CHAPTER 3 ADAPTIVE DECISION BASED MEDIAN FILTER WITH FUZZY LOGIC

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1 48 CHAPTER 3 ADAPTIVE DECISION BASED MEDIAN ILTER WITH UZZY LOGIC In the previous algorithm, the noisy pixel is replaced by trimmed mean value, when all the surrounding pixels of noisy pixel are noisy. In this method the single global trimmed mean value replaces the all the noisy pixels in the noisy image. Hence, the improvement of PSNR and IE are very less. To improve the PSNR and IE the combined uzzy logic and ADBM algorithm is introduced in this chapter. In this algorithm, the fuzzy logic is used to split different possibilities of noisy pixels in the selected window. 3.1 UZZY LOGIC uzzy logic was initiated in 1965 (Zadeh (1965, 1968, 1973, 1984), by Lotfi A. Zadeh. uzzy logic is a multivalued logic, which allows intermediate values to be defined between conventional evaluations like true or false, yes or no, high or low, etc. uzzy logic is well suited to implementing control rules that can only be expressed verbally, or systems that cannot be modeled with differential equations. Rules and membership sets are used to make a decision. The fuzzy systems convert these rules to their mathematical equivalents. This simplifies the work of the system designer and the computer, and results in much more accurate representations of the way systems behave in the real world. Additional benefits of fuzzy logic include its simplicity and its flexibility. It can handle problems with imprecise and incomplete data, and it can model non-linear functions of

2 49 arbitrary complexity. uzzy logic models, called fuzzy inference systems, consist of a number of conditional if then rules. or the designer who understands the system, these rules are easy to write and as many rules are necessary can be supplied to describe the system adequately. In fuzzy logic, unlike standard conditional logic, the truth of any statement is a matter of degree. or example, for the rule if (weather is cold) then (heater is on), both variables, cold and on, map to range of values. uzzy inference systems rely on membership functions to explain to the computer how to calculate the correct value between 0 and 1. The degree to which any fuzzy statement is true is denoted by a value between 0 and 1. Not only do the rule-based approach and flexible membership function scheme make fuzzy systems straightforward to create, but they also simplify the design of systems and ensure that it can easily update and maintain the system over time. 3.2 UZZY SETS AND UZZY RULES A uzzy set theory is a generalization of classical set theory that allows membership degree between zero and one, thus a more gradual transition between belonging to and not belonging to (Siler and Buckley 2005). A fuzzy set in the universe X is characterized by an X [0, 1] mapping, which assigns with every element x in X a degree of membership (x) 0, 1 in the fuzzy set. In our problem, the uzzy membership function is defined based on the number of zeros or 255s in the selected window. or the current pixel within the processing window, the function (x) is given in equation (3.1) (x) ={ 0, 255 } (3.1) 0 = Number of zeros in a selected window 255 = Number of 255s in a selected window

3 50 Let (x) 0, 1 is the membership function of (x). The fuzzy rule enacted for the proposed algorithm is summarized below: Rule 1: if 0 is Large Negative (LN) or 255 is Small Positive (SP) then (x) is Very Low (VL). Rule 2: if 0 is Negative (N) then (x) is Low (L). Rule 3: if 255 is Large Positive (LP) or 0 is Small Negative (SN) then (x) is Very High (VH). Rule 4: if 255 is Positive (P) then (x) is High (H). With these rules the fuzzy membership function is given in equation (3.2). std( X ) std( X ) ( x) mean( X ) if 255 Th1 (3.2) mean( X ) if if Th 0 if Th 2 Th Th Th 1 where, X is the selected neighboring pixel elements, std stands for standard deviation, mean represents average value of the selected window. Th and 1 Th2 are predefined thresholds such that if 0 is greater than Th 1, the pixel belong to lower gray level, if 0 is greater than Th 2 and less than Th1 then the pixel belong to medium gray level, if the 255 is greater than Th, the pixel 1 belong to very high gray level and if the 255 is greater than Th 2 and less than Th1 then the pixel belong to higher gray value. The membership function defined as per equation (3.2) is used to replace the noisy pixel. The graphical representation of the membership function is shown in igure 3.1.

4 51 Negative Positive Th 2 Th Th 2 Th Large Negative Large Positive Th Th igure 3.1 Membership functions The threshold value Th1 and Th 2 are selected based on the following fact: Case 1: The selected window size is 3 X 3, which implies that the number of elements within the window is 9. In the selected window, the number of 0s is more than number of 255s means that 0s should have occurred a minimum of 5 times. The same logic holds well if number of 255s is greater than number of 0s within the window. This enabled us to select the threshold value Th 2 as 4. Case 2: In the selected 3 X 3 window, most frequent occurrence of 255 or 0 means it should have occurred more than 5, this enabled us to fix the threshold Th 1 as 6.

