An Optimal Fuzzy System for Color Image Enhancement

2956 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 10, OCTOBER 2006

An Optimal Fuzzy System forColor Image EnhancementMadasu Hanmandlu, Member, IEEE, and Devendra Jha

Abstract—A Gaussian membership function is proposed tofuzzify the image information in spatial domain. We introduce aglobal contrast intensification operator (GINT), which containsthree parameters, viz., intensification parameter , fuzzifier ,and the crossover point , for enhancement of color images. Wedefine fuzzy contrast-based quality factor and entropy-basedquality factor and the corresponding visual factors for thedesired appearance of images. By minimizing the fuzzy entropyof the image information with respect to these quality factors, theparameters , , and are calculated globally. By using theproposed technique, a visible improvement in the image quality isobserved for under exposed images, as the entropy of the outputimage is decreased. The terminating criterion is decided by boththe visual and quality factors. For over exposed and under plusover exposed images, the proposed fuzzification function needs tobe modified by taking maximum intensity as the fourth parameter.The type of the images is indicated by the visual factor which isless than 1 for under exposed images and more than 1 for overexposed images.

Index Terms—Enhancement, entropy, fuzzifier, fuzzy contrast,image quality, intensification operator, quality factor and visualfactor.

I. INTRODUCTION

IMAGE enhancement techniques are used to improve the ap-pearance of the image or to extract the finer details in the

degraded images. Color image enhancement using RGB colorspace is found to be inappropriate as it destroys the color com-position in the original image.

Image enhancement can be treated as transforming one imageto another so that the look and feel of an image can be improvedfor machine analysis or visual perception of human beings. Forgrayscale image enhancement, the most popular method is his-togram equalization, which is based on the assumption that auniformly distributed grayscale histogram will have the best vi-sual contrast. Some other methods are the variants of histogramequalization. However, generalizing grayscale image enhance-ment to color image enhancement is not a trivial task. Severalfactors, such as selection of a color model, characteristics ofthe human visual system, and color contrast sensitivity, must beconsidered for color image enhancement.

Manuscript received May 30, 2004; revised December 15, 2006. The asso-ciate editor coordinating the review of this manuscript and approving it for pub-lication was Dr. Eli Saber.

M. Hanmandlu is with the Indian Institute of Technology, Delhi, New Delhi110016, India (e-mail: [email protected]).

D. Jha is with Scientific Analysis Group, Defence R&D Organisation,Metcalfe House, Delhi 110054, India (e-mail: [email protected]).

Color versions of Figs. 3–16 are available online at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TIP.2006.877499

The main objective of image enhancement is to process theimage so that the result is more suitable than the original image.Image enhancement methods may be categorized into two broadclasses: transform domain methods and spatial domain methods.The techniques in the first category are based on modifying thefrequency transform of an image. However, computing a two-dimensional (2-D) transform for a large array (image) is a verytime consuming task even with fast transformation techniquesand is not suitable for real time processing.

The techniques in the second category directly operate onthe pixels. Contrast enhancement is one of the important imageenhancement techniques in spatial domain. Other than the twopopular methods, histogram equalization and histogram speci-fications, we have an iterative histogram modification of grayimages [1] and an efficient adaptive neighborhood histogramequalization [2]. The adaptive method achieves better identi-fication of different gray- level regions by an analysis of his-togram in the locality of every pixel. Lindenbaum et al. [3]have used Gabor’s technique for image enhancement, edge de-tection, and segmentation. They have suggested a method forimage deblurring based on directional sensitive filters. Becauseof poor and nonuniform lighting conditions of the object andthe nonlinearity of the imaging system, vagueness is introducedin the acquired image. This vagueness in the image appears inthe form of imprecise boundaries and color values during imagedigitization.

Fuzzy sets [4] offer a problem-solving tool between the pre-cision of classical mathematics and the inherent imprecision ofthe real world. The imprecision in an image is contained withinthe color values and this can be handled using fuzzy sets [5]. Thelinguistic variables like “good contrast” or “sharp boundaries,”“light red,” “dark green,” etc., called hedges, can be perceivedqualitatively by the human reasoning. As they lack precise quan-tification, the machine may not understand them. To overcomethis limitation to a great extent, fuzzy logic tools empower a ma-chine to mimic human reasoning.

