DESIGN OF A MODIFIED FUZZY FILTERING FOR NOISE REDUCTION IN IMAGES

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1 Journal of Theoretical an Applie Information Technology 10 th January 014. Vol. 59 No JATIT & LLS. All rights reserve. DESIGN OF A MODIFIED FUZZY FILTERING FOR NOISE REDUCTION IN IMAGES 1 EHSAN AZIMIRAD, JAVAD HADDADNIA 1 PHD Stuent, Department of Electrical an Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran Associate Professor, Department of Electrical an Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran 1 e.azimi@hsu.ac.ir, haania@hsu.ac.ir ABSTRACT Reucing noise from the color images is a very active research scope in image processing. In this paper, a moifie fuzzy base image filtering algorithm is propose for reucing impulse noise. This paper presents a new fuzzy filter for the removal Impulse noise in color images. For ealing with the Impulse noise, an algorithm is evelope to search for a set of uncorrupte pixels in the neighborhoo of the pixel of interest an to compute the meian of this set. A moifie fuzzy filter consisting of two sub filters with novel membership functions is propose to cancel out the impulse noise. The first sub filter etects the noisy pixel by utilizing three fuzzy membership functions, efine for this purpose. The corrupte pixels are then correcte using the meian of the noise free pixels. The secon sub filter makes use of the relation between ifferent color components of a pixel to remove the resiual noise in the color image. Simulation results shows that the propose fuzzy filter effectively removes the aitive noise by preserving fine etails in the image. Keywors: Impulse Noise, Fuzzy Filter, Reucing Noise, Meian Filter, Membership Functions 1. INTRODUCTION Image restoration is a major research area in image processing. Images can become corrupte uring any of the phase take acquisition, preprocessing, compression, transmission, storage an/or reprouction phases of the processing [1]. Noise reuction is a preprocessing step in image enhancement. Last one ecae research in the image restoration of noise affecte image into original image is going on. Image etail preservation an impulse noise attenuation are ifficult to achieve simultaneously in the area of image restoration esign. The types of the noise are: aitive an multiplicative. The major category in aitive noise is Impulsive noise an Gaussian noise. Speckle noise is the multiplicative noise []. Generally the noise reuction process has two phases. The first phase is calle noise etection, which is use to ientify whether the pixels are corrupte by noise or not. The secon phase is noise reuction. Before applying the filter, the ientifie pixel is iscriminate by either the pixel is noise or image fine etails like ege, texture, color, etc. Then the noise affecte pixel is replace by the filter value. Almost all noise reuction algorithms are execute in two steps, i) etect the corrupte pixels an ii) correct the pixels by replacing the filter estimate values []. The application of fuzzy techniques in image processing is a promising research fiel. Fuzzy techniques have alreay been applie in several omains of image processing (e.g., filtering, interpolation, an morphology), an have numerous practical applications (e.g., in inustrial an meical image processing) [3]. Image filters exist in three omains: spatial, frequency an fuzzy omain. This stuy eals with fuzzy filters which offer several avantages over classical filters even as they preserve the image structure. Moreover, fuzzy filters are easy to realize by means of simple fuzzy rules that characterize a particular noise. In this paper a new fuzzy filter was propose for the removal Impulse noise in color images. Alreay several fuzzy filters for noise reuction have been evelope, e.g., the well-known FIRE-filter from [7,8,9], the weighte fuzzy mean filter from [10] an [11], an the iterative fuzzy control base filter 113

