gaussian mixture model-based contrast...

IET Image Processing

Research Article

Gaussian mixture model-based contrastenhancement

IET Image Process., 2015, Vol. 9, Iss. 7, pp. 569–577& The Institution of Engineering and Technology 2015

ISSN 1751-9659Received on 25th February 2014Accepted on 1st December 2014doi: 10.1049/iet-ipr.2014.0583www.ietdl.org

Mohsen Abdoli1,2 ✉, Hossein Sarikhani1, Mohammad Ghanbari2,3,4, Patrice Brault5

1Department of Computer Engineering, Sharif University of Technology, Tehran, Iran2School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran3Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran4School of Computer Science and Electrical Engineering, University of Essex, Colchester, UK5L2S Laboratory of Signals and Systems, CNRS, Gif-sur-Yvette, France

✉ E-mail: [email protected]

Abstract: In this study, a method for enhancing low-contrast images is proposed. This method, called Gaussian mixturemodel-based contrast enhancement (GMMCE), brings into play the Gaussian mixture modelling of histograms to modelthe content of the images. On the basis of the fact that each homogeneous area in natural images has a Gaussian-shapedhistogram, it decomposes the narrow histogram of low-contrast images into a set of scaled and shifted Gaussians. Theindividual histograms are then stretched by increasing their variance parameters, and are diffused on the entirehistogram by scattering their mean parameters, to build a broad version of the histogram. The number of Gaussiansas well as their parameters are optimised to set up a Gaussian mixture modelling with lowest approximation error andhighest similarity to the original histogram. Compared with the existing histogram-based methods, the experimentalresults show that the quality of GMMCE enhanced pictures are mostly consistent and outperform other benchmarkmethods. Additionally, the computational complexity analysis shows that GMMCE is a low-complexity method.

1 Introduction

As the use of digital images grows in different applications, the needfor more efficient methods of image enhancement to be applied ondegraded images is perceived. One of the common degradationson images is the lack of contrast which can be because of the poorlighting conditions, such as extremely dark or bright environment[1]. The interpretation of low contrast in terms of histogramrepresentation of digital images is that in images with low-contrastcontent, the distribution of intensity values has low variance, andconsequently their histograms have narrow shapes. The solutionsto this problem, called contrast enhancement methods, haveseveral applications in medical imaging [2], remote sensing [3],machine vision applications [4], consumer electronics [5] and soforth.

Although diverse classes of approaches have been proposed forthis problem [6, 7], they can be classified into two generalcategories: histogram-based and non-histogram-based methods.Regarding different applications and their restrictions, onecategory may be preferred to the other.

One of the leading works on contrast enhancement is histogramequalisation (HE) [8], where it tries to spread out the intensityvalues of the histogram on the entire intensity range. In otherwords, it effectively broadens out the narrow histogram of alow-contrast image and generates its broadened version in such away that the visual quality is improved.

Despite its simplicity, this straightforward method suffers frommajor drawbacks such as inability to preserve overall brightness ofthe image when the raw image is too dark or too bright [9] orover-enhancing the histogram when there are large peaks in thehistogram [10]. To overcome these well-known drawbacks someextensions to HE have been proposed.

The first generation of extensions to HE are thebrightness-preserving methods. They choose a specific intensityvalue from the dynamic range of the histogram to be fixed duringthe process of broadening the histogram [9, 11–14]. This intensityvalue acts as a separation point, and consequently the outputhistogram would consist of two sub-histograms, independently

equalised with HE and shared a joint intensity value at theirseparation point.

Preserving a single intensity value of the histogram is notnecessarily adequate to generate a high contrast and at the sametime a visually fine image. Hence, the next generation ofextensions aimed at preserving more than one intensity value ofthe histogram so that the histogram is separated more than once.These methods, called recursive brightness-preserving methods,perform similarly to the brightness-preserving methods, except thatthey use a parameter named ‘recursion level (RL)’ which indicatesthe number of separation points at which the current sub-histogramis split in two [15, 16].