In the field of image enhancement and smoothing using thefuzzy framework, two contributions merit an elaboration. Thefirst one deals with “IF…THEN…ELSE” fuzzy rules [6] forimage enhancement. Here, a set of neighborhood pixels formsthe antecedent and the consequent clauses that serve as the fuzzyrule for the pixel to be enhanced. These fuzzy rules give direc-tives much similar to human-like reasoning. The second onerelates to a rule-based smoothing [7] in which different filterclasses are devised on the basis of compatibility with the neigh-borhood. The above works are confined to gray image enhance-ment and smoothing. A color enhancement technique describedin [8] stretches iteratively three 2-D histograms, (RG, GB, BR).

1057-7149/$20.00 © 2006 IEEE

HANMANDLU AND JHA: OPTIMAL FUZZY SYSTEM FOR COLOR IMAGE ENHANCEMENT 2957

Bockstein [9] has proposed a color image equalization methodfor color image enhancement using the LHS color model. Thenequalization is applied on the luminance (L) and the saturation(S) histograms for the smaller regions whereas the hue value(H) is preserved. Strickland et al. [10] have applied a speci-fied enhancement algorithm on intensity with S and H beingunchanged. However, this algorithm sometimes over enhancesthe image. Soha and Schwartz [11] have enhanced a color imageby stretching the original RGB components along the principalcomponent axis.

In the fuzzy approach [12], some pixel property, like gray toneor color intensity, is modeled into a fuzzy set using a member-ship function. In this, an image can be considered as an arrayof fuzzy singletons having a membership value that denotes thedegree of some image property in the range . Applying anintensification operator globally modifies the membership func-tion. Hanmandlu et al. [13] have proposed a new intensificationoperator, NINT, which is a parametric sigmoid function for themodification of the Gaussian type of membership on the basisof optimization of entropy by a parameter involved in the inten-sification operator. The approach in [14] describes an efficientenhancement based on the fuzzy relaxation technique. Differentorders of fuzzy membership functions and different statisticsare attempted to improve the enhancement speed and quality,respectively. These works have been confined to the enhance-ment of gray images only.

In this paper, we have extended the approach in [13] for theenhancement of color images. We use histogram as the basisfor fuzzy modeling of color images. The main emphasis hasbeen laid on the fuzzy entropy measure. The “entropy” in [12] isused to derive a measure of image quality in the fuzzy domain,although the image quality remains subjective in nature.

Histogram equalization and its variants are quite useful forenhancing the details in grayscale images, but fail when appliedto the three components (R, G, B) of a degraded color image,since they alter the original color composition by producingcolor artifacts. The three R, G, B components are highly corre-lated. Because of this, the enhanced color image would lose itsoriginal color composition. Therefore, the application of colorimage enhancement on the RGB color model is inappropriatefor the human visual system.

A proper color model for the color image enhancementshould decouple the achromatic and chromatic information andshould maintain the color distribution of the original image.The three main attributes generally used to distinguish onecolor from another are hue, saturation and intensity (HSV) andthis model is chosen for the proposed enhancement technique.

In the HSV color model, hue (H), the color content, is sepa-rate from saturation (S), which can be used to dilute the colorcontent and V, the intensity of the color content. By preservingH and S while changing only V, it is possible to enhance colorimages. Therefore, we need to convert RGB to HSV for this pur-pose. A Gaussian type membership function is used to model Vproperty of the image. This is suitable for under exposed im-ages. For over exposed and under plus over exposed images, themaximum intensity has to be taken as the parameter. The con-trast of V is stretched globally by changing a parameter in theglobal intensification operator (GINT). Since our intention is to

use fuzzy-based approaches for automatic image enhancement,we find the parameters of GINT by the fuzzy optimization ofentropy. The minimization of entropy leads to enhancement ofthe image by stretching V component of the pixels about thecrossover point.

The organization of the paper is as follows. In Section II,we introduce fuzzification and intensification of images. InSection III, we develop a method to determine the parametersof GINT. In Section IV, we define quality and visual factorsthat help achieve the desired enhancement. In Section V, wepresent an algorithm for the fuzzy optimization with respectto parameters , and . The results and conclusions arediscussed in Sections VI and VII, respectively.

II. FUZZIFICATION AND INTENSIFICATION

An image of size with intensity levels in the range (0to ) can be considered as collection of fuzzy singletons inthe fuzzy set notation

(1)

where or represents the membership orgrade of some property of , is the color intensityat pixel. For a color image, the membership functionsare taken for the unions of all colors . For thetransformation of the color in the range (0–255) to the fuzzyproperty plane in the interval (0,1), a membership function ofthe Gaussian type

(2)

is suggested in [13] and it contains a single fuzzifier, . Here,is the maximum color value present in the image,

being the number of levels of intensity. Though valid, forunder exposed images, this needs to be modified for under plusover exposed images. Thus, this is also a design parameter aswill be discussed in the Section VI.