2 Journal of Theoretical an Applie Information Technology 10 th January 014. Vol. 59 No JATIT & LLS. All rights reserve. from [1]. Also, [13] represent a robust fuzzy meian filter for impulse noise reuction of gray scale images. Most fuzzy techniques in image noise reuction mainly eal with fattaile noise like impulse noise. These fuzzy filters are able to outperform rank-orer filter schemes (such as the meian filter). Nevertheless, most fuzzy techniques are not specifically esigne for Gaussian noise or o not prouce convincing results when applie to hanle this type of noise [3,4,6]. For ealing with the Impulse noise, an algorithm is evelope to search for a set of uncorrupte pixels in the neighborhoo of the pixel of interest an to compute the meian of this set. A new fuzzy filter consisting of two sub filters with several novel membership functions is propose to cancel out the impulse noise. The first sub filter etects the noisy pixel along with the amount of noise in it by utilizing three fuzzy membership functions, efine for this purpose. The corrupte pixels are then correcte using the meian of the noise free pixels. The secon sub filter makes use of the relation between ifferent color components of a pixel to remove the resiual noise in the color image. The result of this metho can be compare with those obtaine by other filters. This paper is oanize as follows. Section presents the problem statement. Section 3 illustrates the esign of the propose fuzzy filter by introucing the relevant concepts. The main results are etaile in Section 4. Finally, conclusions are rawn in Section 5.. PROBLEM STATEMENT.1. Impulse Noise For Color Images A color image can be represente via several color moels such as RGB, CMY, HSV an CIE. The most well known of these is the RGB moel which is base on Cartesian coorinate system. Images presente in the RGB color moel consists of three component images, one for each primary color (Re, Green an Blue)[4]. Consier a color image represente in the i-j plane, then the thir coorinate k =1,,3 will represent the color component of the image pixel at (. Let A be the image function then A( will represent the Re component of pixel at (. Similarly, A() an A(3) represent the Green an Blue components respectively. Images corrupte with impulse noise contain pixels affecte by some probability. This implies that some of the pixels may not have a trace of any noise at all. Moreover, a pixel can have either all or one or two of its components corrupte with impulse noise. Mathematical moeling of impulse noise in color images is as follows: O( with pk A( = η with (1 pk ) (1) Where, k =1,,3 represents re, green an blue components. The probabilities' p k can have equal or unequal values. In Equation (1), A represents the final corrupte image, while O an η are the numbers of corrupte an uncorrupte pixels respectively [4,5]... Algorithm For Meian Of Noise This paper uses an algorithm to etermine the meian of noise free pixels in the neighborhoo of a pixel uner interest that is presente in[4]. The meian of the noise free pixels is utilize to moify the pixel corrupte with impulse noise. This meian is compute separately for each color component in the following steps: Take a winow of size w w centere on the pixel of interest in the corrupte image. Arrange all the pixels of the winow as a vector. Sort the vector in an increasing orer an compute the meian of the sorte vector. Calculate the ifference between each winow pixel an the meian of the vector. Arrange all the winow pixels having the ifferences less than or equal to a parameter δ 1 in a vector. Sort the new vector an obtain the meian me of the sorte vector. The above Algorithm uses a mask 3 3 for image scanning an meian (me) is use to fin the correction term for each pixel in the noisy image. 3. PROPOSED FUZZY FILTER 3.1. Structure Of Impulse Filter The propose filter is esigne for the reuction of impulse noise in color images. The esigning of Filter is one by treating each color component separately. Interactions among these color components are use to etermine the similarity of the central pixel against the neighboring pixels. The nature of impulse noise is ranom in the sense that it corrupts some pixels while leaving others untouche. So our objective is to ientify the noisy pixels along with the amount of noise present. It may be note that the impulse noise bears similarity with the high frequency content of images like eges an fine etails because both reflect suen 114

