Noise Reduction in Color image using Interval Type-2 ...

P.Murugeswari et al. / International Journal of Engineering Science and Technology (IJEST)

Noise Reduction in Color image using Interval Type-2 Fuzzy Filter (IT2FF) P.Murugeswari1, 1

Department of IT,Sri Vidya College of Engineering and Technology, Virudhunagar

Dr.D.Manimegalai2 2

Professor & Head, Department of IT, National Engineering College, Kovilpatti. Tamil Nadu, India

Abstract: Reducing noise from the images is a very active research area in image processing. In this paper, a new interval type-2 fuzzy based color image filtering algorithm is proposed for reducing additive noise. The proposed Interval Type-2 Fuzzy Filter (IT2FF) consists of two sub filters. The first sub filter computes the distance between the color components of the central pixel and its neighborhood, which determines the degree by which each component should be corrected. The second sub filter computes the local difference with in the color component. Simulation results shows that the proposed filter IT2FF effectively removes the additive noise by preserving fine details in the image. Keywords: Interval Type-2 fuzzy, Noise reduction, KM algorithm. 1.

Introduction:

Image restoration is a major research area in image processing. Images can become corrupted during any of the phase take acquisition, pre-processing, compression, transmission, storage and/or reproduction phases of the processing [1]. Noise reduction is a preprocessing step in image enhancement. Last one decade research in the image restoration of noise affected image into original image is going on. Image detail preservation and impulse noise attenuation are difficult to achieve simultaneously in the area of image restoration design. The types of the noise are: additive and multiplicative. The major category in additive noise is Impulsive noise and Gaussian noise. Speckle noise is the multiplicative noise. Generally the noise reduction process has two phases. The first phase is called noise detection, which is used to identify whether the pixels are corrupted by noise or not. The second phase is noise reduction. Before applying the filter, the identified pixel is discriminated by either the pixel is noise or image fine details like edge, texture, color, etc. Then the noise affected pixel is replaced by the filter value. Almost all noise reduction algorithms are executed in two steps, i) detect the corrupted pixels and ii) correct the pixels by replacing the filter estimated values. A digital color image [10] (denoted as C) can be modeled in certain color space (e.g., RGB, HSV, L*a*b*). As in most applications, the RGB color space is used here as basic color space. By mixing red, green, and blue light in different proportions it is possible to obtain a wide range of colors. For that reason, colors in the RGB model are represented by a 3-D vector, with the first element being the red, the second being the green and the third being the blue, respectively. These pigments are called the three primary components, each quantized to the range [0-2m-1] mostly m=8. In practice, a digital color image can be represented by a 2-D array of vectors where an address defines a position, called a pixel or picture element. If C(i,j,1)denotes the red component, C(i,j,2) the green component and C(i,j,3) the blue component of a pixel at a position in an (noisefree) image, then we can denote the noisy color image N at position (i,j) as follows: [ N(i,j,1) N(i,j,2) N(i,j,3)]=[ (C(i,j,1)+n1) (C(i,j,2)+n2) (C(i,j,3)+n3) ]. In [2], Type-1 fuzzy set (T1 FS) theory was first introduced by Zadeh in 1965 and has been successfully applied in many areas, including image processing, modeling and control, data mining, time-series prediction, etc. An example of a T1 FS is shown in Fig.1

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Fig .1 Type-1 Fuzzy Membership function

In [9], researches have shown that there are limitations in the ability of T1 FSs to model and minimize the effect of uncertainties. This is because a T1 FS is certain in the sense that its membership grades are crisp values. The Fig.2 shows type-2 FSs, characterized by MFs that are themselves fuzzy. Interval type-2 (IT2) FSs, a special case of type-2 FSs, are currently most widely used because of their reduced computational cost. An IT2 FS is bounded from the above and below by two T1 FSs, which are called upper MF (UMF) and lower MF (LMF), respectively. The area between X and X is the footprint of uncertainty (FOU).

Fig .2 Type-2 Fuzzy Membership function

An IT2 FLS is similar to its T1 counterpart, the major difference being that at least one of the FSs in the rule base is an IT2 FS. Hence, the outputs of the inference engine are IT2 FSs, and a type-reducer is needed to convert them into a T1 FS before defuzzification can be carried out. 2.

