(PDF) Fuzzy Based Statistical Method for Image Noise Filtering

Volume 4, Issue 10, October 2014 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com Fuzzy Based Statistical Method for Image Noise Filtering 1 M. A. P. Chamikara*, 2A. A. C. A Jayathilake, 3S. R. Kodituwakku 1 Department of Statistics and Computer Science, Faculty of Science, University of Peradeniya, Shri, Lanka 2 Department of Mathematics, Faculty of Science, University of Peradeniya, Shri Lanka 3 Department of Statistics and Computer Science, Faculty of Science, University of Peradeniya, Shri Lanka Abstract - Noice removal from images is an important activity for successful processing of images. The main objective of this research work is to investigate the applicability of soft computing techniques and statistical techniques for noice filtering. This paper presents a novel method for noise filtering in images using a fuzzy based statistical method. This method uses the outlierdetection technique to recognize the noise pixels. The pixel values are replaced with fuzzy logic techniquewhich depends on the properties of the selected neighbourhoodcorresponding to a particular noise pixel. Since, the algorithm only changes the pixels identified as the noise pixels, the image distortion of the proposed method is very low.The proposed method was tested with a sample of 60 images. Experimental results havebeen comparedagainst that of median filtermethodwhich is one of the frequently used image noise filtering methods. The comparisonshows that the proposed method generates images with less distortion compared to the median filter method. Keywords:Image Processing, Noise Filtering, Fuzzy Logic, Outlier Detection, Inter Quartile Range, Peak Signal to Noise Ratio, Image Entropy I. INTRODUCTION Sometimes images obtained from satellites, conventional and digital cameras lack incontrast and brightness because of the limitations of imaging sub systems and illumination conditions while capturing image. Images may have different types of noise. In image enhancement, the goal is to accentuate certain image features for subsequent analysis or for image display[1]. Examples include contrast and edge enhancement, pseudo-colouring, noise filtering, sharpening, and magnifying. Image enhancement is useful in feature extraction, image analysis and image display. The enhancement process itself does not increase the inherent information content in the data. It simply emphasizes certain specified image characteristics. Enhancement algorithms are generally interactive and application-dependent[2]. In many image processing applications, the input image has noise and thus may not show the features clearly.Image contrast enhancement techniques are of particular interest in photography, imagery, medical applications and display devices.Image enhancement can be clustered into two groups: spatial domain and frequency domain methods. In the spatial method, image pixels are directly modified to enhance the image whereas the frequency domain enhancement is conducted by modifying the frequency transform of the image[3]. However, computing the enhancement in frequency domain is a time consuming process even with fast transformation techniquesand henceit is unsuitable for real time applications[4]. Numerous contrast enhancement techniqueshave been proposed and they normalize the image intensities and often fail to produce satisfactory results for a broad range of non-uniform illumination images. Low contrast images are the images whose intensity levels of the pixels resides densely in a narrow range of the imagehistogram. The objects in this type of images are not clear or distinct. To improve the quality of the images and visual perception of human beings, different enhancement methods can be applied. Some methods work in frequency domain, some work in spatial domain and someothers work in fuzzy domain. The enhancement of noisy data, however, is a very critical process because the sharpening operation can significantly increase the noise. [5]. There are lots of classical filters in the literature to remove noise. The classical filters are the mean filters, the median filter and un-sharp masking. The mean filter or the average filter helps in smoothing operations. It suppresses the noise that smaller in size or any other small fluctuations in the image. It involves in calculating the average brightness values in some neighbourhood × and replaces the grey level with an average value. Smoothing oraveraging