3 Journal of Theoretical an Applie Information Technology 10 th January 014. Vol. 59 No JATIT & LLS. All rights reserve. changes in pixel values. The novel of three ifferent membership functions, viz., Great, Dissimilar an Extreme are use to ifferentiate the noisy pixels from the high frequency contents. The propose impulse filter consists of two sub filters as follows. The primary task of this sub filter is to recognize the noisy pixel along with the amount of noise present, an moify the corrupte pixel value with the meian (me) of the noise-free pixels present in the neighborhoo. The three above mentione novel membership functions are frame subsequently to ientify the noisy pixels. The ifference between the central pixel an the meian of the noise-free pixels in the neighborhoo of a winow is enote as [4,5]: Dm = A me () The ifference equations for the other two color components are obtaine by replacing 1 in Equation () by an 3 respectively. We now suggest a new membership function, to represent a fuzzy set Great that inicates how lae the ifference is. A pixel with higher noise will have a laer ifference with the meian value. This is efine by the membership function as: 1 Dm α Dm α1 great ( Dm ) = α1 Dm < α α 0 Dm < α1 (3) The parameters α1 an α in Equation (3) are obtaine from experimentation. The membership function that represente by Equation (3) is epicte in Figure 1. Similarly the ifferences between re an green components an that between re an blue components of the neighboring pixels at ( i + σ, j + ρ ) are calculate as [4,5]: i + σ, j + ρ,1) i + σ, j + ρ,) i + σ, j + ρ,1) i + σ, j + ρ,3) (5) The secon ifferences of the above pair-wise ifferences in (5) are compute from the following equation: = (6) = We also nee the ifferences between the neighboring pixels an the central pixel of the same color component in the winow given by: r i + σ, j + ρ,1) (7) A secon membership function is evise to measure the egree of similarity of the central pixel to the neighboring pixels. This membership function escribes the fuzzy set calle Dissimilar over the iscrete universe of iscourse N ={0,1,,3,4,5,6,7,8}. Let, N be the number of similar pixels in the winow of size w w. The number N is ecie base on the ifferences calculate in Equations (6) an (7) an the similarity criterion. Consiering a 3 3 winow, the membership function is efine as: 0. O 4anDm < δ (8) issimilar ( O, Dm ) = 0.4 O = 3anDm < δ 1 otherwise Note that D m in Equation (8) is efine in Equation () an the parameter δ is the same as use in the similarity criterion. The membership function for Dissimilar is shown in Figure. Figure 1: Membership Function for fuzzy set Great The egree of similarity of a pixel with respect to its neighborhoo pixels means whether it is noisy or not. To ecie whether a pixel is similar to a neighborhoo pixel, a similarity criterion is evise. For example, for the re component, the ifferences between re an green component an that between re an blue components are compute as follows [4,5]: ) 3) (4) Figure : Membership Function for fuzzy set Dissimilar The thir membership function is characterize as follows. If we arrange pixels of the winow in a vector V an sort them in an increasing orer, we will obtain two extreme pixel values, an. The closer the value of a pixel is to these extremes, the higher is the possibility of the pixel being noisy. This concept is use in obtaining Fuzzy set 115

4 Journal of Theoretical an Applie Information Technology V 10 th min January V max 014. Vol. 59 No JATIT & LLS. All rights reserve. Extreme. The membership function for the fuzzy set Extreme applicable to each color component is given as: 0.01 p V & p V min min ( p Vmin + 0.1) 0.01 extreme ( p) = p V 0.1 & p V max max ( p Vmax 0.1) 0 otherwise (9) Where, p represents the pixel value of each color component. The membership function for the fuzzy set Extreme is shown below. Figure 3: Membership Function for fuzzy set Extreme The egree of noise present in a pixel is ascertaine from the following fuzzy rule [4]: Lemma 3.1. IF D m is Great an A is Dissimilar neighborhoo an the central pixel is Extreme THEN this pixel is noisy. In this rule, noise esignate by N is a fuzzy variable. This rule is the Mamani fuzzy moel. Note that we are not using any membership function for the fuzzy set forme by the variables. Let the membership functions Great, Dissimilar an Extreme be enote by gr, r an er for the re component. Then the egree of noise in the re component of a pixel is evaluate as[4,5]: N = min( ( D gr m ), ( O, D r ), ( A( )} (10) Equation (10) is obtaine using the fuzzy rule in Lemma 3.1. Anteceents in the fuzzy rule are combine using the fuzzy operator AND which is implemente as minimum operation. The correction term for the re component is compute as: A = N (11) ( me( ) As N in Equation (10) gives the egree of noise present in the Re component of the pixel at the location (; It will be zero for noise free pixel an will have some value between 0 an 1 for the noisy pixel. The correction term will become zero if the pixel is noise free an its value is equal to the ifference between the meian (me) of noise free pixels in the neighborhoo