The membership values are restricted to the range , with. For computational efficiency, histogram of

color is considered for fuzzification. So, representsthe membership function of color for a value , with

, defined by

(3)

This function is the same as in (2), with replaced by theindex , the intensity of the color components having the fre-quency occurrence, . As outlined in the introduction, wewill consider to modify its membership function withoutdisturbing the membership functions of other two components.It is observed that values of are higher for a brighter image.The membership values are transformed back to the spatial do-main after the desired operator is applied in the fuzzy domain.


The corresponding inverse operator from the fuzzy domain tothe spatial domain is given as

(4)

where and are the modified membership function andintensity value, respectively.

We restrict the enhancement of the image by whatever is pos-sible with the fuzzy contrast intensification operator. The orig-inal contrast intensification operator, INT [4] depends on themembership function only. It needs to be applied successivelyon an image for obtaining the desired enhancement. This lim-itation is removed in the new intensification (NINT) operatorproposed in [13]. This is a parametric sigmoid function givenby

(5)

Here, we propose a general intensification operator (GINT) byreplacing 0.5 by in (5) leading to

(6)

The unknown parameters in the above equation are inten-sification parameter, and crossover membership function orsimply crossover point, .

III. ENHANCEMENT BY FUZZY OPTIMIZATION

We propose three solutions to the fuzzy optimization for en-hancement. The first solution is based on the optimization offuzzy contrast . The second solution is based on the optimiza-tion of fuzzy entropy function, . Here, the optimization is un-constrained. The third solution arises from the optimization of

with respect to some equality constraints. For example, if weknow the desired fuzzy contrast, we can use this constraint tosolve the constrained fuzzy optimization problem.

A. Fuzzy Image Quality

We introduce here the concept of fuzzy contrast that dependson how far the membership functions are stretched by an oper-ator with respect to the crossover point . This turns out to bethe cumulative variance of the difference between the member-ship function and the crossover point over all pixels. Thus, thefuzzy contrast is written as

(7)

where satisfies the constraint .

Defining the average fuzzy contrast by

(8)

would allow us to define the quality factor.Definition: The quality factor of an image is defined as the

ratio of absolute average fuzzy contrast to the fuzzy contrast

(9)

In the above definition, the fuzzy average contrast gives theoverall intensity of the image whereas the fuzzy contrast givesthe spread of the gradient with respect to the reference (thecross over point). Their ratio is found to give the quality of theimage. The amount of enhancement will be indicated by the vi-sual factor to be defined later.

If we replace by in (7) and (8), we obtain thefuzzy contrast and average contrast for the original image. Theseare given by

(10)

(11)

In view of the above definition, the image quality of the originalimage is given by

(12)

The change in image quality is now given by

(13)

B. Fuzzy Optimization Using Entropy

Entropy that makes use of Shanon’s function is regardedas a measure of quality of information in an image in the fuzzydomain. It gives the value of indefiniteness of an image. Thisquantity is defined by the following equation:

(14)

Since provides the useful information about the extent towhich the information can be retrieved from the image, opti-mization of this should pave the way for the determination of


the parameters , , and . So, the derivatives of with re-spect to , and are obtained as

(15)

(16)

(17)

where is defined in Appendix I as (A15). The abovederivatives are used in the learning of the parameters , and

. Before presenting the algorithm for learning, we need tointroduce certain constraints for generating aesthetic images.These constraints are discussed in Section IV. The initial valueof is taken from [15]

(18)

By defining the entropy-based fuzzy contrast as

(19)

would simplify (15) as

(20)

Defining the entropy-based average fuzzy contrast by

(21)

would simplify (16) as

(22)

Now, the entropy-based quality factor, easily follows fromthe definition of .

Definition: The entropy-based quality factor of an image isdefined as the ratio of entropy-based average fuzzy contrastto the entropy-based fuzzy contrast,

(23)

In view of (23), we can combine (20) and (22) into the following:

(24)

Then (24) can be written as

(25)

The change in the image quality is given by

(26)

Constrained Fuzzy OptimizationIf we know the desired quality factor corresponding to

and the desired entropy-based quality factor, corre-sponding to , then it possible to satisfy these desired qualityfactors treated as constraints by the constrained fuzzy optimiza-tion. However, we need to set up the objective functions as under

(27)

(28)

(29)

The optimization of the above objective functions is given inAppendix I.

