CHAPTER 2 ADAPTIVE DECISION BASED MEDIAN FILTER AND ITS VARIATION

21 CHAPTER 2 ADAPTIVE DECISION BASED MEDIAN FILTER AND ITS VARIATION The main challenge in salt and pepper noise removal is to remove the noise as well as to preserve the image details. The removal of salt and pepper noise is done by two stages: detection and reduction. Standard median filter is used as a backbone for removal of salt and pepper noise. The detection of salt and pepper noise is very simple; the noisy pixel takes the value either 0 or 255. In this thesis, a new approach is proposed to remove the salt and pepper noise. The reduction of salt and pepper noise is based on the decision based median filter. 2.1 DECISION BASED ALGORITHM The decision based algorithm was proposed by Srinivasan and Ebenezer to remove the high density salt and pepper noise in an image. The decision based algorithm processes the corrupted image by first checking the impulse noise. The detection of noisy pixel and noise free pixels decided by checking whether the value of processing pixel is 0 or 255 in a gray scale image. If the value of the pixel processed is within the 0 and 255, then it is an uncorrupted pixel left unchanged. If the value is 0 or 255, then it is a noisy pixel and is replaced by the median value of the window or by its neighborhood values. If the noise density is high, there is a possibility that the median value is also a noisy value. The decision based algorithm is as follows:

22 Step 1) A window of size 3 x 3 is selected. The pixel to be processed is P ij. Step 2) The pixel values inside the window are sorted, and W min, W max, and W med, are determined as follows: (i) The rows of the window are arranged in ascending order. (ii) The columns of the window are arranged in ascending order. (iii) The right diagonal of the window is now arranged in ascending order. Now the first element of the window is the minimum value W min, the last element of the window is the maximum value W max and the middle element of the the window is the median value W med. Step 3) Case 1) The P ij is an uncorrupted pixel if W min < P ij < W max, W min > 0, and W max < 255; the pixel being processed is left unchanged. Otherwise, P ij is a corrupted pixel. Case 2) If P ij is a corrupted pixel, it is replaced by its median value if W min < W med < W max. Case 3) If W min < W med < W max is not satisfied, then W med is a noisy value. In this case, the P ij is replaced by the value of neighborhood pixel value. Step 4) Steps 1 to 3 are repeated until all the pixels in the image are covered. This algorithm performs well up to 95% of noise density but the noise density above 95% it fails. Because of all the pixels in the selected window is 0 or 255 at very high noise density.

23 2.2 DRAWBACK OF DECISION BASED ALGORITHM In the Decision based algorithm (Srinivasan and Ebenezer 2007) is used to denoise the image with 3 x 3 window. If the Processing pixel value is 0 or 255 it is processed or else it is left unchanged. At high noise density the median value will be 0 or 255 which is noisy. In such case, neighboring pixel is used for replacement. This repeated replacement of neighboring pixel produces streaking effect (Jayaraj and Ebenezer 2010). This drawback motivates us to develop a new approach, which is our proposed algorithm, Adaptive Decision Based Median Filter. 2.3 ADAPTIVE DECISION BASED MEDIAN FILTER The adaptive Decision based Median filter algorithm for the restoration of gray scale and colour images that are highly corrupted by salt and pepper noise is proposed in this thesis. The proposed algorithm replaces the noisy pixel by trimmed median value when other pixel values, 0 s and 255 s are present in the selected window and when all the pixel values are 0 s and 255 s then the noisy pixel is replaced by mean value of all the elements present in the selected window. 2.3.1 ADBMF Algorithm The steps of the ADBMF are as follows: Step 1: Select a window of size 3 x 3. Assume that the pixel being processed is P ij. Step 2: If 0 < P ij < 255 then P ij is an uncorrupted pixel and its value is left unchanged.

24 Noisy Image YES 0 < P ij <255 NO Select 3 x 3 window If all the pixels are 0 or 255 or both NO Remove all 0 s and 255 s in a selected window Median filter YES Find Mean value of 3 x 3 window Denoised Image Figure 2.1 Flowchart of the Proposed algorithm Step 3: If P ij = 0 or P ij = 255 then P ij is a corrupted pixel then two cases are possible as given in Case (i) and (ii). Case (i) : All the elements in the selected window are either 0 or 255; then replace P ij with the mean value of the elements of the selected window. Case (ii): If the selected window contains not all the elements as 0 s and 255 s. Then eliminate 0 s and 255 s and find the median value of the remaining elements. Replace P ij with the median value.

