Fuzzy Logic Technique for Image Enhancement

hazy system of logic Technique for epitome EnhancementAbstract Now days applications should be require various types of videos and pictures as sources of knowledge for interpretation and digest. Whenever an kitchen stove is shiftd from unrivaled to a nonher form such(prenominal) as, digitizing, s rearning, transmitting and storing, some of the degradation always occurs at the siding end. Hence, the placeput realise has to go in a solve called image sweetener which consists of a collection of techniques that need to improve the quality of an image. doubling enhancement is basically improving image and its interpretation and perception of the information in digital images and providing good excitant for different other(a) automated image bear upon techniques. The fogged desex hypothesis is always uncertainties ( worry it comes from the information available from situation such as darkness may result from incomplete, imprecise, and non to the full reliable). The misty logic gives a numeral assume for the facsimile and processing of good knowledge. The concept is depends upon if-then rules in approximation of the variables likes threshold point. Also the Uncertainties within image processing tasks often due to vagueness and ambiguity. A blurred technique works as to manage these problems effectively.IndexTerms fuzzed Logic, Image touch on, Image Enhancement, Image Fuzzification, Image DefuzzificationWhenever an image is changed from one and only(a) to another form such as, digitizing, s basening, transmitting and storing, some degradation is always occurs at the output stage. Hence, the output image has to go in a process called image enhancement. Image enhancement consists of a collection of techniques that need to improve the overall quality of an image. Fuzzy image processing is the approaches that understand, represent and process the images and their picture elements with its set as dazed sets. The representation and process ing is depending upon the selected hairy techniques and the problem to be solved. The idea of fuzzy sets is very simple and natural. For instance, if someone want to define a set of gray take aims, one has to define a threshold for gray level from 0 to 100. Here 0 to 100 argon element of this fuzzy set the others do not belong to that set. The basis logic behind fuzzy technique is the basis for human communication. This observation depends upon many of the other statements almost fuzzy logic. As fuzzy logic is built on the logics of qualitative description designd in everyday language, fuzzy logic is very behind to use. A filtering system need to be capable of reasoning with measure outs and uncertain information this suggests the use of fuzzy logic.II. FUZZY IMAGE PROCESSING OVERVIEWFuzzy image processing techniques is not unique possibility. It is a collection of different fuzzy approaches to image processing techniques. The pursuance definition is to be regarded to deter mine the boundaries of fuzzy digital image processingFuzzy image processing is the approaches that understand, represent and process the digital images and their segments and also features as fuzzy sets. The representation of it and processing is always depending on the selected fuzzy techniques and on the problem which need to be solved 9. Below a list of general observations is defined about fuzzy logicFuzzy logic is conceptually very easy to understand.The mathematical concepts behind fuzzy logic reasoning are simple. Fuzzy logic is important approach without the far-reaching complexity.Fuzzy logic is flexible.Everything is one(prenominal) if you look closely enough, but more than that, most things are indefinite. Fuzzy reasoning prepared this understanding into the process rather than just surmisal.Fuzzy logic trick model the nonlinear functions of mathematically complexity.One can create a fuzzy logic system to compare any sets of input and output data. This process is very easy by some of the adaptive techniques such as Adaptive Neuro-Fuzzy demonstration Systems, which is already available in Fuzzy Logic Toolbox.Fuzzy logic can be design on the top of experience of experts.In baptistry of neural ne 2rks, it must need training data and generate the outputs. But fuzzy logic will explain you about the experience of people who already understand the whole systems.Fuzzy logic can be mixed with any conventional control techniques.Fuzzy systems dont replace conventional control methods necessarily. Sometimes fuzzy systems increase them and simplify its implementation.Fuzzy logic is ground on natural language communications.The basis for fuzzy logic is the basis for human communication and this observation explain many of the other statements