operation blurs the image and does not preserve the edges[6]. These are not useful in removing noise spikes. Fuzzy filters provide promising results in imageprocessing tasks that cope withsome drawbacks of classical filters. Fuzzy filters are capable of dealing with vague and uncertaininformation.Fuzzy set theory is very useful in recovering a heavily noise corrupted image. Each pixel in the image is represented by a membership function and different types of fuzzy rules remove the noise with blurry edges[7]. A work based on features of imageenhancement and fuzzy logic has been carried out by Harish Kundra[8].This work deals with Fuzzy inference system (FIS)which helps to take the decision about the pixels of the image. Itfocuses on the removal of impulse noise with the preservation of edgesharpness and image details along with improving the contrast of the images. Also, the conventionalmean and median filters fail in this context even at low corruption levels. © 2014, IJARCSSE All Rights Reserved Page | 49 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 Moreover, a fuzzy grey scale enhancement technique has been developed by Jaspreet[9] for low contrast images corrupted by Gaussian noise. It indicates that the proposed method enhances the images while edge preservation and smoothing compared with conventional methods. Manu Gupta and AmanpreetKaurhave proposed another hybrid technique by optimizing Fuzzy Logic and Artificial Neural Network (ANN)[10]. Experimental results have obtained and compared them against other methods using parameters like MSE (Mean Square Error), RMSE (Root Mean Square Error), SNR (Signal to Noise Ratio), and PSNR (Peak Signal to Noise Ratio). Another algorithm has been developed to modify the median filter driven by fuzzy membership functions. Experimental results are compared to static median by numerical measures and visual inspection. The effectiveness of this method has been compared using binary and grey scale images[11]. Another fuzzy rule base algorithm has been developed for detecting edges from the grey scale images. In this algorithm, edginess at each pixel of a digital image is calculated using three 3*3 linear spatial filters such as low-pass, high-pass and edge enhancement (Sobel) filters through spatial convolution process and the results have been compared with that of the other algorithms such as Sobel, Robert, and Prewitt.The edge strengthinformation has been derived using three masks to avoid detection ofspurious edges corresponding to noise, which is often the casewith conventional gradient-based techniques. The three edgestrength values used as fuzzy system inputs were fuzzifiedusing Gaussian membership functions. Fuzzy if-then rules have beenapplied to modify the membership to one of low, medium, orhigh classes. Finally, Mamdanidefuzzifier method hasbeen appliedto produce the final edge image[12]. A new filtering approachbased on fuzzy-logic which has high performance in mixed noise environmentshas been introduced by Farzam[13]. This filter is mainly based on the idea that each pixel is not allowed to be uniformly fired by each of the fuzzy rules. Several test experiments have been performed in order to highlight the merit of the proposed method. A new algorithm has been proposed to enhance colour Image corrupted by Gaussian noise using fuzzy logic which describes uncertain features of images with modification of median filter[14]. The performance of the proposed technique has been evaluated and compared to the existing mean and median filter. The problem with many of the methods which are available in the literatureis that they destroy very sensitive data from the original image introducing blurriness to the restored image. Due to this fact, the restored images seem to have unsharp edges. Therefore, the necessity of introducing a noise filtering method that does not harm the picture quality is raised. This paper presents an imagenoise filtering technique based on fuzzy logic and statistics to increase the quality of an image.The proposed method recognizes the noise pixels using an outlier detection method and it works only with the detected noise pixels to compensate with. Therefore, the proposed method does not harm any sensitive data available in the image. Compared to the median filter technique, the proposed fuzzy basedstatistical method can manage the ambiguity in a better manner with respect to the quality of the image. II. MATERIALS AND METHODS In descriptive statistics, the quartiles