25 Step 4: Repeat steps 1 to 3 until all the pixels in the entire image are processed. The flow chart of the proposed algorithm is shown in Figure 2.1. 2.3.2 Illustration of ADBMF Algorithm Each and every pixel of the image is checked for the presence of salt and pepper noise. Case (i) illustrates the processing of uncorrupted pixel. Case (ii) illustrates the processing of corrupted pixel and case (iii) illustrates the processing of highly corrupted pixel. Case (i): If the selected window contains a noise free pixel as the processing pixel, it does not require further processing. For example, if the processing pixel is 151 then it is noise free pixel: 150 152 156 155 (151) 157 152 155 154 where (151) is a processing pixel. Since 151 is a noise free pixel it does not require further processing. Case (ii): If the selected window contains salt or pepper noise as the processing pixel and only some elements in the window are noisy: 150 152 156 0 (255) 255 255 155 154 where (255) is processing pixel.

26 That is, elimination of 0 s and 255 s. The 1-D array of the above matrix is [150 0 255 152 255 155 156 255 154]. After elimination of 0 s and 255 s the remaining pixel values in the selected window will be [150 152 155 156 154]. Here the median value is 154. Hence replace the processing pixel P ij by 154. Case (iii): If the selected window contains salt/pepper noise as processing pixel (i.e., 255/0 pixel value) and all neighboring pixels are noisy: 255 0 255 0 (0) 255 255 255 0 where (0) is pixel P ij. Since all the elements surrounding (P ij ) are 0 s and 255 s, the median value of the selected window will also be 0 or 255 which is again noisy. To solve this problem, the mean of the selected window is found and the pixel P ij is replaced by this mean value. Here the mean value is 142, and the pixel P ij is replaced by 142. 2.4 SIMULATION RESULTS AND DISCUSSION The proposed ADBMF algorithm is applied for test images like Lena, Boat, Bridge and Barbara (colour) images. All the images are with the size of 512 x 512 x 8 bit gray and colour. The simulation is carried out in MATLAB 7.0.1 environment with Pentium Duo core 2.80 GHz processor with 1 GB RAM. The salt and pepper noise is added to the original image using the MATLAB command imnoise. The noise density of the salt and pepper noise is varied from 10 to 97%. In this work, the performance of the

27 ADBMF is compared against the performance of the existing algorithms like SMF, AMF, PSMF, DBA, and MDBA for different noise densities. 2.4.1 Lena Image The performance of the proposed algorithm is tested using Lena image which does not contain large amounts of high frequency or oscillating patterns. The performance of the proposed algorithm is compared against existing denoising algorithms for the noise densities from 10 to 90%. Table 2.1 PSNR comparison for Lena image Noise Density in % PSNR in db SMF PSMF AMF DBA MDBA ADBMF (Proposed) 10 31.5103 36.3797 25.1800 40.2130 40.2438 41.4942 20 28.3274 31.9396 25.1529 36.3012 36.3069 37.8086 30 23.3061 27.9749 25.0050 33.8097 33.8134 35.5357 40 18.8983 24.5887 24.4354 31.4999 31.5337 33.2160 50 15.2538 20.3783 22.6663 29.6288 29.7376 31.6803 60 12.3081 12.2215 19.3930 27.6333 27.6942 29.5470 70 10.0260 9.9653 15.2828 25.3394 25.4633 27.2607 80 8.1611 8.1236 11.5756 22.8589 22.9872 24.2479 90 6.6248 6.6092 8.2278 19.6312 19.8991 20.3747 Table 2.1 shows the performance of the ADBMF algorithm for different noise density. From this table, it can be observed that the proposed ADBMF algorithm gives 1 db PSNR better than the existing algorithms for 10 to 50% noise density. But the noise density from 60 to 80% the ADBMF algorithm gives almost 2 db better than the existing algorithms.

28 The proposed ADBMF algorithm is also tested with the Image Enhancement Factor (IEF), which gives the smoothness of the denoised image. The IEF value of the ADBMF and existing algorithms for Lena image is given in Table 2.2. From the Table 2.2, it is evident that the IEF value of the ADBMF algorithm gives better performance than the existing algorithms. From the table, it is evident that the IEF value of the proposed algorithm is higher than the existing algorithms. Table 2.2 IEF comparison for Lena image Noise IEF Density in % SMF PSMF AMF DBA MDBA ADBMF (Proposed) 10 40.4264 124.0502 9.4047 299.8705 301.9992 402.7603 20 39.0382 89.6832 18.7757 244.8320 245.1567 346.4227 30 18.3712 53.8291 27.1476 206.3024 206.4781 306.9720 40 8.8723 32.8909 31.7728 161.5099 162.7716 239.7761 50 4.7844 15.5695 26.3643 131.0163 134.3404 210.1279 60 2.9157 2.8581 14.8885 99.3729 100.7745 154.3955 70 2.0082 1.9803 6.7323 68.2579 70.2322 106.2373 80 1.4937 1.4808 3.2805 44.0595 45.3798 60.6641 90 1.1814 1.1772 1.7084 23.6068 25.1091 28.0145 The correlation factor is a quantitative measure, which provides the correlation between original image and denoised image. The correlation factor (CF) for the ADBMF algorithm and existing algorithms for Lena image is shown in Table 2.3. The highest value of correlation factor is one if both images are perfectly matched. The lowest value of correlation factor is zero, which indicates the un-correlation between the original image and denoised image (i.e., two images are fully mismatched).