Related Work

Different existing Type-1 and Type-2 fuzzy based noise reduction algorithms are studied. It is found that huge number of mean, median based fuzzy filtering methods was used to achieve noise reduction while preserving the significant image details. In recent years, more number of applications [3], [7] are developed using the type-2 fuzzy logic system. In the conventional (type-1) FLSs membership functions are scalar, but in the type-2 FLSs the membership function itself is fuzzy. This extra degree of fuzziness provides a more efficient way of handling uncertainty, which is certainly encountered in noisy environment. Hence type-2 FLS may be utilized to design efficient filtering operators exhibiting much better performance in noisy environments. Based on the literature review it is found that only very few numbers of filters based on type-2 FLSs are available to reduce the additive noise from the image. S.T. Wang et. al. have proposed the Gaussian noise filter based on interval type-2 fuzzy systems using selective feedback fuzzy neural network (SFNN). Adaptive type-2 fuzzy median filter design for removal of impulse noise (A2FM) is proposed by Own et. al. A2FM filter, adopts a powerful scheme for overcoming restrictions of the membership function in the type-1 FM filter. Yıldırım et. al. Impulse Noise Removal From Digital Images by a Detail-Preserving Filter Based on Type-2 Fuzzy Logic is proposed. This filter is based on the neuro fuzzy operator. 3.

Proposed Work(IT2FF)

In this paper a new two step filter called Interval Type-2 Fuzzy Filter (IT2FF) is proposed. This filter has the two sub filters. In the first sub filter the correlation between the color components are calculated. Not just taking the average of pixels from its neighborhood, but simultaneously seeing the image fine details such as edges and color component distances which should not be destroyed by the filter. The main concept of the first IT2FF is to distinguish between local variations due to noise and due to image structures such as edges. This is realized by using the color component distances instead of component differences as done in most current filters. For example, to filter certain red component at position (i,j), use the distance between red-green and redblue of certain neighborhood in the red component array. The difference between this new proposed filter and other Type-1 fuzzy based approaches is that Type -2 fuzzy gives more fuzziness and reduces the noise effectively. For each pixel position (i,j) the following couples are defined: the couples red and green denoted as rg(i,j)=(N(i,j,1),N(i,j,2)) the couple red and blue denoted as rb(i,j)=(N(i,j,1), N(i,j,3)) and the couple green and blue denoted as b(i,j)=N(i,j,2),N(i,j,3). To filter the current image pixel at position (i,j), The window of size 3X3

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centered at (i,j) is used. Next, certain weights are assigned to each of the pixels in the window. These weights are assigned according to the following fuzzy rules, where TSK fuzzy model is used. To compute the value that expresses the degree to which the distance of two couples is small or large, the fuzzy set small will be used. Fuzzy sets are commonly represented by membership functions. From such functions can derive the corresponding membership degrees. Since the membership function small µrgs, µrbs, µgbs are interval membership functions for red-green, red-blue and green-blue component. The boundaries of FOU and upper membership functions for small which is shown in the are characterized by their lower Fig.3 Sub Filter-I 1.

The fuzzy set small is defined as bellow.

Membership function

 P1

P

Distance

Fig.3 Membership function small

where P1,P2 are obtained from experimentation. 2.

Following rule base for the inputs are defined. 2.1 To calculate distance between the color component the Euclidean distance is used. Rule 1: IF distance between the couple rg(i,j) and rg(i+k,j+l) is small AND the distance between the couple rb(i,j) and rb(i+k,j+l) is small THEN the weight w(i+k,j+l,1) is large Rule 2: IF distance between the couple rg(i,j) and rg(i+k,j+l) is small AND the distance between the couple gb(i,j) and gb(i+k,j+l) is small THEN the weight w(i+k,j+l,2) is large Rule 3: IF distance between the couple rb(i,j) and rb(i+k,j+l) is Large AND the distance between the couple gb(i,j) and gb(i+k,j+l) is small THEN the weight w(i+k,j+l,3) is large

3. 4. 5. 6.

For computing the weight for the given inputs, compute the firing interval for the nth rule. The lower and upper boundaries of wi is determined by using the iterative procedure proposed by Karnik and Mendel. The weighting factor wi of the rule is calculated by evaluating the membership expressions.  (1) The output of the wi is also the interval type-2 set. The centroid defuzzifier is used to convert the interval type-2 fuzzy set into type-1 fuzzy. (2)

7.

The final output of sub filter-I is denoted as F, ie., (3)

The filter method for the green and blue component is similar to the same. Sub Filter – II The second sub filter is used to calculate the local differences for each color component separately. The second sub filter used in [3] is used to calculate the local difference for each component of the window denoted as LDR, LDG, and LDB for the red, green and blue environment respectively. If the output of the previous sub filter is denoted as F, then the differences are calculated as follows:

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(4) (5) (6) for all k,l € { -L ….+L}.These differences are finally combined to calculate the following correction terms: (7) Calculate the average of the difference for the red, green and blue component at the same position. Finally, the output of the sub filter-II, denoted as out, ie., (8) (9) (10) 4. Experimental Work Experiments are performed on four standard test color images (Lena, Baboon, Bird, & Parrot) corrupted by additive noise with corruption levels of 10% to 50%. The performance of the discussed filter has been evaluated and compared with conventional filters dealing with additive noise, using MATLAB tool. As a measure of objective similarity between a filtered image and the original one, the peak signal-to-noise ratio (PSNR) in decibels (dB) is used.     (11) This similarity measure is based on another measure, namely the mean-square error (MSE). (12) where org is the original color image, img is the filtered color image of size N.M, and S is the maximum possible intensity value (with m-bit integer values, S will be 2m-1).