an the value of the m er pixel itself in the case of extremely corrupte pixels. Now the moifie pixels arising out of the first sub filter (i.e. the output) are obtaine as: A F (1) 1( + A( The extremely corrupte color components are replace with the meian (me) of the noise free color components of the neighborhoo while the noise free components are left untouche. Pixels having noise in between are treate accoring to the amount of noise present in it. It can be observe that the above moifie pixels are immeiately put to use to correct the subsequent pixels. The output from the first sub filter serves as the input to the secon sub filter. This filter invokes the interactions among the color components to remove the impulse noise. Differences between the color pairs are given as [4]: gb = A = A = A A A ) A ) 3) 3) (13) A fuzzy rule is frame to express the egree of noise present in the color component of a pixel as part of this sub filter. For example for the Re component have [4]: Lemma 3.. IF is Great an is Great THEN the re component of the pixel is noisy. This rule oes not hol always. Suppose there is a re color region then the above ifferences will be lae even without any noise but in that case the meian of the region is again re. Hence this situation oesn t affect the performance of our filter. Similar fuzzy rules are coine for other color components. We fuzzify aaptive ifferences (13) to evolve the membership function (3) with two parameters an α. Note that an will α 1 α α replace the original 1 an in the function Great so as to have ifferent shapes. Correction terms for this filter are compute in similar lines as in the first sub filter. The egree of noise present in a pixel is[4]: n = min{, } g g g (14) Where, g an are the membership functions of Great sets of color pairs, re-green an re-blue respectively. The correction term is given by: AMeian (me) values are calculate again as (15) = n ( me( A ) in the first sub filter whose output is A. The final output of the impulse filter is a set of moifie pixels given by: A = A + A ) (16) F ( k β 1 β 116

5 Journal of Theoretical an Applie Information Technology 10th January 014. Vol. 59 No JATIT & LLS. All rights reserve. ISSN: E-ISSN: The moifie pixels from the secon sub filter are immeiately employe to correct the subsequent pixels [4,5]. 3.. ALGORITHM FOR IMPULSE FILTER The steps of the algorithm for Impulse filter by consier one color component are as follows [4,5]: Step 1: Compute the meian of noise free pixels (me) as per algorithm in.1. Step : Compute Dm ( j,1) j,1) me ( j,1) an Determine great in the fuzzy set Great using (3). Step 3: Calculate no. of pixels similar to central pixels O using Similarity Criteria. Step 4: Determine the egree of similarity of A (i, j,1) in the fuzzy set Dissimilar using (8). Step 5: Determine the membership value of pixel in the fuzzy set Extreme using (9). Step 6: Calculate the correction term using (11) an a it to original value to obtain enoise value. Repeat the steps for other color components. Apply the process for the whole image pixel by pixel. Step 7: For the image obtain in above, Compute the ifferences:, an gbas per (13) an fuzzify them using membership function Great with parameter βan.β 1 Step 8: Use (14) to calculate correction term for re component an for other similar equations are use. Step 9: Final output of impulse filter is obtaine using (16). 4. MAIL RESULTS A color image consisting of an M N 3 array of pixels at locations ( was seen as three gray scale images corresponing to RGB components. The ata class of the component images etermines their range of values. If an image is of class ouble, the range of values is [0,1]. Similarly, the range of values is [0,55] or [0,65535] for RGB images of class uint8 or uint16, respectively[4].the color images as follows with the impulse noise are consiere as test images. The original images are shown in figure 4. Figure 4: Original Images for Simulation The impulse noise is ae to above original images. Percentage of the ae impulse noise to images or noise ensity is %0. The noisy images are shown in figure 5. (a) (b) Figure 5: Impulse Noise in Images: (a). Noisy ensity is 0%, (b). Noisy ensity is 30% Results Of The Impulse Noise Fuzzy Filter In this paper, the winow size of 3 3 is experimente. The primary process of simulation is one by meian filter. A comparison between meian filter an propose fuzzy filter for ifferent noisy ensities (up to 0% an 30%) are rawn in Figures 6 an 7. The best results for higher percentages of the impulse noise, as the winow size of 3 3 prouces better results up to 30% impulse noise, this filter is meant to eal with low an mile percentages of the impulse noise. This level of noise is usually foun in many practical applications. (a) (b) Figure 6: The comparison of between meian filter an esigne fuzzy filter (noisy ensity is 0%): (a). Results of Meian Filter, (b). Results of fuzzy filter. 117

