pixel in the image have relatively largeralues and stronger contrast enhancement is achieved overhe whole image. The second term, �uv, adjusts the contrastain pixel by pixel according to its spatial activity. Thepatial activity can be estimated using various measuresuch as the variance of xuv. In the proposed scheme, thepatial activity suv is chosen to be the average absoluteifference normalized by the local mean as follows:

uv =

1

8· �

n=u−1

u+1

�m=v−1

v+1

xnm − xuv

1

9· �

n=u−1

u+1

�m=v−1

v+1

xnm

, �8�

here the numerator denotes the average absolute differ-nce from the adjacent pixels and the denominator denoteshe local mean of the 3�3 pixels. Normalizing with theocal mean reflects Weber’s law, which states that the ratiof the just noticeable change and the intensity of the back-round is constant for a wide range of intensity.24 Since theange of �uv should be �0, 1� and proportional to the spatialctivity, we define �uv such that

uv = 1 − e−�·suv, �9�

here � determines the slope of the function and ��0.lthough other functions that satisfy the necessary condi-

ions mentioned in Subsection 3.2 can be used in �9�, weust choose the exponential form for the sake of simplicity.s the value of � increases in �9�, a difference in the spatial

ctivity produces a greater change in �uv, resulting in areater change in the contrast gain.

As a result, the fractional count ruv can be represented

y

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ruv = � · �1 − e−�·suv� , �10�

where � and � are two parameters with which users cancontrol the degree of contrast enhancement depending onsituations. The effect of these two parameters will be ex-plained in the next section with experimental results.

4 Experimental ResultsTo verify the efficacy of the proposed method, we havetested the conventional histogram equalization methods andthe proposed method for various images. Although localhistogram equalization produces relatively good results formany images, it may cause contrast overenhancement forthe images, which include locally homogeneous regionssuch as the background. Even for these images, the pro-posed method can generate visually pleasing results by ad-justing the contrast gain according to the regional charac-teristics. As an example, we present the results from thebuilding image in Fig. 1. The building image shown in Fig.1�a� has 512�512 pixels and is digitized to 8 bits, that isto say, Q=256. Fig. 1�b� shows the resulting image of glo-bal histogram equalization. We see that the contrast overthe whole image is somewhat enhanced, but global histo-gram equalization degrades the contrast of the details in thesmall regions such as the cars in the bottom of the image.Fig. 1�c� shows the result of local histogram equalizationwith a 41�41 square window. In this result, we see thatlocal histogram equalization enhances the contrast of thedetails in the small regions, but its overall appearance isquite unnatural to human observers due to excessive ampli-fication of the image contrast. Fig. 1�d� shows the result ofthe proposed method with �=0.6 and �=5. A 41�41square window, the same as the local region of local histo-gram equalization, is used in the proposed method. Thisresult shows that the proposed method enhances the con-trast of small details without radical change of visual im-pression. To analyze these results from another viewpoint,we select an example local region, A195,355 shown in Fig.2�a�, and plot the histogram hij�k� and the generalized his-togram gij�k� for the local region in Fig. 2�b�. In this figure,the hij�k� for around the 240 intensity level shows highvalues because the intensity levels of most pixels in the skyare around 240. Although contrast preserving is desirablefor visually pleasing results in relatively homogeneous re-gions, these high values of hij�k� around k=240 causestrong contrast stretching in the result of local histogramequalization, as shown in Fig. 1�c�. On the other hand, thegij�k� for around the 240 intensity level are far smaller thanthe hij�k� for the corresponding intensity levels because thesignal activities of most pixels in the sky are small. As aresult, the intensity levels of the pixels in the sky are lesschanged in the result of the proposed method shown in Fig.1�d�, and the appearance of the image is preserved afterapplying the proposed method.

An additional experimental result is given in Fig. 3. Fig.3�a� shows the original harbor image of 512�512 pixelsand Q=256. Figures 3�b�–3�d� show the results of globalhistogram equalization, local histogram equalization, andthe proposed method, respectively. These results from the

harbor image show similar features as described above for

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he building image. As a result, we can conclude that theroposed method produces visually pleasing contrastnhancement.

