Fuzzy Logic Technique for Image Enhancement

Abstract Now day’s applications should be demand equivocal molds of issues and pictures as sources of referable attributable attributableice restraint solution and dissection. Whenever an issue is modifiable from undivided to another contrive such as, digitizing, scanning, transmitting and storing, some of the suspension frequently occurs at the extinguishedput purpose. Hence, the extinguishedput issue has to go in a order denominated issue recouple which consists of a assemblage of techniques that insufficiency to amend the condition of an issue. Issue recouple is basically beseeming issue and its solution and recognizeing of the referable attributable attributableice in digital issues and providing amiable input restraint incongruous other automated issue ordering techniques. The fuzzy cemal speculation is frequently equivocalties (approve it comes from the referable attributable attributableice helpful from post such as dimness may extinguishedcome from marred, imprecise, and referable attributable attributable attributable easily received). The fuzzy logic gives a dishonorableplace mold restraint the illustrateation and ordering of amiable attainments. The concept is depends upon if-then governments in access of the waverings approves origin purpose. So the Equivocalties amid issue ordering tasks repeatedly ascribable to anonymousness and ambiguousness. A fuzzy technique achievements as to direct these substances issueively.

IndexTerms Fuzzy Logic, Issue Ordering, Issue Repair, Issue Fuzzification, Issue Defuzzification

Whenever an issue is modifiable from undivided to another contrive such as, digitizing, scanning, transmitting and storing, some suspension is frequently occurs at the extinguishedput mark. Hence, the extinguishedput issue has to go in a order denominated issue repair. Issue recouple consists of a assemblage of techniques that insufficiency to amend the overperfect condition of an issue. Fuzzy issue ordering is the entrancees that recognize, illustrate and order the issues and their pixels with its estimates as fuzzy cemals. The illustrateation and ordering is depending upon the chosen fuzzy techniques and the substance to be solved. The issue of fuzzy cemals is very pure and penny. Restraint illustration, if someundivided lack to bound a cemal of frosty smooths, undivided has to bound a origin restraint frosty smooth from 0 to 100. Here 0 to 100 are part of this fuzzy cemal; the others do referable attributable attributable attributable befit to that cemal. The account logic astern fuzzy technique is the account restraint anthropological despatch. This contemplation depends upon divers of the other statements environing fuzzy logic. As fuzzy logic is built on the logics of imported style portraitured in dishonorable,humdrum discourse, fuzzy logic is very quiet to portraiture. A filtering species insufficiencys to be choice of curbced with estimates and equivocal referable attributable attributableice; this suggests the portraiture of fuzzy logic.


Fuzzy issue ordering techniques is referable attributable attributable attributable rare speculation. It is a assemblage of incongruous fuzzy entrancees to issue ordering techniques. The aftercited determination is to be cherished to individualize the boundaries of fuzzy digital issue ordering:

Fuzzy issue ordering is the entrancees that recognize, illustrate and order the digital issues and their segments and so features as fuzzy cemals. The illustrateation of it and ordering is frequently depending on the chosen fuzzy techniques and on the substance which insufficiency to be solved [9]. Adown a schedule of open contemplations is boundd environing fuzzy logic:

  • Fuzzy logic is conceptually very quiet to recognize.

The dishonorableplace concepts astern fuzzy logic curbced are pure. Fuzzy logic is opineable entrance externally the wide-spread entanglement.

  • Fuzzy logic is lithe.

Everyunnaturalness is ambagious if you face air-tight sufficient, save past than that, most unnaturalnesss are ambagious. Fuzzy curbced prepared this recognizeing into the order rather than sound speculation.

  • Fuzzy logic can mold the nonstraight businesss of dishonorableplacely entanglement.

Undivided can educe a fuzzy logic species to parallel any cemals of input and extinguishedput axioms. This order is very quiet by some of the adaptive techniques such as Adaptive Neuro-Fuzzy Conclusion Speciess, which is already helpful in Fuzzy Logic Toolbox.

  • Fuzzy logic can be artifice on the summit of proof of expeditionss.

In condition of neural networks, it must insufficiency luxuriance axioms and beacquire the extinguishedputs. Save fuzzy logic acquire decipher you environing the proof of populace who already recognize the entire speciess.

  • Fuzzy logic can be qualified with any social guide techniques.

Fuzzy speciess don’t re-establish social guide methods necessarily. Rarely fuzzy speciess extension them and facilitate its toolation.

  • Fuzzy logic is fixed on penny discourse despatchs.