of a ranked set of data values are the three points that divide the data set into four equal groups, each group comprising a quarter of the data. A quartile is a type of quantile. The first quartile (Q1) is defined as the middle number between the smallest number and the median of the data set. It is also called the lower quartile or the 25th percentile. The second quartile (Q2) is the median of the data. The third quartile (Q3) is the middle value between the median and the highest value of the dataset and it is the upper quartile or the 75th percentile.Interquartile range (IQR) is the difference between the upper and lower quartiles (IQR = Q3 - Q1)[15].The box plot is a standardized way of displaying the distribution of data based on the five number summary: minimum, first quartile, median, third quartile, and maximum. In the simplest box plot, the central rectangle spans the first quartile to the third quartile (the interquartile range orIQR)as depicted in Figure 01. A segment inside the rectangle shows the median and the segments above and below the box shows the locations of the minimum and maximum [16]. Figure 1: The diagram of a sample box plot An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. The following quantities (called fences) are needed for identifying extreme values in the tails of the distribution using the method of modified box plot[17]: © 2014, IJARCSSE All Rights Reserved Page | 50 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 Lower Inner Fence(LIF): Q1-1.5*IQR Upper Inner Fence (UIF): Q3-1.5*IQR where 1.5*IQR is the maximum whisker length. The values outside the fences are considered to be the outliers.  x  med x  [18] . The average absolute deviation can be used to study about how the values in the A very robust scale estimator is the average absolute deviation about the median of a sample data set x1 , x2 ,...,xn is n 1 given by i 1 i j n population are distributed around the median. Image entropy is a quantity which is used to describe the `busyness' of an image. The busyness is the amount of information which must be coded for, by a compression algorithm. An image that is perfectly flat will have entropy of zero. Consequently, they can be compressed to a relatively small size. On the other hand, high entropy images such as an image of heavily cratered areas on the moon have a great deal of contrast from one pixel to the next and consequently cannot be compressed as much as low entropy images[19]. In Statistics, the mean squared error (MSE) of an estimator measures the average of the squares of the "errors", that is, the difference between the estimator and what is estimated [20]. Peak Signal to Noise Ratio (PSNR) is a measure of the "noise" referenced to the peak intensity, when comparing two images, by calculating the mean square error between pixel intensities, and referring that to the max possible intensity, calculated in dB (decibel) where higher is better[21]. The term “fuzzy logic” refers to logic of approximation. Boolean logic assumes that every fact is either entirely true or false. Fuzzy logic allows for varying degrees of truth. Computers can apply this logic to represent vague and imprecise ideas, such as “hot”, “tall” etc. Fuzzy set theory offers a variable notion of membership [22]. A fuzzy relation acts as an elastic constraint on the values that may be assigned to a variable. In the following formula, a person of age 25 could still belong to the set of young people, but only to a degree of less than one, say 0.9. Now the set of young contains people with ages between 20 and 30, with a linearly decreasing degree of membership. Elements of a fuzzy set are mapped to a universe of membership values using a function-theoretic form. This function maps elements of a fuzzy set A to a real numbered value on the interval 0 to 1. If an element in the universe, say x, is a member of fuzzy set A, then the mapping is given in the following form [22]. Fuzzy expert system is a collection of membership functions and rules that are used to reason about data. Usually, the rules in a fuzzy expert system have the following form [22]: “if is low and is high then is medium” A fuzzy inference system (FIS) essentially defines a nonlinear mapping of the input data vector into a scalar output, using fuzzy rules [11].The mapping process involves 1. input/output membership functions 2. fuzzy logic operators 3. fuzzy if–then rules 4. aggregation of output sets 5. defuzzification Figure 2 shows the architecture