In the proposed method, the amount of contrast enhance-ent is determined by the fractional count ruv for each

ixel. If ruv has the maximum value 1 for all pixels in themage, the generalized histogram becomes the conventionalistogram and thus the proposed method reduces to theocal histogram equalization. In the other extreme casehen ruv=0 for all pixels in the image, the generalizedistogram becomes the uniform distribution and the pro-osed scheme is equivalent to linear mapping, which pre-erves the contrast. Therefore, we can conclude that the

Fig. 2 The histogram and the generalized histolocal region, A195,355; �b� hij�k� and gij�k� for A19

roposed method can give results with a varying degree of

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contrast by adjusting ruv. As we can see in �7� and �9�, thevalue of ruv is determined from � and �. � adjusts the valueof ruv over the whole image according to user’s require-ment and � determines the relationship between the frac-tional count for a pixel and its spatial activity. In order toshow the effect of variation of � and �, we present resultsfrom the building image in Fig. 4. With these results, wesee that the user can control the amount of contrast en-hancement over the whole image by adjusting the value of�. � reflects the increment of the contrast gain pixel bypixel according to the spatial activity. As � increases, adifference in the spatial activity produces a greater change

r A195,355 in the building image. �a� An example

gram fo.

in the contrast gain. In these experiments, we use a 41

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41 square window as the local region Aij for every pixeln the image. Selecting the size and the shape of the localegion for each pixel is an issue studied actively, and aumber of research on finding a better local region for eachixel than a simple square window with a fixed size haveeen conducted.20–23 These techniques can be readily incor-orated into the proposed method. For simplicity, however,

Fig. 3 Contrast enhancement results with the 5global histogram equalization; �c� result of locmethod.

e employ a square window with a fixed size in this paper.

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5 Conclusions

In this paper, we have proposed a novel contrast enhance-ment method using the generalized histogram. To reduceoverenhancement associated with the conventional histo-gram, we introduced the generalized histogram with thefractional count. By adjusting the fractional count for each

2 harbor image. �a� Original image; �b� result ofgram equalization; �d� result of the proposed

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ty, the amount of contrast enhancement is controlled ap-ropriately to the human observers. Therefore, the proposedethod can achieve visually more pleasing contrast en-

ancement than the conventional histogram equalizationethods. Through experiments, the efficacy of the pro-

osed method is verified.

cknowledgmentshis work was supported by the Brain Korea �BK� 21 Pro-ram funded by the Ministry of Education and HY-SDResearch Center at Hanyang University under the ITRCrogram of MIC, Korea.

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Byoung-Woo Yoon was born in Seoul,Korea, on May 13, 1975. He received hisBS and MS degrees in electronics engi-neering from Pohang University of Scienceand Technology �POSTECH� in 1998 and2000, respectively. Since 1998, he hasbeen a research assistant at the Depart-ment of Electronic and Electrical Engineer-ing, POSTECH, where he is currentlyworking toward his PhD degree. His re-search interests include digital image pro-

cessing, in particular, contrast enhancement and radar imageprocessing.

Woo-Jin Song was born in Seoul, Korea,on October 23, 1956. He received his BSand MS degrees in electronics engineeringfrom Seoul National University in 1979 and1981, respectively and his PhD degree inelectrical engineering from RensselaerPolytechnic Institute in 1986. During 1981–1982, he worked at Electronics and Tele-communication Research Institute �ETRI�,Korea. In 1986, he was employed by Po-laroid Corporation as a senior engineer,

working on digital image processing. In 1989, he was promoted toprincipal engineering at Polaroid. In 1989, he joined the faculty atPohang University of Science and Technology �POSTECH�, Korea,where he is a professor of electronic and electrical engineering. Hiscurrent research interests are in the area of digital signal process-ing, in particular, radar signal processing, signal processing fordigital television and multimedia products, and adaptive signalprocessing.

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