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Fig.4 Original Images

Both MSE and PSNR measure the difference in the intensity values of a pixel in original and enhanced images. Table.1 shows the comparison of various filters’ performance at various noise levels in terms of MSE and high PSNR. From the table it is clear that the higher percentage of noise removal and lower percentage of image bluring. 5. Conclusion A fuzzy filter for restoring color images corrupted with additive noise is proposed in this paper. The proposed filter is efficient and produces better restoration of the color images compared to other filters. Numerical measures such as PSNR & MSE and visual observation have shown better results. Also the proposed method is preserving the image fine details. Further work can be focused on the construction of other fuzzy filtering methods for color images to suppress multiplicative noise such as speckle noise.

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Acknowledgement We would like to acknowledge the Tijuana Institute of Technology and Baja California Autonomous University, Tijuana Campus, Mexico to provide the Interval Type-2 Fuzzy toolbox.

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Fig.6 Experimental result for various filters(a) Noisy Image (20%) (b) Using FF(c ) Using FNR(d) Using FCCN(e) Proposed IT2FF

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Fig.6 Experimental result for various filters(a) Noisy Image (20%) (b) Using FF(c ) Using FNR(d) Using FCCN(e) Proposed IT2FF

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Fig.7 Experimental result for various filters(a) Noisy Image (20%) (b) Using FF(c ) Using FNR(d) Using FCCN(e) Proposed IT2FF

References [1]

Dimitri Van De Ville,Mike Nachtegael, Dietrich Van der Weken, Etienne E. Kerre, Wilfried Philips, and Ignace Lemahieu, “Noise Reduction by Fuzzy Image Filtering”, IEEE Transaction on Fuzzy System, Vol. 11, NO. 4, August 2003. [2] Dongrui Wu “A Brief Tutorial on Interval Type-2 Fuzzy Sets and Systems”,July 22, 2010 [3] Jerry M. Mendel,Robert I. John, and Feilong Liu,” Interval Type-2 Fuzzy Logic Systems Made Simple”, IEEE Transaction on Fuzzy System, Vol. 14, NO. 6, December 2006 [4] Juan R. Castro, Oscar Castillo, Luis G.Martínez, ”Interval Type-2 Fuzzy Logic Toolbox, Engineering Letters, 15:1, EL_15_1_14, August, 2007. [5] M. Tulin Yıldırım, Alper Bas¸turk, and M. Emin Yuksel,Impulse Noise Removal From Digital Images by a Detail-Preserving Filter Based on Type-2 Fuzzy Logic, IEEE Transaction on Fuzzy System, Vol. 16, NO. 4, August 2008 [6] Om Prakash Verma, Madasu Hanmandlu, Anil Singh Parihar and Vamsi Krishna Madasu, “Fuzzy Filters for Noise Reduction in Color Images”, ICGST-GVIP Journal, Volume 9, Issue 5, September 2009. [7] Olivia Mendoza1 Patricia Melin2 Juan R. Castro1, “The Use of Interval Type-2 Fuzzy Logic as a General Method for Edge Detection”, IFSA-EUSFLAT, 2009 [8] Own, C-M; Tsai, H-H; Yu, P-T; Lee, Y-J,”Adaptive type-2 fuzzy median filter design for removal of impulse noise “, Imaging Science Journal, The, Volume 54, Number 1, March 2006 , pp. 3-18(16) [9] Saikat Maity, Jaya Sil, “Color Image Segmentation using type-2 Fuzzy sets”, International Journal of Computing and Electrical Engineering, vol.1.No.3,August 2009 [10] Stefan Schulte, Valérie De Witte, and Etienne E. Kerre, “A Fuzzy Noise Reduction Method for Color Images” ,IEEE Transaction on Image Processing ,Vol. 16, NO. 5, May 2007. [11] Stefan Schulte, Samuel Morillas, Valentín Gregori, and Etienne E. Kerre, “A New Fuzzy Color Correlated Impulse Noise Reduction Method”, IEEE Transaction on Image Processing, VOL. 16, NO. 10, October 2007.

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