All above-mentioned derivatives of HE can be considered as‘static’ methods, since the number of selected separation pointsand their positions on the histogram before and after enhancementremain unchanged. As an alternative idea, two other sub-categoriesnamed ‘semi-dynamic’ and ‘dynamic’ methods have beenintroduced where the separation points and their positions are nolonger predetermined. In the semi-dynamic methods, either thenumber of separation points is fixed, yet their positions mightchange during the contrast enhancement [17–19], or the positionsof the separation points are fixed, but their numbers are variable[20]. In the dynamic methods, both the number of separationpoints and their positions can change depending on thecharacteristics of the image [21, 22].

As mentioned, there are also non-histogram-based methods whichimprove the visual quality of images by taking advantage of featuresother than histogram characteristics. Generally, these methods needto have access to spatial attributes instead of global histogramcharacteristics. For instance, in order to enhance the contrast, anon-histogram-based method might exploit over and underexposure versions of a low-contrast image [23], statistical featuresof image related to stochastic resonance [24] or agenetic algorithm with non-histogram-based chromosome structure[25]. Actually, there are several research works fitting inthe non-histogram-based category, but they are out of the scopeof this study as they do not concern the proposed method in thispaper.

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In the present paper, a dynamic histogram-based contrastenhancement method is proposed. The main idea behind thismethod is based on the fact that in natural images eachhomogeneous area is assumed to have a correspondingGaussian-shaped region in the histogram of the image. Thereforeeach histogram can be approximated with a combination of alimited number of Gaussian-shaped sub-histograms correspondingto its major regions. A greedy optimisation method is proposed toobtain the optimum number of Gaussians as well as theirparameters. Since mean parameters of the found Gaussianscorrespond to the average intensity value of major regions, theyare assumed to be the most dominant intensity levels of the image.Consequently, the process of contrast enhancement is performedby spreading out these dominant intensity levels on the entirerange of the histogram. This technique increases the contrastbetween the individual major regions of the image which improvesthe global contrast of the image.

The rest of this paper is organised as follows: in Section 2, detailsof the histogram modelling as well as the proposed method arediscussed. In Section 3, the experimental results plus somediscussion on the relative performance of the proposed methodagainst the other existing methods are presented, and finallySection 4 concludes this paper.

2 Gaussian mixture model-based contrastenhancement

In this section, first the idea behind using the Gaussian mixturemodelling (GMM) to model the structure of a histogram isclarified, and then the details of the proposed Gaussian mixture

Fig. 1 Five major near-homogeneous regions as well as their corresponding sub

a Natural image and its global histogramb–f Five near-homogeneous regions and their independently calculated sub-histograms

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model-based contrast enhancement (GMMCE) method areexplained.

2.1 Histogram modelling by Gaussians

Any arbitrary image can be assumed to be composed of individualmeaningful regions occupying near-homogeneous areas of theimage. Each region in natural images has a Gaussian-shapedhistogram where the means of the Gaussian histograms indicatetheir corresponding average intensity levels and the variancecorresponding to their texture details. These Gaussians areseparated by their mean values and spread out with theirvariances, thus forming the global histogram [22]. On the basis ofthe fact that low-contrast images have narrow histograms, if onedeparts the important means from each other, the contrasts ofindividual areas are enhanced and the visual quality of the imageis improved.

In other words, the structure of an image is directly reflected in itshistogram in a manner that any significant peak in the histogram isactually the mean intensity value corresponding either to a vastnear-homogeneous zone of the image or to several zones whichtogether occupy a major portion of the area. In either case, theseintensity levels are particularly important to the global visualquality of the image and should be carefully treated during anyenhancement process.

Fig. 1 shows an image with five major near-homogeneous regionsas well as their corresponding sub-histograms. Fig. 1a is the originalimage with its histogram and Figs. 1b–f are the regionscorresponding to the dominant intensity levels with theirsub-histograms. Note that the dark backgrounds in all sub-imagesare related to the discarded areas that have been extracted from the

-histograms


original image and are not included in the sub-histograms. Theseimages are generated by the proposed method which will bediscussed in this section.