of an FIS. Input Membership Functions Rules / Inferences Crisp Input Fuzzification Fuzzy Input Rule Evaluation Fuzzy Output Output Membership Functions Defuzzification Figure 2: Architecture of an FIS Crisp Output © 2014, IJARCSSE All Rights Reserved Page | 51 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 A. Proposed Noise Filtering Algorithm Figure 3 depicts the flow of events of the proposed algorithm. Input Image Selecting the neighborhood of the Generating the statistics for the Select a pixel to be pixel in consideration selected neighborhood for further processed processing Checking whether the selected pixel is a noise pixel Go to the next pixel [Noise pixel] [Not a Noise pixel] Generating the new pixel value for the noise pixel using a Mamdani based FIS Replacing the noise pixel using the value generated from the FIS Figure 3: Flow of events of the proposed algorithm B. Selecting the neighbourhood of the pixel in consideration A neighborhood of n pixels (�� ) is selected around the pixel in consideration. (�� ) can be �8 , �24 , �48 …, as shown in figure 05 where each neighborhood contains a total of 9, 25, 49 pixels respectively.Figure 05shows two neighborhoods selected in two separate situations. Total number of pixels =9 �� Total number of neighborhood pixels = 8 Figure 4: Neighborhood of 8 pixels Total number of pixels =25 �� Total number of neighborhood pixels = 24 Figure 5: Neighborhood of 25 pixels The neighborhoods do not always have to be symmetric.Since the selected neighborhoods are not taken as convolution matrices, thesymmetricity of the neighborhoods does not affect the algorithm. When the algorithm starts, the initial size of the neighborhood must be preserved. Figure06 depicts how the neighborhoods are considered for the edge pixels and the internal pixels of an image against the current pixel in consideration (�� ). Figure 6: Neighborhood selection of an image for the internal and edge pixels C. Generating the statistics for the selected neighbourhood for further processing For a particular neighborhood of a pixel in consideration, the first quartile (Q1), median (M), third quartile(Q3) and the minimum (MIN) and maximum (MAX) values are generated. It will result the Boxplot depicted in figure 7. © 2014, IJARCSSE All Rights Reserved Page | 52 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 Figure 7: Box plot generated for a given neighborhood of a pixel in consideration Now the Inter Quartile Range can be found asIQR= Q2-Q1 D. Checking whether the selected pixel is a noise pixel To check whether Xc is an outlier a modified box plot is generated as shown in figure 08. In the modified box plot, LIF (Lower Inner Fence) is found by using LIF= Q1- MWL where MWL is the maximum whisker length which can be obtained by MWL= IQR*1.5. The UIF (Upper Inner Fence) is found by using UIF= Q3- MWL. Figure 8: Modified box plot for a given neighborhood The values lower than the LIF and the values higherthan the UIF are considered to be the outliers as depicted in figure 8[17]. Now, �� is checked to determine whether it lies in the set of outliers. If it is found to be an outlier, �� will be considered as a noise pixel and will be subjected to further processing. Otherwise, it will be considered as a normal pixel and further processing will not be laid upon it and the algorithm will move into the next adjacent pixel. The same outlier detection techniques will becarried out for the newly selected pixel. E. Generating the new pixel value for the noise pixel using FIS The noise pixel value will be replaced by a Mamdani based FIS, which is composed of two fuzzy inputs, MEDIAN fuzzy input and the MAD fuzzy inputs. The MEDIAN fuzzy input is modeled according to the median values observed in a particular neighborhood. Since only the 8-bit images are considered in this study, the minimum expected MEDIAN is 0 and the maximum expected MEDIAN is 255. The crisp input of MEDIAN is the median obtained for a particular neighborhood. The MEDIAN fuzzy input has been mapped with three membership functions LOW, AVERAGE, and HIGH as depicted in figure 09. Figure 9: MEDIAN fuzzy input MAD fuzzy input is modeled based on the Average median absolute deviation which was calculated for the modified box plot that is within the range of LIF to UIF. The MAD was considered as one fuzzy input because it can be used to study how the values inside the LIF and UIF are distributed around the median which has already been selected as one fuzzy input. It