IV. VISUAL FACTORS

For the purpose of judging the entropy-based quality factor,we define the normalized quality factor called the visual factor

(30)

The definition of the visual factor allows us to specify a rangefor the desired normalized quality factor such that increasingbeyond this range; the image would start losing the pleasing na-ture. By experimentation, we have found a value in the range of0.4 to 0.65 for the visual factor. The visual factor also indicateswhether the images are under exposed if its value is less than 1or over exposed if its value is more than 1 after enhancement.Thus, the visual factor justifies the definition of quality factor.

Algorithm for Fuzzy Optimization

The problem at hand is optimization of the entropy with re-spect to the parameters , and with certain constraints. Fora solution of this problem, we adapt the univariate method of[18] by multiplying the step size, by the derivative,of the objective function with respect to the base point, .In this method, we change only one parameter at a time, andproduce a sequence of improved approximations to reach theminimum point. By starting at a base pointin the th iteration, we fix the values of any one of pa-rameters and vary the remaining parameter. The purpose is toproduce a new base point . The search is now continued in


Fig. 1. Flowchart of the enhancement technique.

a new direction. The new direction is obtained by changing anyone of the parameters that has been fixed in the previousiteration. After all the directions are searched sequentially, thefirst cycle is completed and then we repeat the entire process ofsequential minimization till no further improvement is possiblein the objective function in any of the directions. The choiceof the direction and the step length in the modified univariatemethod is summarized here.

Modified Univariate Algorithm

1) Choose a starting point and set .

2) Find the search direction as

...

3) For the current direction , find whether the functionvalue decreases in the positive or negative direction. Forthis, we take a small probe length , also called learningfactor, and evaluate , , and

. If , will be the correctdirection for decreasing the value of , and if ,will be the correct direction. If both and are less than

, we take as the minimum of the two.

4) Set ; .

5) .

6) Set and go to Step 2). Continue this procedureuntil no significant change is observed in the value of theobjective function.

We have taken a unit step length for computational simplicity.The flow chart detailing the enhancement technique is shown inFig. 1 and the algorithm for the same is as follows.

Algorithm for Image Enhancement

1) Input the given image file and convert RGB to HSV.

2) Calculate histogram where .

3) Calculate the initial using (18).

4) Fuzzify to get using (3).

5) Initialize , and calculate , , and .


TABLE IINITIAL PARAMETERS OF TEST IMAGES

TABLE IIOPTIMIZATION OF E WITH Q = 0:4, � = 0:2

6) Initialize , and choose any desired factor fromand set it to 0.4 to learn the parameters

iteratively.

7) Optimize the objective function using the ModifiedUnivariate method. The stopping criteria are: error,

, Lagrange multiplier, , visual factor,, and number of iterations, .

8) Modify the membership function with the optimizedparameters .

9) Defuzzify for the enhanced value using (4). Display theenhanced HSV image.

V. RESULTS AND DISCUSSION

The RGB image is first converted into HSV domain to pre-serve the hue and saturation of the image. The fuzzifier, , thecrossover point, and the intensification parameter, for thecomponent are calculated separately. Throughout the intensifi-cation process, the value of hue and saturation are kept constant.The initial value of the intensification parameter is taken as 5 andthat of the crossover point as 0.5. The values of the fuzzifier ,the intensification parameter , and the fuzzy domain crossoverpoint are optimized by minimizing the entropy of the imagewith quality factor as the constraint.

We have considered many images, viz., Lena, girl, face, water,timber, doctor, meeting, plane, lab, and fruit. The original im-ages have poor brightness, i.e., under exposed and the detailsare not discernable. Also colors are not perceivable to the eye.

TABLE IIIOPTIMIZATION OF E WITH Q = 0:4, � = 0:2

TABLE IVOPTIMIZATION OF E WITH C = 0:4, � = 0:3

The initial parameters required for fuzzy optimization aregiven in Table I. The results of constrained optimization for thedesired quality factor and for an initial value of Lagrangecoefficient are given in Table II. Table III gives the results forthe desired entropy-based quality factor . Table IV corre-sponds to the results of optimization with the desired contrast

. The original images and the enhanced images are shownin Figs. 2–11, and the images correspond to results of Table II.The enhanced images corresponding to Tables III and IV do notshow much difference, hence, they are not shown. A clear im-provement is seen as far as the details are concerned after theapplication of the proposed enhancement method.