As can be seen, each meaningful area in the original image isexplicitly related to a local peak in the global histogram. Moreimportantly, the frequencies around these peaks form aGaussian-shaped curve. Thus, it can be concluded that thisobservation can lead us to represent all natural images by GMMwhere the number of Gaussians depends on the complexity of thecontent. A greedy algorithm is adopted to find the number ofGaussians as well as the parameters of their probability densityfunctions (PDFs) which will be discussed later in this section.

2.2 GMM formulation

Each arbitrary histogram can be formulated as a weighted sum of kGaussians which requires to estimate three vectors of k parameters,namely mean µ, variance σ2 and scaling factor ω. Thus, thecontinuous GMM of the histogram can be expressed as

hkGMM(I |m, s2, v) =∑kj=1

vjN (I |mj, s2j ), I = 0, 1, . . . , L− 1

(1)

where N (I |mj, s2j ) is the jth Gaussian PDF at intensity level I∈ [0,

L− 1] with variance s2j and mean μi [26]. According to (1), the

height of each Gaussian is scaled by ωj which is proportional tothe area is occupied by its corresponding region in the image. Inother terms, the larger is a region, the more dominant is itscorresponding Gaussian in the histogram, by having the highestpeak in the global histogram.

Fig. 2 demonstrates the effect of increasing the number ofGaussians k, on the accuracy of the approximated histogram. Ascurves in Fig. 2d show, the absolute residual approximation errorwith ten Gaussians (i.e. GMM(10) in Fig. 2c) is small, virtuallymaking the resulting GMM accurate enough to be used in theenhancement process. However, increasing the number ofGaussians can be interpreted as increasing the number of dominantintensity levels. This has the drawback of having many Gaussians,

Fig. 2 GMM reconstruction of a histogram by

a With three Gaussiansb With five Gaussiansc With ten Gaussiansd The approximation errors corresponding to a–c


as well as Gaussians with minor peaks, which represent a smallfraction of the global intensity. The ultimate effect is that theincreased number of Gaussians not only increases the complexityof image enhancement, but also has a negative effect on itsquality. Since, having many Gaussians to decrease the absoluteresidual error would cause considering non-dominant regions asimportant as the actual dominant regions.

Therefore there should be a balance between using not too fewGaussians to miss the dominant intensity levels and not too manyGaussians to include the non-dominant intensity levels. This isconsidered in the proposed model by limiting the number ofGaussians to a value where the area under their resultant GMM isno more than α per cent of the area under the original histogram.

In GMMCE, given a histogram, it searches for an optimalcomposition of Gaussians to construct the histogram. As anobjective function, the optimality of a composition is measured byits similarity to the original histogram. The difference between aGMM and the original histogram is optimised, in a least-squaresense, as

argminm,s,v

∑L−1

I=0

horg(I)− hkGMM(I |m, s2, v)( )2

(2)

where horg is the original histogram of the image. As discussedearlier, µ, σ and ω are the unknown parameters of the GMM to beestimated.

For optimisation, one might use the expectation maximisation(EM) algorithm (like almost all other GMM-based optimisationproblems) which is an iterative approach to estimate the latentvariables of a statistical model [20, 22, 26, 27]. In GMMCE, thestatistical model is a combination of a specific number ofGaussians and the latent variables include the means and thevariances of the Gaussians as well as their scaling factors (i.e.vectors µ, σ and ω).

Although EM has proven to be a very accurate solution forGMM-based problems, it has short falls that make it ‘not the bestapproach’ for some conditions. The main drawback of EM is itscomplexity and inability of implementation for real-timeapplications [27]. For example, if the application is auto contrastin digital video recorders [28], it is not feasible to apply EM forevery single frame. Moreover, EM-based methods are highlydependent on the starting points. Choosing a bad set of startingpoints might cause the solution to diverge, which is the case inhistogram representation, especially in the presence of abnormallocal peaks in the histogram.