5 52 Case 3: The extreme case is all the pixels within the selected window are either 0 or 255. In such case, the processing pixel is replaced by the average of the two extreme gray levels which is ALGORITHM OR ADAPTIVE DECISION BASED MEDIAN ILTER WITH UZZY LOGIC The proposed algorithm combines uzzy logic with Adaptive Decision Based Median ilter to process the image which is highly corrupted by impulse noise. The algorithm starts with the detection of impulse noise. That is, if the processing pixel lies within the maximum and minimum gray level values, then it is noise free pixel, it is left unchanged. If the processing pixels take the maximum or minimum gray level then it is noisy pixel which is processed by the proposed algorithm. The steps followed in the proposed algorithm are given below: Step 1: Select 2-D window of size 3 x 3. The processing pixel is denoted as P ij. Step 2: If 0 < P ij < 255 then P ij is a noise free pixel and its value is unaltered. Step 3: If P ij = 0 or P ij = 255 then P ij is a noisy pixel then apply the proposed algorithm to the processing pixel. Step 3a: In the selected window (3 x 3) if all the elements are not 0 s and 255 s, then replace P ij with the trimmed median value (Nair et al 2008).

6 53 Read Noisy Image YES 0 < P ij < 255 NO Select a 2D 3 x 3 window (X) with centre element as P ij as a processing pixel NO Selected window (X) contain all the elements as 0 s or 255 s or both YES Compute the 0 and 255 of the selected window (X) NO YES P ij is replaced by trimmed median value Pij NO std(x) Th 2 < 0 < Th 1 YES 0 < 255 YES Th 2 < 255 < Th 1 Pij NO Mean(X) P ij 0 std(x) 255 P ij Mean(X) Denoised Image igure 3.2 lowchart of the proposed algorithm

7 54 Step 3b: If the selected window contain all the elements as 0 s and 255 s, then four possible combinations defined based on impulse noise density using fuzzy rule which is discussed in section 3.2, are Very High, Very Low, Low and High. Here Very High refers to frequent occurrence of 255 and Very Low corresponds to frequent occurrence of gray level 0. Then replace the processing pixel by fuzzy membership function output value as given in the flow chart shown in igure 3.2. Step 4: Repeat steps 1 to 3 until all the pixels in the entire image are processed. 3.4 SIMULATION RESULTS AND DISCUSSION The proposed uzzy-adaptive Decision based Median ilter (ADBM) algorithm is applied for test images like Lena, Boat, Bridge and Barbara (colour) images. In this work, the performance of the ADBM is compared against the performance of existing algorithms like SM, AM, DBA, Modified Decision Based Algorithm (MDBA) (Nair et al 2008), ADBM (Veerakumar et al 2011) and TM (Veerakumar et al 2012) for different noise densities Lena Image The performance of the proposed algorithm is tested for Lena image. The performance of proposed algorithm is compared against existing denoising algorithms for noise densities varying from 10 to 90%. The performance measures used are PSNR, IE and C.

8 55 Table 3.1 PSNR values for Lena image Noise Density in % PSNR in db SM AM DBA MDBA ADBM TM ADBM (Proposed) Table 3.1 shows the PSNR values obtained for Lena image using ADBM algorithm for different noise density. rom the table, it can be observed that the proposed ADBM algorithm gives better PSNR than the existing algorithms for above 80% of noise density. All the neighborhood pixels of the processing pixels are noisy at above 80%, hence the ADBM algorithm is better than the existing algorithms for above 80% of noise density. The Image Enhancement actor (IE), which measures the smoothness of the denoised image, is calculated for Lena image obtained by the ADBM and existing algorithms and shown in Table 3.2. rom the table, it is observed that the IE value of the proposed algorithm is higher than the existing algorithms above 80% of noise densities.

9 56 Table 3.2 IE values for Lena image Noise IE Density ADBM SM AM DBA MDBA ADBM TM in % (Proposed) The correlation factor (C) for the ADBM algorithm and existing algorithms for Lena image is shown in Table 3.3. rom the Table 3.3, it is evident that the performance of the ADBM algorithm gives better result than the performance of the existing algorithms. Table 3.3 Correlation factor for Lena image Noise Density in % Correlation actor SM AM DBA MDBA ADBM TM ADBM (Proposed)

10 57 The original and noisy image of Lena is shown in igure 3.3. The denoised images using different state-of-art denoising algorithms are illustrated in igure 3.4. The noise density of the salt and pepper noise affected image is 85%. rom the igure 3.4, it is clear that the visual quality of the ADBM algorithm gives better results than the visual quality of the existing algorithms. (a) Original image (b) Noisy image (85%) igure 3.3 Original and Noisy Lena image (a) SM (b) AM igure 3.4 Denoised Lena images (Continued)

11 58 (c) DBA (d) ADBM (e) TM (f) ADBM igure 3.4 Denoised Lena images Boat Image The performance of the ADBM algorithm and existing algorithms for different noise densities of salt and pepper noise of Boat image is shown in igure 3.5. rom the figure, it obvious that the PSNR value of the proposed ADBM algorithm outperforms the existing algorithms at high noise densities.