From the tables, we note that as the parameter is increasedfor the enhancement of under exposed image the entropy de-creases. The initial value of does not change much after es-timation with optimization. The quality factor depends on allthe three parameters, viz., . The quality factor beforeand after enhancement may be more or less depending on thegray level distribution of the image. For under-exposed images,it decreases while it increases for over exposed images after en-hancement. This can be seen from different case studies, fromwhich we can say it is nonlinear. Note that the pleasing naturearises from proper stretching of the membership values. The vi-sual factor gives an idea of pleasing nature. From our simula-tion studies, we have found a value of visual factor in the range0.4–0.8 to yield the pleasing image for under exposed images.For over exposed images like the one in Fig. 16 (i.e., naturalscene) the visual factor is more than 1. For the mixed imagethat has both under and over exposed pixels, the visual factor


Fig. 2. Top to bottom: (a) Original image and (b) enhanced image of doctor.

Fig. 3. Top to bottom: (a) Original image and (b) enhanced image of face.

depends on the relative dominance of one over another. For ex-ample in Fig. 15 (the cougar) the under exposed portion domi-nates the over exposed portion. Hence, it is treated as the underexposed, thus giving the visual factor below 1.

The proposed approach works better; in other words it is wellsuited for the enhancement of under exposed images because ofthe choice of the fuzzification function, in which we are takingthe difference of gray levels with respect to maximum gray leveland because of the property of global intensification operator.

Fig. 4. Top to bottom: (a) Original image and (b) enhanced image of timber.

When it comes to the over exposed images, this function fails toperform properly. However, by changing the maximum value inthe fuzzification function, which serves then as a fourth param-eter we can achieve a significant enhancement of both over-ex-posed and mixed images. For over exposed images the max-imum must be increased by a suitable value so that the mem-bership values are decreased. Alternatively, we can reduce thefuzzifier or increase the cross over point. For mixed type themaximum value must be decreased by a suitable value. Thus,a proper choice of four parameters is essential for the enhance-ment of all types of images. We have not taken recourse to op-timization in case of over and mixed type images. This will re-quire an overhaul of our optimization technique.

The results of this technique have been compared with thoseof Histogram Equalization for a fruit image in Fig. 11. The RGBhistograms of fruit image are shown in Fig. 12 and the cor-responding histograms due to the proposed approach and his-togram equalization are shown in Figs. 13 and 14, respectively.The proposed technique preserves the histogram modes of theoriginal image at the same time intensifying the color composi-tion whereas the histogram equalization makes the image morebrighter. The values of quality factor after histogram equaliza-tion are given in Table V for all images.

VI. CONCLUSION

Fuzzy logic-based image enhancement method is presentedby fuzzifying the color intensity property of the image usingGaussian membership function, which is suitable for under ex-posed images. Enhancement of the fuzzified image is carriedout using a general intensification operator GINT of sigmoidtype, which depends on the crossover point and the intensi-fication parameter . The optimum values of these parametersare obtained by the constrained fuzzy optimization. A modifiedunivariate method involving gradient descent learning is used


Fig. 5. Top to bottom: (a) Original image and (b) enhanced image of lab.

Fig. 6. Top to bottom: (a) Original image and (b) enhanced image plane.

Fig. 7. Top to bottom: (a) Original image and (b) enhanced image of meeting.

Fig. 8. Top to bottom: (a) Original image and (b) enhanced image of girl.

for the optimization. We have also introduced quality and vi-sual factors as constraints in the optimization of entropy. A vi-sually pleasing image is obtained with the appropriate choice ofquality factors. It may be noted that GINT is guided by thesefactors since ultimate enhancement leads to the binarization ofthe image. The results of enhancement using fuzzy entropy op-timization are compared with those of histogram equalization.

Fig. 9. Top to bottom: (a) Original image and (b) enhanced image Lena.

Fig. 10. Top to bottom: (a) Original image and (b) enhanced image of water.

Fig. 11. Comparison of enhancement of fruit image: (a) Original, (b) proposedapproach, and (c) histogram equalization.

For over-exposed and mixed-type images, the maximum in-tensity of the color in the Gaussian fuzzification function be-comes another parameter in addition to the three parameters.


Fig. 12. RGB histograms for fruit image: (a) Original, (b) proposed approach, and (c) histogram equalization.



Fig. 15. Comparison of enhancement of under + over exposed cougar image: (a) Original, (b) proposed approach, and (c) histogram equalization.

Fig. 16. Comparison of enhancement of over exposed natural scene: (a) Original, (b) proposed approach, and (c) histogram equalization.