is an obvious fact that the minimum value of MAD is equal to 0. Intuitively the most spread out distribution of two pixels around a median of 255 would be 0, 0. That gives a maximum expected MAD of (255+0+255)*(1/3) = 170. MAD fuzzy input is modeled with three membership functions: LOW, AVERAGE and HIGH as depicted in figure 10. Figure 10: MAD fuzzy input © 2014, IJARCSSE All Rights Reserved Page | 53 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 The fuzzy OUTPUT produces the new pixel value for an identified noise pixel. The fuzzy OUTPUT is mapped with three membership functions: DARK, GRAY and BRIGHT as depicted in figure 11. It is obvious that the output range lies between 0 and 255. Figure 11:Fuzzy output The effect of distribution upon the median to provide the three levels of MAD was observed in generating the rules. Since, MAD provides an estimate of understanding the distribution of other pixels of the neighborhood from the MEDIAN pixel, with a LOW value of MAD the output totally depends on the MEDIAN generating the output of DARK under LOW medians, GRAY under average medians and BRIGHT under HIGH medians. If the MAD gives a HIGH value for a LOW median, the neighborhood is more biased to have very high values. Therefore, the output values are also chosen to be in the range of BRIGHT values. To give a HIGH MAD for a HIGH median, there should be lower pixel values in the neighborhood. Therefore, the output is considered to be within the range of DARK values. Likewise, the consequents for all the antecedents are generated as depicted in figure 12. Therefore, the rule base of the FIS is composed of 7 rules which areshownin figure 13. Figure 12: Rules of theFIS Figure 13: Rule Matrix This set of 7 rules which map the consequents and antecedents, generated the rule surface depicted in figure 14. Figure 14: Rule surface of the Mamdani based FIS III. RESULTS AND DISCUSSION The proposed method was tested and compared with other existing methods using MATLAB R2011a. All the results were obtained using a windows 7, core 2 duo machine with a RAM of 4 GB. The proposed method was applied for 60 different gray scale images and the outputs were compared against the output generated from the median filter. In each of these comparisons, the three measurements, Image Entropy, MSE (Mean Square Error) and the PSNR (Peak Signal to Noise Ratio) were used for the quantitative comparisons. © 2014, IJARCSSE All Rights Reserved Page | 54 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 Figure 15: Results returned from the proposed method filter and the median filter Figure 15 shows the results obtainedfor the „cameraman.tif‟ image.Figure 16 shows the results returned for the „girl.png' image. The image entropy, and peak signal to noise ratio are higher for the proposed method in both the cases. The MSE for the proposed method is lower than the median filtered image in both the cases. The median filter incorporates blurriness to the image and it results in dissolving very important sensitive information from the image. Since the proposed method only considers the noise pixels, it does not harm other information of the images. Figure 16: Results returned from the proposed method filter and the median filter The test results of the images which were tested with the proposed fuzzy based method are tabulated in Table 1. Table 2 shows the results returned for the images filtered with the median filter. Table 1: Test results for sixty images filtered with the proposed method Image actor Albert albert2 angel barbara body Boxing bridge bridge2 buildings Entropy 7.7031 6.5294 3.5162 6.5837 7.6399 6.3445 6.8959 7.7465 7.7178 7.7342 MSE 3.0156 4.222 2.3653 2.4936 2.3894 2.6491 2.5998 2.6711 3.2781 2.4836 PSNR/dB 43.371 41.9096 44.4259 44.1966 44.3819 43.9338 44.0154 43.898 43.0086 44.214 cameraman car car2 cat catsweet cell charlie child children circuit © 2014, IJARCSSE All Rights Reserved Page | 55 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 7.0241 7.5128 7.7458 7.2844 7.2744 4.6543 5.8341 7.8937 7.8346 6.9621 2.7995 2.9062 2.31 2.6484 2.57 2.6556 2.7094 2.3692 2.3737 2.6112 43.6939 43.5315 44.5287 43.9349 44.0655 43.9231 43.836 44.4187 44.4106 43.9964 City coins dog elan fields flower forest galaxy girl girlbooks 7.7519 6.3788 7.7484 7.5051 7.4893 6.9752 7.6816 4.4152 7.1243 6.9362 6.0817 2.6424 2.492 2.6788 3.9519 2.5759 3.1183 3.0329 3.1748 2.7017 40.3246 43.9448 44.1993 43.8853 42.1968 44.0555 43.2257 43.3462 43.1477 43.8484 Jeniffer lady