2.3 Parameter estimation

In this section, low-complexity greedy approaches are introduced toestimate the above-mentioned parameters. In the following sections,three algorithms to be used in GMMCE for parameter estimation ofeach Gaussian are described. These greedy algorithms are iterativelycompleted and, at each iteration, the parameters of one Gaussian areestimated and the approximated Gaussian is excluded from thehistogram for the estimation of the next Gaussians. These steps areperformed until a portion α (e.g. %95) of the underneath area isextracted.

2.3.1 Mean parameter estimation: For mean parameterestimation, given a histogram, the algorithm looks for the intensitylevel which the sub-histogram around it, has a shape as close to aGaussian PDF as possible. The algorithm then picks this intensityas the mean of that Gaussian. For this purpose, an objectivefunction is devised that measures this optimality in terms of signalsimilarity and that finds the best I∈ [0, L− 1] which satisfies

m = argImax

∑L−1

j=0

N j|I , s20

( ).horg(j), I = 0, 1, . . . , L− 1 (3)

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where N (j|I , s20) is the value of a normalised Gaussian PDF at j,

with I and s20 as its mean and variance, respectively. Actually, (3)

aims at maximising the correlation (i.e. similarity) between anormalised Gaussian PDF and a region of the original histogramin order to find the best intensity level I where the normalisedGaussian best fits with the original histogram. For any constantvalue of s2

0, the correlation between a normalised Gaussian andthe histogram can locate the position of the largest peak, which isthe mean value of that histogram.

One might find mean parameters simply by applying a maxoperation or using the Dirac delta function instead of N (j|I , s2

0) in(3). These alternative techniques can be useful only in idealconditions (i.e. where the shape of the histogram is smooth andlocal peaks are located exactly on the means of the Gaussians).However, in histograms of natural images it is common to observedistortions in the shape of peak areas, so the output of maxoperation or Dirac delta function might not accurately locate thecorresponding mean parameter. Moreover, since the meanparameter found in this step is the basis for calculations in thefollowing steps, it is essential to find the most accurate value toavoid the error propagation, especially in the variance estimationstep.

Implementations show that when the peak value of aGaussian-shaped sub-histogram is deliberately displaced, the abovecorrelation can still estimate the actual m based on otherfrequencies in that neighbourhood. This means that compared withDirac delta function, (3) is more robust to distortions. Thisrobustness is vital for the accuracy of future estimations.

It is also important to note that the selection of the constant values20 is almost independent from the final value of m , since the

implementations show that as long as the selected value is notvery high, the output will be the same. The reason is that inlow-contrast images, the histogram is mainly narrow and choosinga small value for variances at this very first step is acceptable.

2.3.2 Gaussian boundary analysis: Before furtherestimations, it is required to determine the original territory of theongoing Gaussian-shaped sub-histogram around its estimated meanparameter m . Owing to the nature of Gaussian mixture models,each point on the x-axis is actually affected by all Gaussians,proportionally to their tail thickness at that point. In other words,these undesirable effects which exist everywhere on the dynamicrange of the histogram are unavoidable when a Gaussian-shapedsub-histogram needs to be merely evaluated. Hence, it is best tofind the purest neighbourhood around the mean parameter in bothdirections. Here, a neighbourhood is considered as pure if thestrength of the current Gaussian is dominant compared with bothprevious and next Gaussians in the histogram.