about fuzzy logic as well. Actually Fuzzy logic is built on the structures of quality description used in everyday languages used for communications. Fuzzy logic is very easy to use.Natural language, which people use d on a daily basis, has been comes by thousands of years of human history to be efficient. Sentences that are written in ordinary language always represent a triumph of efficient communication 3.Fuzzy image processing has three stages 1) Image Fuzzification 2) Modification of rank value 3) Image Defuzzification.Figure 1. Basic Fuzzy Image processing 5The fuzzification and defuzzification steps are that in which we do not take fuzzy hardware. So, the coding of image data often called as fuzzification and decoding of the results called as defuzzification are the steps to process images with fuzzy techniques. The main thing of fuzzy image processing is in the intermediate stage that is modification of social status values (See Figure 1). After the image data are transformed from grey-level to the membership plane that is known as fuzzification is appropriate fuzzy techniques which modify the membership values which can be a fuzzy clustering and a fuzzy rule based approach and also it can be a fuzzy integration approach.The Fuzzy set theoryFuzzy set theory is the extension of crisp set theory. It works on the concept of partial truth (between 0 1). Completely true is 1 and completely false is 0. It was introduced by Prof. Lotfi A. Zadeh in 1965 as a mean to model the vagueness and ambiguity in complex systems 3.Definition Fuzzy setA fuzzy set is a pair (A, m) where A is a set and m A- 0, 1. For each, x A m(x) is called the grade of membership of x in (A, m). For a finite set A = x1,,xn, the fuzzy set (A, m) is denoted by m(x1) / x1,,m(xn) / xn. Let x A Then x is called not included in the fuzzy set (A, m) if m(x) = 0, x is called fully included if m(x) = 1, and x is called fuzzy member if 0 m(x) x A = m(x)0 is called the support of (A, m) and the set x A m(x)=1 is called its kernel.Fuzzy sets is very easy and natural to understand. If one want to define a set of gray levels one have to determine a threshold, say the gray level from 0 to 100. every gray levels from 0 to 100 are element of this set the others do not belong to the set (See Figure 2). But the darkness is a matter. A fuzzy set can be model this property in better way. For defining this set, it needs two different thresholds 50 and 150. All the gray levels which are less than 50 are the full member of this set and all the gray levels which are greater than 150 are not the member of this set at all. The gray levels that are between 50 and 150 have a partial membership in the set.Figure 2. authority of dark gray-levels with a fuzzy and crisp set.Fuzzy HyperbolizationAn image I of size MxNand L gray levels can be considered as anarray of fuzzy singletons and out of which each are having a value of membership denoted its brightness relative to its brightness levels Iwith I=0 to L-1. For an image I, we can write in the distinction of fuzzy setsWhere g, is the brashness of (m, n)th pixel and mn its membership value. The membership function characterizes a suitable property of im age (e.g. edginess, darkness, textural property) and it can be defined globally for the whole image or topically. The main principles of fuzzy image enhancement is illustrated in Figure.Figure 3. Fuzzy histogram hyperbolization image enhancements 2Image FuzzificationThe image fuzzification transforms the gray level of an image into values of membership function 01. 2 types of transformation functions are used, the triangle membership function, and Gaussian membership functions. A triangular membership functions is shown in Figure 4 and its equation is written as,Figure 4. Triangular membership functionsThe Gaussian membership function is shown in the Figure 5 and is characterized by two parameters c, . The equation for the Gaussian membership function is written as,Figure 5. Gaussian membership functionModification of Membership FunctionThis process needs to change the values of the membership functions resulted from fuzzification process. In this algorithm, the shape of the members hip function is set to triangular to characterize the hedges and value of the fuzzifier . The fuzzifier is a linguistic hedge such that = -0.75 + 1.5, so that has a range of 0.5 2. The modification is carried out to the membership values by a hedges operator. The operation is called dilatation if the hedge operator is enough to 0.5 and it is called concentration if is equal to 2. If A is a fuzzy set and its represented as a set of ordered pairs of element x and its membership value is defined as , then A is the modified version of A and is indicated by at a lower