The account restraint fuzzy logic is the account restraint anthropological despatch and this contemplation decipher divers of the other statements environing fuzzy logic as well-mannered. Actually Fuzzy logic is built on the structures of condition style portraitured in dishonorable,humdrum discourses portraitured restraint despatchs. Fuzzy logic is very quiet to portraiture.

Penny discourse, which populace portraitured on a daily account, has been comes by thousands of years of anthropological faithfulness to be prolific. Sentences that are written in humdrum discourse frequently illustrate a achievement of prolific despatch [3].

Fuzzy issue ordering has three marks: 1) Issue Fuzzification 2) Qualification of companionship estimates 3) Issue Defuzzification.

Form 1. Basic Fuzzy Issue ordering [5]

The fuzzification and defuzzification steps are that in which we do referable attributable attributable attributable hold fuzzy hardware. So, the coding of issue axioms repeatedly denominated as fuzzification and decoding of the extinguishedcomes denominated as defuzzification are the steps to order issues with fuzzy techniques. The ocean unnaturalness of fuzzy issue ordering is in the comprised mark that is qualification of companionship estimates (See Coercionm 1). After the issue axioms are transformed from grey-smooth to the companionship roll that is knhold as fuzzification is withhold fuzzy techniques which dissimilate the companionship estimates which can be a fuzzy clustering and a fuzzy government fixed entrance and so it can be a fuzzy integration entrance.

  1. The Fuzzy cemal speculation

Fuzzy cemal speculation is the extension of crisp cemal speculation. It achievements on the concept of specific faithfulness (betwixt 0 & 1). Entirely penny is 1 and entirely dishonorable is 0. It was introduced by Prof. Lotfi A. Zadeh in 1965 as a balance to mold the anonymousness and ambiguousness in close speciess [3].

  1. Determination Fuzzy cemal

A fuzzy cemal is a couple (A, m) where A is a cemal and m: A-> [0, 1]. Restraint each, x A m(x) is denominated the gait of companionship of x in (A, m). Restraint a restricted cemal A = {x1,…,xn}, the fuzzy cemal (A, m) is personated by {m(x1) / x1,…,m(xn) / xn}. Let x A Then x is denominated referable attributable attributable attributable middle in the fuzzy cemal (A, m) if m(x) = 0, x is denominated easily middle if m(x) = 1, and x is denominated fuzzy component if 0 < m(x) < 1. The cemal {x A |= m(x)>0} is denominated the aid of (A, m) and the cemal {x A | m(x)=1} is denominated its meat.

Fuzzy cemals is very quiet and penny to recognize. If undivided lack to bound a cemal of frosty smooths undivided feel to individualize a origin, repeat the frosty smooth from 0 to 100. Perfect frosty smooths from 0 to 100 are part of this cemal; the others do referable attributable attributable attributable befit to the cemal (See Coercionm 2). Save the dimness is a stuff. A fuzzy cemal can be mold this possessions in reform practice. Restraint defining this cemal, it insufficiencys span incongruous origins 50 and 150. Perfect the frosty smooths which are near than 50 are the liberal component of this cemal and perfect the frosty smooths which are superior than 150 are referable attributable attributable attributable the component of this cemal at perfect. The frosty smooths that are betwixt 50 and 150 feel a specific companionship in the cemal.

Form 2. Illustrateation of “dark frosty-levels” with a fuzzy and crisp cemal.

  1. Fuzzy Hyperbolization

An issue I of bulk MxNand L frosty smooths can be opineed as anarray of fuzzy unmarriedtons and extinguished of which each are having a estimate of companionship personated its clearness referring-to to its clearness smooths Iwith I=0 to L-1. Restraint an issue I, we can transcribe in the referable attributable attributableation of fuzzy sets:

Where g, is the tension of (m, n)th pixel and µmn its companionship estimate. The companionship business identifys a adequate possessions of issue (e.g. edginess, dimness, textural possessions) and it can be boundd globally restraint the entire issue or concentratively. The ocean principles of fuzzy issue recouple is graphic in Coercionm.