For this purpose, the proposed algorithm performs a preprocessingfiltering to smooth horg. First, horg is padded by inserting theadequate number of horg(0) and horg(L− 1) in the beginning andthe end of histogram, respectively

horg(−i) = horg(0)horg(255+ i) = horg(255)

{, i = 1, 2, . . . , n (4)

Then, a one-dimensional averaging filter of size 2 × n + 1 is appliedon each intensity level to replace each value of the histogram withthe average of its neighbourhood

hS(I) =∑nj=−n

horg(j − I)× 1

2n+ 1, I = 0, 1, . . . , 255 (5)

After applying the averaging filter, the algorithm sets the lower andupper boundaries (i.e. LB and UB) of the current Gaussian by

s = Mediand��

2. ln (Rdfw)

√ |d = 1, 2, . . . , UB− m

⎧⎪⎨⎪⎩

⎛⎜⎝

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choosing the nearest local minima of the smoothed histogram (i.e.hS) before and after m , respectively.

2.3.3 Variance parameter estimation: In this section, theestimated mean of a Gaussian-shaped sub-histogram as well as itsboundaries (i.e. m , LB and UB) are used as the inputs for thealgorithm to estimate the variance. This method brings into playthe essential characteristics of a Gaussian PDF and based on thefrequency of adjacent intensity levels around the estimated mean,it finds the most probable value for the variance.

Considering a discrete Gaussian PDF with highest similarity to theongoing Gaussian-shape sub-histogram, one can use the drop ratiosof consecutive frequencies in the smoothed histogram to estimate thevariance. For instance, (6) approximately estimates the drop ratio inthe smoothed histogram for the displacement d, from peak value atm , towards forward and backward directions (Rd

fw and Rdbw,

respectively)

Rd(fw/bw) =

hS(m)

hS(m + d)� v.N (m|m , s2)

v.N (m + d|m , s2)

=v. 1/

��2ps2

√( )e− (m−m)2/2s2( )

v. 1/��2ps2

√( )e− (m+d−m)2/2s2( )

=v. 1/

��2ps2

√( )

v. 1/��2ps2

√( ).e−(d2/2s2)

= e(d2/2s2) (6)

Ideally, when the ongoing Gaussian-shaped sub-histogram hasthe exact same distribution as a discrete Gaussian PDF, only onedrop ratio, either in forward or backward direction, is adequate toexactly estimate the variance parameter of every Gaussian-shapedhistogram by simply calculating

s = d��2. ln Rd

(fw/bw)

( )√ , d = 1, 2, . . . (7)

However in natural images, even after smoothing the originalhistogram, the histogram is not purely Gaussian so the exact scannot be estimated only with one drop ratio. One solution is toderive it from several ratios around the neighbourhood of m withinthe lower and upper bounds (see (8))

From the practical point of view, the wider is the boundary of theGaussian-shaped sub-histogram, the more probable is theconvergence of s to its final value. As an example, this method isimplemented for the sub-histogram in Fig. 1e to estimate thevariance parameter for the highest peak of the histogram in theforward direction. Fig. 3 indicates that, as the algorithm progressesin the forward direction, the estimated s approaches its real value.

2.3.4 Scaling factor estimation: After identifying the mostdominant sub-histogram by estimating its mean and variance, itshould be removed from the global histogram. This can help thenext dominant sub-histogram to appear and be identified. Formerely considering the ongoing sub-histogram and to avoidaffecting other sub-histograms in that neighbourhood, theestimated Gaussian PDF can be used. Therefore the estimatedGaussian PDF is scaled based on the height of the ongoingsub-histogram, and is subtracted from the original histogram

ht+1S (I) = htS(I)− v .N I |m , s2( )

, I = 0, 1, . . . , L− 1 (9)

⎫⎪⎬⎪⎭<

d��2. ln (Rd

bw)√ |d = 1, 2, . . . , m − LB

⎧⎪⎨⎪⎩

⎫⎪⎬⎪⎭

⎞⎟⎠ (8)


Fig. 4 Whole process of broadening a narrow histogram

a Input narrow histogram of Fig. 1ab Estimating five Gaussiansc Diffusing mean parametersd Stretching Gaussians by increasing variancese Broadened GMM

Fig. 3 Convergence of variance estimation algorithm for the sub-histogramin Fig. 1e