TABLE VHISTOGRAM EQUALIZATION RESULTS WITH � = 0:5

We have not determined this by optimization as this param-eter has been manipulated by visual assessment without goingthrough the rigors of optimization procedure. The maximumvalue is decreased for mixed type image and increased for overexposed images. The visual factor provides a clue for knowingthe type of the image. However, this information is availableafter enhancement.

APPENDIX I

Case I: Optimization of With the Image Quality as the Con-straint: For this, consider the objective function

(A1)

where is the desired image quality. Now, the derivatives are

(A2)

(A3)

(A4)

(A5)

(A6)

(A7)

(A8)

(A9)

(A10)

(A11)

The derivatives in (A9)–(A11) are as follows:

(A12)

(A13)

(A14)

but

(A15)

(A16)

(A17)

(A18)

(A19)

Case II: Optimization of With the Entropy-Based ImageQuality as the Constraint: For this, consider the objectivefunction

(A20)

where is the desired image quality. Differentiatingwith respect to the unknown parameters yields the followingderivatives:

(A21)where

(A22)

(A23)


(A24)

(A25)

Case III: Optimization Using the Fuzzy Contrast: This defini-tion of fuzzy contrast gives one way for the image enhancement,when we optimize with respect to the parameters , , and

. If is the desired fuzzy contrast, we can find the parame-ters , and by

(A26)

The differentiation of with respect to these parameters yieldsthe following:

(A27)

(A28)

(A29)

ACKNOWLEDGMENT

The authors would like to thank the Director, ScientificAnalysis Group, Defence R&D Organization, Metcalfe House,Delhi, for allowing them to carry out this work.

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Madasu Hanmandlu (M’02) received the B.E. de-gree in electrical engineering from Osmania Univer-sity, Hyderabad, India, in 1973, the M.Tech degreein power systems from R.E.C. Warangal, JawaharlalNehru Technological University, India, in 1976, andthe Ph.D. degree in control systems from Indian In-stitute of Technology (IIT), Delhi, in 1981.

From 1979 to 1981, he was a Senior Scientific Of-ficer in the Applied Systems Research Program, De-partment of Electrical Engineering, IIT Delhi, wherehe joined the Electrical Engineering Department as a

Lecturer in 1981 and became a Professor in 1997. He was with the Machine Vi-sion Group, City University, London, U.K., in 1988, and the Robotics ResearchGroup, Oxford University, Oxford, U.K., in 1993, as part of the Indo-U.K. re-search collaboration. He was a Visiting Professor with the Faculty of Engi-neering, Multimedia University, Malaysia, from March 2001 to March 2003. Heworked in the areas of power systems, control, robotics, and computer vision,before shifting to fuzzy theory. His current research interests mainly includefuzzy modeling of dynamic systems and applications of fuzzy logic to imageprocessing, document processing, bio-medical imaging, and intelligent control.He has authored a book on computer graphics and also has over 160 publica-tions to his credit.

Dr. Hanmandlu is an Associate Editor of the Pattern Recognition Journal,as well as a Reviewer for several journals, including the IEEE TRANSACTIONS

ON FUZZY SYSTEMS, the IEEE TRANSACTIONS ON IMAGE PROCESSING, and theIEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS. He is listed inReference Asia, Asia’s Who’s Who of Men and Women of Achievement, 5000Personalities of the World (1998), and the American Biographical Institute.

Devendra Jha was born in Sarhad, Madhubani(Bihar), India. He received the B.Sc. degree fromB.I.T., Sindri, India, in 1987, the M.E. degree fromthe Delhi College of Engineering, Delhi, India, in1993, both in electronics and communication engi-neering, and the Ph.D. degree in fuzzy approachesin image analysis from the Department of ElectricalEngineering, Indian Institute of Technology (IIT),Delhi, in 2003.

He joined DRDO as a Scientist in 1989 aftercompleting his fourth electronics fellowship course

at IAT, Pune, India, and after a brief stay in the fertilizer industry as anInstrumentation Engineer. He has worked on acousto-optic FH spread spectrumreceivers and secure communication system analysis. Presently, he is workingon a project which aims at analyzing satellite communication signals. Besidesconference papers, he has published in the Defence Science Journal and PatternRecognition Letters. His current research includes fuzzy pattern recognition,secure communication system design and analysis, cognition-based signal andimage processing, steganography, and biometry.

Dr. Jha is a member of IETE, Delhi.

An Optimal Fuzzy System for Color Image Enhancement

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