Form 3. Fuzzy histogram hyperbolization issue repairs [2]

  1. Issue Fuzzification

The issue fuzzification transforms the frosty smooth of an issue into estimates of companionship business [0…1]. 2 molds of alter businesss are portraitured, the triangle companionship business, and Gaussian companionship businesss. A triangular companionship businesss is shhold in Coercionm 4 and its equation is written as,

Form 4. Triangular companionship businesss

The Gaussian companionship business is shhold in the Coercionm 5 and is identifyd by span parameters {c, σ}. The equation restraint the Gaussian companionship business is written as,

Form 5. Gaussian companionship business

  1. Qualification of Companionship Business

This order insufficiencys to alter the estimates of the companionship businesss extinguishedcomeed from fuzzification order. In this algorithm, the mould of the companionship business is cemal to triangular to identify the hedges and estimate of the fuzzifier β. The fuzzifier β is a linguistic hedge such that β = -0.75 + μ 1.5, so that β has a file of 0.5 – 2. The qualification is carried extinguished to the companionship estimates by a hedges operator. The agency is denominated dilatation if the hedge operator β is similar to 0.5 and it is denominated ardor if β is similar to 2. If A is a fuzzy cemal and it’s illustrateed as a cemal of ordered couples of part x and its companionship estimate is boundd as μ, then Aβ is the qualified account of A and is indicated by adown equation

The hedge operator operates on the estimate of companionship business as fuzzy linguistic hedges. Carrying hedge operator can be extinguishedcome in reducing issue dissimilarity or increasing issue dissimilarity, depending on the estimate of the β. The hedge operators may portraiture to alter the overperfect condition of the dissimilarity of an issue.

  1. Issue Defuzzification

After the estimates of fuzzy companionship business has been qualified, the direct step is to beacquire the novel frosty smooth estimates. This order portraitures the fuzzy histogram hyperbolization. And this is ascribable to the nonlinearity of anthropological clearness recognizeing. This algorithm modifies the companionship estimates of frosty smooths by a logarithmic business:

Where, μmn (gmn) is the frosty smooth in the fuzzy companionship estimates, β is hedge operator, and g’mn is the novel frosty smooth estimates.

  1. Fuzzy Conclusion Species (FIS)

Form 6. Fuzzy Conclusion Speciess

Fuzzy conclusion is the order of mapping from the input-output using fuzzy logic. Mapping provides a account from which it is practicable to fabricate the sentences. Order of fuzzy conclusion are oceanly, the Companionship Businesss, the Logical Agencys, and If-Then Governments. There are basically 2 molds of fuzzy conclusion speciess that is practicable to tool in Fuzzy Logic Toolbox. 1) Mamdanimold and 2) Sugeno-type. These 2 molds of conclusion speciess modify in the practice extinguishedputs are individualized.

Fuzzy conclusion speciess has been successeasily applied in fields such as axioms species, sentence dissection, unimpassioned guide and computer trust. As fuzzy is multidisciplinary, it can be portraitured in fuzzy conclusion speciess such as fuzzy-rule-fixed speciess, fuzzy associative perpetuation, fuzzy expeditions speciess, fuzzy molding, and fuzzy logic guidelers, and barely fuzzy speciess.

Mamdani’s fuzzy conclusion method is the most invariably portraitured fuzzy method. Mamdani’s method was the primitive guide speciess artificeed using fuzzy cemal speculation. It was primitively cunninged in 1975 by Ebrahim Mamdani [7] to guide a fume engine and boiler league by synthesizing a cemal of some linguistic guide governments which can be obtained from proofd anthropological operators. Mamdani’s mold was fixed on Lotfi Sade’s 1973 on fuzzy algorithms or close speciess and sentence orderes [8].

Mamdani-mold conclusion, which boundd restraint Fuzzy Logic Toolbox expects the extinguishedput companionship businesss insufficiencys to be fuzzy cemals. After the composition order, there is a fuzzy cemal restraint perfect the extinguishedput wavering that insufficiencys defuzzification. In divers conditions a unmarried spike as an extinguishedput companionship businesss are portraitured. This mold of extinguishedput is usually knhold as a unmarriedton extinguishedput companionship business. It frequently repairs the aptitude of the defuzzification order as it simplifies the consequence demandd by the past pure Mamdani method, which perceives the centroid of a 2D businesss. Instead of integrating athwart the 2D business to perceive the centroid, undivided can portraiture the weighted mean of some of the axioms purposes. Sugeno-mold species aid this mold of mold. Sugeno-mold speciess can be portraitured to artifice dishonorableplace mold of any conclusion species in which extinguishedput companionship businesss are straight or uniform.

  1. Fuzzy government fixed species

Undivided other entrance to infrared issue dissimilarity recouple using fuzzy logic is a Takagi-Sugeno fuzzy government fixed species. Takagi-Sugeno governments feel consequents which are numeric businesss of the input estimates. This entrance is portraitured to repair the dissimilarity of a frosty-scale digital issue which proposes the aftercited governments:

IF a pixel is dark, THEN fabricate it darker

IF a pixel is gray, THEN fabricate it mid-frosty

IF a pixel is bright, THEN fabricate it brighter

Companionship businesss in a fuzzy cemal map perfect the parts of a cemal into some veritable aggregate in the file [0, 1]. When the estimate of companionship is conspicuous, the “truth” that the cemal part befits to that detail component business is conspicuous as badness versa.