12 SM AM DBA MDBA ADBM TM ADBM Noise Density in % igure 3.5 PSNR curves for Boat image SM AM DBA MDBA ADBM TM ADBM Noise Density in % igure 3.6 Correlation factor plot for Boat image

13 60 The IE value of the proposed ADBM algorithm and other existing algorithms for boat image is given in Table 3.4. rom this table, it is evident that the proposed algorithm claims far better IE value than the existing algorithms at high noise densities. Table 3.4 IE values for Boat image Noise Density in % IE SM AM DBA MDBA ADBM TM ADBM (Proposed) The correlation factor results obtained for different denoising algorithms for different noise densities of Boat image as shown in igure 3.6. rom this figure, it is obvious that the ADBM algorithm performs well for Boat image than the other denoising algorithms.

14 61 (a) Original image (b) Noisy image (87%) igure 3.7 Original and Noisy Boat image The original and noisy (87%) Boat image is given in igure 3.7. The denoised Boat images using different denoising alogirthms is illustrated in igure 3.8. rom this figure, it is clear that the visual quality of the proposed ADBM alogorithm is far better than the other algorithms. (a) SM (b) AM igure 3.8 Denoised Boat images (Continued)

15 62 (c) DBA (d) ADBM (e) TM (f) ADBM igure 3.8 Denoised Boat images Bridge Image The performance of the proposed algorithm is tested using Bridge image which contain large amounts of high frequency or oscillating patterns. The performance of proposed algorithm is compared against existing denoising algorithms for the noise densities from 10 to 90%. The PSNR value of the proposed ADBM algorithm and existing denoising algorithms is tabulated in Table 3.5. rom the table, it shows that the proposed ADBM

16 63 algorithm gives better PSNR than the existing algorithms. The proposed ADBM algorithm claims more than 0.5 db PSNR greater than the other denoising algorithms for Bridge image. Table 3.5 PSNR values for Bridge image Noise Density in % PSNR in db SM AM DBA MDBA ADBM TM ADBM (Proposed) The proposed ADBM algorithm tested with IE for Bridge image and the result is shown in igure 3.9. rom the figure, it shows that the IE value of the proposed ADBM algorithm is far better than the existing algorithms at high noise densities. The correlation factor for different denoisng algorithms of Bridge image is given in Table 3.6. At high noise density the correlation factor of ADBM algorithms almost 0.8, which indicates the 80% of denosied image matched with the original image.

17 SM AM DBA MDBA ADBM TM ADBM Noise Density in % igure 3.9 IE curves for Bridge image Table 3.6 Correlation factor for Bridge image Noise Correlation actor Density in % SM AM DBA MDBA ADBM TM ADBM (Proposed) The original and 90% of noisy image is shown in igure The denoised images for different denoising algorithms are shown in igure 3.11.

18 65 rom the figure, it is illustrated that the denoised image of ADBM algorithm is better than the other algorithms. (a) Original image (b) Noisy image (90%) igure 3.10 Original and Noisy Bridge image (a) SM (b) AM igure 3.11 Denoised images for Bridge image (Continued)

19 66 (c) DBA (d) ADBM (e) TM (f) ADBM igure 3.11 Denoised images for Bridge image Barbara (colour) Image The proposed algorithm is tested with Barbara (colour) image. The plot of PSNR values versus noise densities for the different denoising algorithm for Barbara (colour) image is shown in igure rom the figure, it shows that the proposed algorithm perform well than the other denoising algorithms.

20 67 The IE value of different denoising algorithms for Barbara (colour) image is illustrated in igure rom the figure, it is clearly observed that the proposed ADBM algorithm gives better IE values than the other denoising algorithms. The correlation factor (C) for the ADBM algorithm and existing algorithms for Barbara (colour) image is given in Table 3.7. rom the table, it is evident that the performance of the ADBM algorithm gives better result than the performance of the existing algorithms. Table 3.7 Correlation factor for Barbara (colour) image Noise Density in % Correlation actor SM AM DBA MDBA ADBM TM ADBM

21 SM AM DBA MDBA ADBM TM ADBM Noise Density in % igure 3.12 PSNR curves for Barbara (colour) image SM AM DBA MDBA ADBM TM ADBM Noise Density in % igure 3.13 IE plot for Barbara (colour) image

22 69 The original and 80% of noisy image is given in igure The denoised images for different denoising algorithms are shown in igure rom the figure, it is illustrated that the denoised image of ADBM algorithm is better than the other algorithms. Hence, the proposed ADBM algorithm performs well for colour image. (a) Original image (b) Noisy image (80%) igure 3.14 Original and Noisy Barbara (colour) image (a) SM (b) AM igure 3.15 Denoised images for Barbara (colour) image (Continued)

23 70 (c) DBA (d) ADBM (e) TM (f) ADBM igure 3.15 Denoised images for Barbara (colour) image 3.5 SUMMARY The summary of the chapter as follows: 1. The experimental results in this chapter shows that the ADBM algorithm gives better denoised image quality at high noise density of salt and pepper noise.

24 71 2. The ADBM algorithm effectively removes the salt and pepper noise with image details are better retained when compared to the existing algorithms. 3. The ADBM algorithm considers three classifications when all the pixels in the selected window are noisy. This classification gives much improved result in denoised image than the existing one. 4. At very high noise density, the ADBM algorithm fails to retain the fine details and smoothness of the original image. To overcome this difficulty, Spline interpolation method is introduced in the next chapter.