lake leaf lena liftingbody lion mandi mountain nature 6.6288 5.3846 7.7811 7.6655 7.2605 6.4869 7.496 7.0634 7.5855 7.6758 5.1649 2.2631 2.6453 2.516 3.7886 2.821 2.51 8.2254 2.6366 2.5766 41.0342 41.6477 43.94 44.1577 42.38 43.6608 44.1681 39.0132 43.9544 44.0543 Night paddy parrot pianocat pout pumpkin puppy rose sand scenery 6.2416 6.791 7.7334 7.5529 5.794 7.1344 7.4495 7.8681 7.0777 7.8005 3.2685 2.9142 2.2201 2.6987 2.4803 3.0144 2.339 2.8765 2.5683 2.4504 43.0213 43.5196 44.7011 43.8532 44.2198 43.3729 44.4744 43.5762 44.0683 44.2724 shoeflower shoeflower2 statue stone tire tom tree woman1 wood zebra 6.9116 7.1318 6.8807 7.5001 6.9356 7.5895 7.166 7.359 7.4653 7.4229 2.7592 2.5068 2.4797 2.7177 2.3295 2.3808 2.5964 3.0477 3.408 2.4059 43.757 44.1735 44.2209 43.8228 44.4922 44.3976 44.021 43.3251 42.8398 44.352 Table 2: Test results for the samesixty images filtered with the median filter barbar bridge building Image actor Albert albert2 angel body boxing bridge a 2 s Entropy 7.6775 6.5148 3.3541 6.5592 7.5871 6.2674 6.866 7.7258 7.691 7.6828 10.376 13.041 12.862 12.476 MSE 9 6.2435 8 2 26.6246 4.4694 1 6.7713 13.6182 18.4926 PSNR/d 40.210 37.011 37.071 41.662 33.858 B 38.005 5 4 7 33.912 3 37.204 1 36.8236 35.4948 cameraman car car2 cat catsweet cell charlie child children circuit 6.9504 7.497 7.7074 7.2711 7.2613 4.1508 5.7586 7.8582 7.8797 6.9123 18.7691 5.8881 30.6808 3.9061 6.4899 6.8796 4.7395 13.7261 10.9055 7.7801 35.4304 40.465 33.2961 42.2474 40.0424 39.7892 41.4075 36.7893 37.7883 39.2549 City coins dog elan fields flower forest galaxy girl girlbooks 7.7139 6.2194 7.7139 7.4849 7.4094 6.9236 7.6153 3.9036 7.1083 6.93 8.5002 10.1861 15.7491 10.7059 22.0219 10.4143 33.3845 7.8293 6.0575 10.6384 38.8705 38.0847 36.1923 37.8686 34.7362 37.9885 32.9294 39.2276 40.3419 37.896 Jeniffer lady lake leaf lena liftingbody lion mandi mountain nature 6.5394 5.3359 7.7638 7.5897 7.2238 6.4521 7.4634 7.0371 7.5527 7.5988 10.0478 8.6952 7.9409 26.162 8.8613 3.3959 28.8936 17.0015 18.8155 7.9753 38.1441 38.772 39.1661 33.9881 38.6898 40.8442 33.5568 35.8599 35.4197 39.1473 Night paddy parrot pianocat pout pumpkin puppy rose sand scenery © 2014, IJARCSSE All Rights Reserved Page | 56 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 6.1764 6.714 7.7138 7.5707 5.7162 7.1124 7.4536 7.8505 7.0363 7.7468 15.2486 19.4475 20.4922 14.2927 4.6187 4.4623 14.3432 11.1056 15.1677 27.1465 36.3325 35.2762 35.0489 36.6137 41.5196 41.6692 36.5893 37.7094 36.3556 33.8277 shoeflower shoeflower2 statue stone tire tom tree woman1 wood zebra 6.8973 7.0519 6.9019 7.4571 6.8999 7.5237 7.1453 7.3372 7.2397 7.4992 3.8672 15.8519 31.9973 21.3973 13.6359 10.1966 16.4218 9.2385 59.8517 39.1392 42.2908 36.164 33.1137 34.8612 36.818 38.0803 36.0106 38.5088 30.394 32.2397 The Image Entropies returned for both the methods were plotted in line with the image entropies of the original images as shown in figure 17. The plots comparatively show that the proposed filter provides images with high entropies and the median filter has reduced the entropies of the images compared to the entropies generated from the original images and the images generated with the proposed method. The proposed method always seems to generate entropies which are close to the entropies of the original images. 8.5 8 7.5 7 6.5 6 Proposed 5.5 5 Median 4.5 4 Original 3.5 3 1 4 7 1013161922252831343740434649525558 Figure 17: Entropies of the original image compared to proposed method and the median filter. Mean Square Errors (MSE) of the filtered images are plotted as depicted in figure 18. The Proposed method always returns less mean square errors concluding the fact that the resulting image of the proposed method is more close to the original image. 80 60 40 Proposed 20 Median 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 Figure 18: MSE of the images filtered with the proposed and median filters The proposed method has produced high Noise Signal to Peak Ratios (NSPR) compare to the median filter concluding that the proposed method reconstructs images with high quality compared to the median filter as depicted in figure 19. 