place equationThe hedge operator operates on the value of membership function as fuzzy linguistic hedges. Carrying hedge operator can be result in reducing image contrast or increasing image contrast, depending on the value of the . The hedge operators may use to change the overall quality of the contrast of an image.Image DefuzzificationAfter the values of fuzzy membership function has been modified, the side by s ide(p) step is to generate the new gray level values. This process uses the fuzzy histogram hyperbolization. And this is due to the nonlinearity of human brightness perception. This algorithm modifies the membership values of gray levels by a logarithmic functionWhere, mn (gmn) is the gray level in the fuzzy membership values, is hedge operator, and gmn is the new gray level values.Fuzzy Inference System (FIS)Figure 6. Fuzzy Inference SystemsFuzzy inference is the process of mapping from the input-output using fuzzy logic. Mapping provides a basis from which it is possible to perform the decisions. Process of fuzzy inference are mainly, the Membership Functions, the Logical Operations, and If-Then Rules. There are basically 2 types of fuzzy inference systems that is possible to implement in Fuzzy Logic Toolbox. 1) Mamdanitype and 2) Sugeno-type. These 2 types of inference systems vary in the way outputs are determined.Fuzzy inference systems has been successfully applied in field s such as data classification, decision analysis, automatic control and computer vision. As fuzzy is multidisciplinary, it can be used in fuzzy inference systems such as fuzzy-rule-based systems, fuzzy associative memory, fuzzy expert systems, fuzzy modeling, and fuzzy logic controllers, and simply fuzzy systems.Mamdanis fuzzy inference method is the most commonly used fuzzy method. Mamdanis method was the first control systems designed using fuzzy set theory. It was firstly proposed in 1975 by Ebrahim Mamdani 7 to control a locomote engine and boiler combination by synthesizing a set of some linguistic control rules which can be obtained from experienced human operators. Mamdanis model was based on Lotfi Sades 1973 on fuzzy algorithms or complex systems and decision processes 8.Mamdani-type inference, which defined for Fuzzy Logic Toolbox expects the output membership functions needs to be fuzzy sets. After the aggregation process, there is a fuzzy set for all the output variable that needs defuzzification. In many cases a single entwine as an output membership functions are used. This type of output is usually known as a singleton output membership function. It always enhances the efficiency of the defuzzification process as it simplifies the computation required by the more simple Mamdani method, which finds the centroid of a 2D functions. Instead of integrating across the 2D function to find the centroid, one can use the weighted average of some of the data points. Sugeno-type system support this type of model. Sugeno-type systems can be used to design mathematical model of any inference system in which output membership functions are linear or constant.Fuzzy rule based systemOne other approach to infrared image contrast enhancement using fuzzy logic is a Takagi-Sugeno fuzzy rule based system. Takagi-Sugeno rules have consequents which are numerical functions of the input values. This approach is used to enhance the contrast of a gray-scale digital ima ge which proposes the hobby rulesIF a pixel is dark, THEN make it darker IF a pixel is gray, THEN make it mid-gray IF a pixel is bright, THEN make it brighterMembership functions in a fuzzy set map all the elements of a set into some real numbers in the range 0, 1. When the value of membership is higher, the truth that the set element belongs to that particular member function is higher as vice versa.The input membership functions for an image contrast enhancement system is shown in Figure 7. The set of all input image pixel values is mapped to 3 different linguistic terms Dark, Gray Bright. The values i(z) quantify the degree of membership of a particular input pixel intensity value to the each of the 3 member functions denoted by the subscript (i). Thus, dark(z) assigns value from 0 to 1 and in between to how truly dark an input pixel intensity value (z) is. Same way, gray(z) and bright(z) characterize how truly Gray or Bright a pixel value z is. The Dark and Bright input member ship functions can be implemented by using a sigmoid functions and the Gray input membership function can be implemented by the Gaussian function. The sigmoid function, also known as the logistic function that is continuous and non-linear. This can be defined mathematically as followsWhere x is input and g(x) is gain. The Gaussian function is defined as belowFigure 