6 Journal of Theoretical an Applie Information Technology 10 th January 014. Vol. 59 No JATIT & LLS. All rights reserve. filter. Simulation results shows that the propose fuzzy filter effectively removes the aitive noise by preserving etails in the color images. Experimental results show the feasibility of the new filter. (a) (b) Figure 7: The comparison of between meian filter an esigne fuzzy filter(noisy ensity is 30%): (a).results of Meian Filter, (b). Results of fuzzy filter. The performance of this filter is illustrate through a set of color images with the impulse noise of ensities up to 30%. The optimal values for the parameters of α1, α, β1, β, δ1, iscusse δ in Section 3 are experimentally etermine to be 0.078, 0.15, 0.5, 0.6, an respectively. They are obtaine using a winow size of 3 3 for the lower an the mile percentage of the impulse noise. It can also be observe visually that the propose filters are quite effective in noise reuction. The uner tables emonstrate the result of experiments. Table 1: The Comparison Of Between Methos (N=0) Noisy Percentage of Methos Density(ND) Improvement Meian Filter %0 %60 Fuzzy Filter (Propose) %0 %90 5. CONCLUSION This paper propose a new fuzzy filter for aitive noise reuction consisting of only impulse noise. This filter recognizes the noisy pixel, moifies the corrupte pixel value an removes impulse noise. Its main feature is that this filter with the new propose of membership functions in equations (3), (8) an (9), removes the impulse noise of ensities up to 30% (Table 1) an tries to etermine corrupte pixels to reuce their contribution in smoothing process. The shape of the applie membership functions is moifie an aapte accoring to the remaining amount of noise after each iteration, such that the performance of esigne fuzzy filter is excellent towar meian REFRENCES: [1] Dimitri Van De Ville, Mike Nachtegael, Dietrich Van er Weken, Etienne E. Kerre, Wilfrie Philips, Ignace Lemahieu, Noise Reuction by Fuzzy Image Filtering, IEEE Transaction on Fuzzy System, Vol. 11, NO. 4, August 003. [] P. Murugeswar D. Manimegala Noise Reuction in Color image using Interval Type- Fuzzy Filter (ITFF), International Journal of Engineering Science an Technology (IJEST), Vol. 3 No. Feb 011. [3] Mahesh T R, Prabhanjan S, M Vinayababu, Noise Reuction by Using Fuzzy Image Filtering, Journal of Theoretical an Applie Information Technology, Islamaba PAKISTAN, Vol.15. No.., 31st May 010. [4] Om Prakash Verma, Maasu Hanmanlu, Anil Singh Parihar, Vamsi Krishna Maasu, Fuzzy Filters for Noise Reuction in Color Images, ICGST-GVIP Journal, Volume 9, Issue 5, September 009. [5] Stefan Schulte, Mike Nachtegael, Valerie De Witte, Dietrich Van er Weken, Etienne E. Kerre, A Fuzzy Impulse Noise Detection an Reuction Metho, Fuzziness an Uncertainty Moelling Research Unit. [6] Dimitri Van De Ville, Wilfrie Philips, Noise Reuction by Fuzzy Image Filtering, IEEE Transaction on Fuzzy System, VOL. 11, NO. 4, AUGUST 003. [7] F. Russo, G. Rampon A fuzzy operator for the enhancement of blurre an noisy images, IEEE Trans. Image Processing, vol. 4, pp , Aug [8] F. Russo, A fuzzy filter for images corrupte by impulse noise, IEEE Signal Processing Letters, vol. 3, pp , June [9] F. Russo, Fire operators for image processing, Fuzzy Sets Syst., vol. 103, no., pp , [10] C.-S. Lee, Y.-H. Kuo, P.-T. Yu, Weighte fuzzy mean filters for image processing, Fuzzy Sets Syst., no. 89, pp ,

7 Journal of Theoretical an Applie Information Technology 10 th January 014. Vol. 59 No JATIT & LLS. All rights reserve. [11] C.-S. Lee, Y.-H. Kuo, Fuzzy Techniques in Image Processing, Stuies in Fuzziness an Soft Computing, ch. Aaptive fuzzy filter an its application to image enhancement, (New York: Springer-Verlag 000, vol. 5, pp ). [1] F. Faiz, M. B. Menha Fuzzy Techniques in Image Processing, Stuies in Fuzziness an Soft Computing, ch. A fuzzy logic control base approach for image filtering, (New York: Springer-Verlag 000, vol. 5, pp ). [13] Jagaish H. Pujar, Robust Fuzzy Meian Filter for Impulse Noise Reuction of Gray Scale Images, Worl Acaemy of Science, Engineering an Technology