Seemingly, an acceptable variance would be estimated if more than seven intensitylevels are available within the boundary

where htS and ht+1S are the smoothed histograms before and after

removal of the current Gaussian-shaped sub-histogram. Now thescaling factor of this sub-histogram v can be calculated byconsidering the fact that the subtraction in (9) would modifyht+1S (m) to zero

htS(m)− vN m|m , s2( ) = 0 ⇒ v = htS(m)

N m |m , s2( )

= htS(m)

1/��2ps2

√( )e− (m−m)2/2s2( )

=��2ps2

√.htS(m) (10)

2.4 Intensity transform function

To form the broadened version of the low-contrast histogram, themean parameters are uniformly diffused in the entire range ofthe histogram (i.e. 0 through 255). First, the dynamic range of thelow-contrast histogram is set to [L, U ] by finding L and U,respectively, as first and last non-zero significant frequencies (e.g.some sporadic and rare values may be ignored) of the narrowhistogram, respectively. Then, the distributed mean values arecalculated as

mi =mi − L

U − L× 255, i = 1, 2, . . . , k (11)

In addition to the mean parameters, the variances of Gaussians areincreased by

si = si ×256

U − L, i = 1, 2, . . . , k (12)

With the same scaling factors as those of the narrow histogram(i.e. v), the broadened histogram is formed by a new GMM

HkGMM(I |m, s2, v) =

∑kj=1

vj.N (I |mj, s2j ), I

= 0, 1, . . . , L− 1 (13)

After calculating the destination histogram, a transfer function, that


we call T, needs to be defined to broaden the narrow histogram.For this purpose, the histogram matching algorithm isimplemented. Given two histograms, the source and thedestination histograms, histogram matching first calculates theircumulative distribution functions

CDFsrc(I) =∑Ij=0

horg(j), I = 0, 1, . . . , L− 1 (14)

CDFdst(I) =∑Ij=0

HkGMM(j), I = 0, 1, . . . , L− 1 (15)

Then for each intensity level G1∈ [0, L− 1] in the sourcehistogram, it approximates the intensity level G2 in the destinationhistogram which satisfies CDFsrc(G1) = CDFdst(G2). Finally, thealgorithm assigns the approximated intensity level as the output ofthe histogram matching function T for the input G1

T (G1) = G2 (16)

The enhancement technique of GMMCE is then completed bysimply applying the resultant transfer function of T to every pixelof the low-contrast image.

Considering all steps described in this section, Fig. 4 pictoriallydemonstrates the whole process of broadening a narrow histogram.

3 Experimental results

To demonstrate the performance of GMMCE, the proposed methodwas compared with other existing histogram-based contrastenhancement methods: HE [8], brightness-preserving Bi-HE

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Fig. 5 Contrast enhancement result for image Cars

a Originalb HEc BBHEd DSIHEe RSWHE-Mf QDHEg EMCEh GMMCE

(BBHE) [9], dualistic sub-image HE (DSIHE) [11], mean-basedrecursively separated and weighted HE (RSWHE-M with r = 2 asits best-tuned RL) [29] and quadrants dynamic HE (QDHE) [17].For thorough comparison, the proposed GMMCE was alsocompared with a GMM-based method called expectationmaximisation contrast enhancement (EMCE) [20]. It can be usefulto note that in EMCE all GMM parameters (i.e. means, variances,weights and the number of Gaussians) are estimated by performingthe time-consuming EM algorithm which makes EMCE a complexcontrast enhancement method.

3.1 Visual quality assessment

Figs. 5–7 show three low-contrast images and the visual quality oftheir enhanced versions by GMMCE and the other methods. Theonly parameter used for GMMCE is α = 0.95. Underneath eachpicture, its histogram is also depicted. For quality comparison,since there is no universally agreed method measuring the qualityof contrast enhanced images, we address to their visual quality, asmost published works do. Moreover, note that sincehistogram-based contrast quality algorithms process the histogramsof the images, then inspection of their histograms, as shownthroughout the pictures, may help in this quality evaluation.