7. Input Membership Functions for the Fuzzy Rule-Based Contrast EnhancementThree linguistic terms can be defined for the output member functions and these are referred to as Darker, Mid-gray and Brighter. Because it is common in some of the implementations of Takagi-Sugeno systems, the output fuzzy sets are usually defined as fuzzy singleton that says the output membership functions are single-valued constants. Here the output membership function values can be selected as followsDarker = 0 (d)Mid-gray = 127 (g)Brighter = 255 (b)These are shown belowFigure 8. Output Membership Functions for the Fuzzy Rule-Based Contrast En hancementFor a Takagi-Sugeno system design, the fuzzy logic rules which determine the outputs of system have been used the following linear combination of input and output membership function value. As the output membership functions are constants, the output o to any input zo, is given up byWhere, dark(z), gray(z) and bright(z) = the input pixel intensity values and (vd, vg and vb) = the output pixel intensity values. This relationship accomplishes the processes of implication, aggregation and defuzzification together with a numeric computation.In case of image processing, fuzzy logic is computationally intensive, as it requires the fuzzification, processing of all rules, implication, aggregation and the defuzzification on every pixel in the input digital image. utilize a Takagi-Sugeno design which uses singleton output membership functions can reduce computational complexity Figure 9 is the block diagram of the process developed for the fuzzy logic technique implemented for this work.Figure 9. Flow chart for the implemented fuzzy logic processContrast enhancement using an INT-Operator from fuzzy theoryMany researchers have applied the fuzzy set theory to develop new techniques for contrast improvement. A basic fuzzy algorithm for image enhancement, using a global threshold, has been briefly recalled. Let us consider a gray level digital image, represented by the gray level values of the pixels with the range 01 and Let l be any gray level of a pixel in this digital image, l 01 .Contrast improvement is a basic point processing operation which mainly used to maximize the dynamic range of the image. A higher contrast in an image can be achieved by darkening the gray level in the lower luminance range and brightening the ones in the upper luminance range. This processing generally implies the use of a non-linear function Form of such a function could be the one presented in Figure 10. Mathematical expression of such a nonlinear function, Int (l) is as belowThe expression represents operator in the fuzzy set theory, namely the intensification (INT) operator. When it is applied on digital images, it has the effect of contrast enhancement.Figure 10. Fuzzy intensificationLet us denote the resulting gray levels in the contrast enhanced image by g given byThus, the contrast enhanced image have gray levels of its pixels given by the nonlinear point-wise transformation in Figure 10, applied to the original gray level image.Implementation on MatlabThe following are the steps which are carried out for the implementation to get the outputRead the original image. I = imread(Input image)Convert it into Gray Scale image if it is RGB image. I = rgb2gray(I)Add the noise to the image. Z = imnoise(I,gaussian,0.2)Calculate size of original image. row col = size(Z)Perform morphological operation on image.To find Maximum pixel value of image mx = max(max(Z))To find Minimun pixel value of image mn = min(min(d))To find Mid point of image mid = (mx+mn)/2Apply f uzzy algorithm. establish the output. figure,imshow(output),title (output enhanced image)ConclusionFour different fuzzy approaches has been implemented to enhancement the high voltage images. Compared to the basic approaches, one can notice that fuzzy methods suffer a powerful mathematical model for developing new enhancement algorithms. The global fuzzy approaches not gives satisfactory results. But here a locally adaptive procedure for fuzzy enhancement has been proposed. The contrast enhancement of high voltage images is also not satisfactory sometimes. The reason behind that is the physics of EPIDs which produces images with abject dynamics qualities and that is why sometimes there is no information in MVI to be improved. The fuzzy logic algorithms offer many different possibilities to optimize its performance, like parameters of membership functions, due to that it can certainly be expected that fuzzy image enhancement techniques can be applied in many areas of medical imagin g in future.References1Farzam Farbiz, Mohammad Bager Menhaj, Seyed A. Motamedi, and Martin T. 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