50 45 40 Proposed 35 30 Median 25 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 Figure 19: Peak signal to noise ration of the filtered images with the two methods. © 2014, IJARCSSE All Rights Reserved Page | 57 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 Table 3 shows the time taken by the proposed method to reconstruct a noisy image. When the image resolution is increased, the time elapsed also gets increased. It has taken 1775.6620 seconds to process the mandi.tif image which is of size 3039*2014, proving that the proposed method takes extensive amount of time to process large images. Table 3: Processing time of the proposed method for the sixty different images. barbar bridge building Image Actor albert albert2 angel body Boxing bridge a 2 s Image 600*73 600*55 500*28 300*42 512*51 600*51 400*22 251*20 600*45 Resolutio 284*177 8 1 1 4 2 4 5 1 0 n Processin 105.025 84.9706 32.696 33.9959 61.7289 71.1977 20.82 11.6122 61.848 11.4842 g Time/s 8 cameraman Car car2 cat catsweet cell charlie child children circuit 256*256 700*656 300*168 600*338 400*300 191*159 512*619 170*204 550*397 272*280 15.4667 132.0457 11.0204 45.5437 26.5799 7.1954 70.67 8.3936 50.0114 16.8154 city Coins dog elan fields flower forest galaxy girl girlbooks 600*375 300*246 192*192 512*512 400*320 500*375 284*177 800*701 400*250 540*432 53.2929 17.3241 8.2887 58.042 33.9233 41.177 11.6172 131.5986 22.9236 52.5624 jeniffer Lady lake leaf lena liftingbody lion mandi mountain nature 500*375 500*597 284*177 500*409 512*512 512*512 300*168 3039*2014 600*405 500*375 45.0573 65.8396 11.7847 47.6539 60.0268 61.597 11.5189 1775.662 55.5101 43.8669 night paddy parrot pianocat pout pumpkin puppy rose sand scenery 500*400 267*184 150*200 600*300 240*291 600*399 332*300 300*224 512*512 284*177 46.4781 11.7676 7.0812 40.3206 16.3682 56.0717 22.4325 15.4504 73.4808 11.3686 shoeflower shoeflower2 statue stone tire tom tree woman1 wood zebra 600*450 259*194 284*177 600*399 232*205 300*200 600*402 500*373 275*173 218*231 60.8648 11.8402 11.2346 54.5205 11.467 13.8316 580098 44.3155 13.05259 12.14757 The proposed method was tested only against 8-bit gray scale images. The method was extended forremoving noise of colored images as depicted in figure 20 and figure 21. The method was extended for the coloured images in such a way that it can be applied for the RGB component images of the original image separately. Results were then concatenated to produce the final results. Since, the RGB component images were processed separately; it takes approximately three times the processing time of processing the corresponding 8-bit gray scale image of the RGB image with the same resolution. The median filter was applied in the same manner in order for the comparison. As justified above for the gray scale images, the proposed method has shown better results compared to the median filter. Figure 20: Results returned from the proposed method filter and the median filter for a coloured image © 2014, IJARCSSE All Rights Reserved Page | 58 Chmikara et al., International Journal of Advanced Research in Computer Science and Software Engineering 4(10), October - 2014, pp. 49-60 In coloured images also, the median filter tends to produce blurry images as shown in both figure 20 and figure 21. Figure 21: Results returned from the proposed method filter and the median filter for a coloured image The proposed method seems to work in a less acceptable manner for high contrast images. Figure 22 shows an example which elaborates this issue. The fuzzy method can further be modified to overcome this issue. Figure 21: Results returned from the proposed method filter and the median filter for a coloured image The efficiency of the proposed algorithm could be increased using a computer with a higher performance, compared to the machine which was used in the testing phase. But the algorithm is still open for modification in order to reduce the time taken for the image reconstruction procedure.However, the results prove that the FIS produces acceptable pixel values to the noise pixels. IV. CONCLUSION A novel fuzzy logic based statistical method is introduced in image noise filtering. The proposed method generates very good results with respect to image quality. The quality of the images which are reconstructed by the proposed method is higher than the images reconstructed with the median filter method. Also, the new algorithm does not destroy sensitive information of the image by paying attention only to the noise pixels. Though the new approach takes more time to process images, it preserves the quality of the image. The test results conclude that the proposed method is a good method in the enhancement of noisy images. REFERENCES [1] J.Ying, D. Yubo. Research and Implementation of Image Enhancement Based on Fuzzy Sets. 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