In the ‘Cars’ image (Fig. 5) whose original low-contrast image hasnearly 50 unique intensity levels (i.e. extremely low contrast), it canbe seen that the outputs of HE, BBHE and DSIHE are extensivelysaturated and the output of RSWHE-M is clearly washed-out.However, the results of GMMCE and EMCE can efficiently revealthe details which have been concealed in the original image.Inspections of their histograms also confirm this claim. As seen,

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the histograms of GMMCE and EMCE are very similar and of thesame shape to the original one, reflecting their near identicalsubjective quality, but are broadened to improve the quality ofinput picture. For the others, the histogram looks unnatural,especially too much broadened in the vicinity of the main peak.These histograms very well explain the possible artefacts thatmight appear when shape of an input histogram is not preservedduring the enhancements. In this picture, the input narrowhistogram has about three dominant peaks and the second one isthe most important one. In Figs. 5b–d, the Gaussian-shapedsub-histogram around the most important peak has beenextensively modified, so there is almost no mid-grey intensity levelremained.

In ‘Cameraman’ (Fig. 6), the main artefact in the outputs of HE,BBHE, DSIHE, QDHE and RSWHE-M is the non-uniform skybehind the cameraman. This highly bright artefact which is verycommon in the enhancement of extremely low-contrast imageswith one or more vast uniform regions can be verified in theircorresponding histograms. In the original low-contrast image, theuniform background related to the second dominant peak (i.e. thewider Gaussian-shaped area in the middle of histogram in Fig. 6awhich is assumed to be dominant both because of its height andwidth), is deformed in the enhanced histogram of Figs. 6b–f.Moreover, in Figs. 6e and f the enhanced images are alsowashed-out which are clearly because of the abnormalconcentration of intensity levels in the middle of dynamic range ofthe histograms.

Finally, the ‘Solvay’ image (Fig. 7) which is a noisy picture, wasenhanced by the above-mentioned methods. In this test image, as canbe seen from the histogram of Fig. 7a, there are two equally


Fig. 6 Contrast enhancement results for image Cameraman


dominant intensity values in the original image which have formedtwo peaks in the histogram.

On the basis of the outputs of the methods in Fig. 7, anotherbenefit of histogram shape preservation is demonstrated. For thistest image, HE, BBHE, DSIHE and QDHE have magnified thenatural noise in the original image, by keeping concentrated onlythe centre of the original histogram (noise) and spreading bothdominant values over the rest of the dynamic range. Among all ofthe unsuccessful methods in the previous images, only RSWHE ispreserving the shape of the input histogram which has resulted ina satisfying enhanced image, without amplifying the noise. Inaddition, this image also verifies that EMCE and GMMCE areable to effectively broaden narrow histograms with more than oneGaussian-shaped peak.

3.2 Subjective quality assessment

Although the visual quality of GMMCE in preserving the shape ofthe original image histogram appears to be natural and good, somemight argue this is a biased view. People prefer quantitativefigures of how good a method can be. This can be achieved byeither objective measures or subjective quality scores.

Unfortunately published objective measures are not very reliable.For example, none of the known objective measures consider thesaturation effect that might arise from over-enhancing the image.On the other hand, the subjective measures should be used withsome care, as they normally evaluate the quality of a processedimage against its original quality, which in contrast enhancementbecomes meaningless, since the processed image, no matter whichmethod is used, is always better than the original one. In our test,


we used an alternative method, where any two enhanced imagesby two different methods were compared against each other by 19subjects, In case the assessor could not decisively rate one betterthan the other, the images share the same score. Thus when twoimages are compared, the better one obtains a score of 1, thepoorer one obtains 0 and when they are equally rated, each obtains0.5. In the seven methods tested here, the maximum score onemethod can obtain is 6 and the minimum is 0. In addition to thetest images in the previous section, three more images shown inFig. 8 are added. The scores along with the average score of eachtest image by various methods are tabulated in Table 2. As can beseen, the GMMCE along with EMCE, which both have the shapepreserving property of the histogram are always rated first orsecond. On the average, EMCE comes slightly above the GMMCE.