The input companionship businesss restraint an issue dissimilarity recouple species is shhold in Coercionm 7. The cemal of perfect input issue pixel estimates is mapped to 3 incongruous linguistic stipulations: Dark, Frosty & Bright. The estimates μi(z) quantify the “degree of companionship” of a detail input pixel tension estimate to the each of the 3 component businesss; denoted by the subscript (i). Thus, μdark(z) assigns estimate from 0 to 1 and in betwixt to how really “dark” an input pixel tension estimate (z) is. Same practice, μgray(z) and μbright(z) identify how really Frosty or Bright a pixel estimate z is. The Dark and Bright input companionship businesss can be tooled by using a sigmoid businesss and the Frosty input companionship business can be tooled by the Gaussian business. The sigmoid business, so knhold as the logistic business that is consecutive and non-linear. This can be boundd dishonorableplacely as follows:

Where x is input and g(x) is compel. The Gaussian business is boundd as adown:

Form 7. Input Companionship Businesss restraint the Fuzzy Government-Fixed Dissimilarity Repair

Three linguistic stipulations can be boundd restraint the extinguishedput component businesss; and these are referred to as Darker, Mid-frosty and Brighter. Becaportraiture it is dishonorable in some of the toolations of Takagi-Sugeno speciess, the extinguishedput fuzzy cemals are usually boundd as fuzzy unmarriedton that repeats the extinguishedput companionship businesss are unmarried-valued uniforms. Here the extinguishedput companionship business estimates can be chosen as follows:

Darker = 0 (νd)

Mid-frosty = 127 (νg)

Brighter = 255 (νb)

These are shhold adown:

Form 8. Extinguishedput Companionship Businesss restraint the Fuzzy Government-Fixed Dissimilarity Repair

Restraint a Takagi-Sugeno species artifice, the fuzzy logic governments which individualize the extinguishedputs of species feel been portraitured the aftercited straight league of input and extinguishedput companionship business estimate. As the extinguishedput companionship businesss are uniforms, the extinguishedput νo to any input zo, is abandoned by:

Where, μdark(z), μgray(z) and μbright(z) = the input pixel tension estimates and (vd, vg and vb) = the extinguishedput pixel tension estimates. This analogy accomplishes the orderes of spiral, composition and defuzzification simultaneously with a numeric consequence.

In condition of issue ordering, fuzzy logic is consequenceally intensive, as it demands the fuzzification, ordering of perfect governments, spiral, composition and the defuzzification on perfect pixel in the input digital issue. Using a Takagi-Sugeno artifice which portraitures unmarriedton extinguishedput companionship businesss can narorder consequenceal entanglement Coercionm 9 is the arrest diagram of the order familiar restraint the fuzzy logic technique tooled restraint this achievement.

Form 9. Flow chart restraint the tooled fuzzy logic order

  1. Dissimilarity recouple using an INT-Operator from fuzzy speculation

Divers researchers feel applied the fuzzy cemal speculation to clear novel techniques restraint dissimilarity amendment. A basic fuzzy algorithm restraint issue repair, using a global origin, has been little recalled. Let us opine a frosty smooth digital issue, illustrateed by the frosty smooth estimates of the pixels with the file [0;1] and Let l be any frosty smooth of a pixel in this digital issue, l [0;1] .

Dissimilarity amendment is a basic purpose ordering agency which oceanly portraitured to maximize the dynamic file of the issue. A conspicuous dissimilarity in an issue can be achieved by darkening the frosty smooth in the inferior luminance file and brightening the undivideds in the conspicuous luminance file. This ordering openly implies the portraiture of a non-straight business; Contrive of such a business could be the undivided presented in Coercionm 10. Dishonorableplace look of such a nonstraight business, Int (l) is as adown:

The look illustrates operator in the fuzzy cemal speculation, namely the intensification (INT) operator. When it is applied on digital issues, it has the issue of dissimilarity repair.

Form 10. Fuzzy intensification

Let us personate the extinguishedcomeing frosty smooths in the dissimilarity repaird issue by g abandoned by:

Thus, the dissimilarity repaird issue feel frosty smooths of its pixels abandoned by the nonstraight purpose-wise alter in Coercionm 10, applied to the ancient frosty smooth issue.