3.3 Computational complexity analysis

In addition to subjective quality assessment, the computationalcomplexities of the above-mentioned algorithms are measured. Forthis purpose, a general-purpose personal computer (PC) with2.16 GHz Intel® Core 2 Duo processor with 3 MB shared L2cache and 4 GB of memory is used.

All the seven algorithms were implemented optimally and theiraverage execution times for multiple standard test images werecalculated (the used database may be found here: http://www.decsai.ugr.es/cvg). To avoid any skepticism, all algorithms wererun for adequate number of iterations and averages of theexecution times are presented in Table 1. For this purpose, eachimplemented algorithm in MATLAB was run 60 times for eachimage. For eliminating the influence of background processing

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Fig. 7 Contrast enhancement for image Solvay


load of the host PC’s operating system, executions of theprogrammes were carried out under the same central processingunit load condition (i.e. monotask). It is also useful to note that,since all methods are histogram-based, their computational loadsare mostly related to their processes after calculation of histogramfrom the raw files. Thus, results in Table 1 are not grouped byresolution of the test images.

Fig. 8 Three additional low-contrast images chosen for the subjective quality as

a F16b Astroc Trees

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As discussed earlier, the main reason that EMCE and GMMCEperform well in enhancing very low-contrast images, is that theyboth model histograms by GMMs which is supposed to be acomplex process. However, Table 2 shows that replacing EM withgreedy algorithms in GMMCE, still places GMMCE amonglow-complexity methods. In contrast, the time-consuming EMalgorithm in EMCE costs it a major increase in execution time.

sessment test


Table 1 Comparison of mean opinion score for the test images enhanced by the benchmark methods (Bolded items for each row indicate the bestenhancement method for the test image corresponding to that row)

Images HE BBHE DSIHE RSWHE-M QDHE EMCE GMMCE

F16 1.07 3.21 1.85 4 2.21 4.64 4.14Trees 2.42 2.85 2.85 3.28 3.14 3 3.42Cameraman 1.57 1.71 1.71 4.21 1.21 4.78 5.78Astro 2.42 2.07 2.07 4.07 1.64 4.64 4.07Solvay 1.28 2.64 1.64 4.14 0.71 5.92 4.5Cars 0.92 3.35 0.85 3.71 1.92 4.71 5.35average 1.61 2.64 1.83 3.9 1.81 4.61 4.54

Table 2 Computational complexity measurement

Method Execution time in seconds

HE 0.013BBHE 0.166DSIHE 0.162RSWHE-M 0.128QDHE 0.159EMCE 0.654GMMCE 0.241

4 Conclusion

In this paper, a new contrast enhancement method named GMMCEhas been introduced. First, it is claimed that the shape preservation ofnarrow histograms during contrast enhancement can avoid unnaturalartefacts, such as saturation and wash-out. On the basis of this claim,the proposed method models the histogram of low-contrast image bythe combination of a limited number of Gaussians where eachGaussian presents a dominant intensity level of the image. Thismodelling attempts to reflect the shape of a narrow histogram inthe parameters of individual Gaussians, to convey it to abroadened version.

The global contrast enhancement of the image was achieved bythe enhancement of sub-histograms separated by the mean valueof the Gaussians of the GMM. Experimental results show that theshape preserving method of GMMCE enhances the contrast of theimage without generating any undesirable artefact. Moreover,computational complexity analyses show that the greedy parameterestimation algorithms (i.e. instead of time-consuming methodssuch as the expectation maximisation in other GMM-basedmethods) in GMMCE categorise it as a low-complexity methodand make it suitable for real-time applications.

5 Acknowledgment

This research was in part supported by a grant from the Institute forResearch in Fundamental Sciences (IPM) (no. CS1393-2-04).

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