  1. Implementation on Matlab

The aftercited are the steps which are carried extinguished restraint the toolation to acquire the extinguishedput:

  1. Read the ancient issue.

>> I = imread(‘Input issue’)

  1. Convert it into Frosty Scale issue if it is RGB issue.

>> I = rgb2gray(I)

  1. Add the sound to the issue.

>> Z = imnoise(I,’gaussian’,0.2);

  1. Calculate bulk of ancient issue.

>> [order col] = bulk(Z);

  1. Percontrive morphological agency on issue.

To perceive Maximum pixel estimate of issue

>> mx = max(max(Z));

To perceive Minimun pixel estimate of issue

>> mn = min(min(d));

To perceive Mid purpose of issue

>> mid = (mx+mn)/2;

  1. Apply fuzzy algorithm.
  1. Show the extinguishedput.

>> coercionm,imshow(output),inscription (‘output repaird issue’)

  1. Conclusion

Four incongruous fuzzy entrancees has been tooled to recouple the exalted voltage issues. Paralleld to the basic entrancees, undivided can referable attributable attributableice that fuzzy methods present a potent dishonorableplace mold restraint clearing novel recouple algorithms. The global fuzzy entrancees referable attributable attributable attributable gives exquisite extinguishedcomes. Save here a concentratively adaptive process restraint fuzzy recouple has been cunninged. The dissimilarity recouple of exalted voltage issues is so referable attributable attributable attributable exquisite rarely. The discuss astern that is the physics of EPIDs which produces issues with thin dynamics qualities and that is why rarely there is no referable attributable attributableice in MVI to be amendd. The fuzzy logic algorithms present divers incongruous possibilities to optimize its enterprise, approve parameters of companionship businesss, ascribable to that it can unquestionably be expected that fuzzy issue recouple techniques can be applied in divers areas of medical imaging in advenient.


[1]Farzam Farbiz, Mohammad Bager Menhaj, Seyed A. Motamedi, and Martin T. Hagan, “A novel Fuzzy Logic Filter restraint issue Repair” IEEE Transactions on Speciess, Man, And Cybernetics-Part B: Cybernetics, Vol. 30, No. 1, February 2000.

[2]Om Parkas Verma, Madasu Hanmandlu, Anil Singh Pariah and Vamp Krishna Madasu “Fuzzy Filter restraint Sound Reduction in Color Issues,” ICGST-GVIP Journal, Vol. 9, No. 5, September 2009, pp.29-43.

[3]Rafael C.Gonzalez and Richard, E. Woods “Digital Issue Ordering,” Novel Jersey, Pearson Prentice Hall, Third Edition – 2008.

[4]Aboul Ella Hassanien and Amr Bader, “A proportionately con-over on digital mammography Recouple algorithms fixed on Fuzzy Speculation,” International Journal of Studies in Informatics and Guide, SIC – Volume 12 Number 1, March 2003, pp. 21-31.

[5]Alper Pasha “Morphological issue ordering with fuzzy logic,” Aeroquantity and quantity technology magazines, Vol. 2, No. 3, 2006, pp.27-34.

[6]Tamalika Chaira, Ajoy Kumar Ray, “Fuzzy Issue Ordering and Applications with MATLAB,” CRC Press, vol. 1, 2010,pp. 47-55.

[7]Mamdani, E.H. and S. Assilian, “An trial in linguistic collocation with a fuzzy logic guideler,” International Journal of Man-Machine Studies, Elsevier, Vol. 7, No. 1, 1975, pp. 1-13.

[8]Zadeh, L.A., “Outline of a novel entrance to the dissection of close speciess and sentence orderes,” IEEE Transactions on Speciess, Man, and Cybernetics, Vol. 3, No. 1, Jan. 1973, pp. 28-44.

[9]H. R. Tizhoosh, G. Krell and B. Michaelis, “On Fuzzy Recouple of Megavoitage Issues in Radiation Therapy,” Proceedings of the 6th IEEE International Conference on Fuzzy Speciess, July 1997.

[10]Stefan Schulte, Valerie De Witte, and Etienn, E.Kerre, “A Fuzzy Sound Reduction Method restraint Color Issues,” IEEE Transactions on Issue Ordering, Vol. 16, Issue 5, May 2007, pp. 1425-1436.

[11]C.Castiello, G.Castellano, L.Caponetti and A.M.Fanelli, “Fuzzy Species of Issue Pixels,” IEEE International Symposium on Intelligent Signal Ordering, 2003

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