29 Table 2.3 Correlation factor for Lena image Noise Density in % Correlation Factor SMF PSMF AMF DBA MDBA ADBMF (Proposed) 10 0.9900 0.9968 0.9569 0.9987 0.9987 0.9990 20 0.9793 0.9911 0.9567 0.9967 0.9967 0.9977 30 0.9367 0.9785 0.9552 0.9941 0.9941 0.9960 40 0.8431 0.9555 0.9492 0.9900 0.9900 0.9932 50 0.6960 0.8966 0.9252 0.9846 0.9849 0.9904 60 0.5244 0.5485 0.8529 0.9755 0.9759 0.9842 70 0.3643 0.3911 0.6883 0.9586 0.9597 0.9732 80 0.2242 0.2463 0.4658 0.9268 0.9289 0.9458 90 0.0934 0.1051 0.2172 0.8459 0.8543 0.8636 (a) Original image (b) Noisy image (80%) Figure 2.2 Original and Noisy Lena image

30 (a) SMF (b) PSMF (c) AMF (e) MDBA (d) DBA (f) ADBMF Figure 2.3 Denoised Lena images

31 The original and noisy Lena image is given in Figure 2.2. The denoised images using different state-of-art denoising algorithms are illustrated in Figure 2.3. The noise density of the salt and pepper noise affected image is 80%. From the Figure 2.3, it is clear that the visual quality of the ADBMF algorithm gives better results than the visual quality of the existing algorithms. 2.4.2 Boat Image The performance of the ADBMF algorithm and existing algorithm for different noise densities of salt and pepper noise of Boat image is shown in Figure 2.4. From the figure, it obvious that the PSNR value of the proposed ADBMF algorithm always outperforms the existing algorithms. The noise densities of salt and pepper noise from 10% to 50%, the proposed ADBMF algorithm gives almost 2 db better than the existing algorithms. From 60% to 90%, the ADBMF algorithm gives nearly 1 db better than the existing denoising algorithms. 45 40 35 30 SMF PSMF AMF DBA MDBA ADBMF 25 20 15 10 5 10 20 30 40 50 60 70 80 90 Noise Density in % Figure 2.4 PSNR plot for Boat image

32 Table 2.4 IEF values for Boat image Noise IEF Density ADBMF SMF PSMF AMF DBA MDBA in % (Proposed) 10 32.6570 60.0404 6.9213 207.3494 207.3698 307.7004 20 30.8158 56.7868 13.4596 171.4425 171.2771 262.1466 30 17.2417 44.4345 19.6156 145.0813 144.3409 216.4522 40 8.2137 29.0537 24.0496 114.9888 115.4746 172.8577 50 4.6078 15.7070 21.3761 89.3168 89.5137 135.3251 60 2.8855 7.4026 13.2032 69.8565 70.7526 100.1068 70 2.0196 2.0102 6.4657 48.8729 50.1976 67.3484 80 1.4899 1.4847 3.2086 32.7959 33.2040 41.4280 90 1.1890 1.1870 1.7048 18.8907 19.0199 20.2112 The IEF value of the proposed ADBMF algorithm and other existing algorithms for boat image is given in Table 2.4. From this table, it is evident that the proposed algorithm claims far better IEF value than the existing algorithms at noise densities from 10 to 60%. The correlation factor results obtained for different denoising algorithms for different noise densities of Boat image as shown in Figure 2.5. From this figure, it is obvious that the ADBMF algorithm performs well for Boat image than other denoising algorithms.

33 1 0.8 0.6 0.4 0.2 SMF PSMF AMF DBA MDBA ADBMF 0 10 20 30 40 50 60 70 80 90 Noise Density in % Figure 2.5 Correlation factor for Boat image (a) Original image (b) Noisy image (90%) Figure 2.6 Original and Noisy Boat image

34 (a) SMF (b) PSMF (c) AMF (d) DBA (e) MDBA (f) ADBMF Figure 2.7 Denoised Boat images

35 The original and noisy Boat image is shown in Figure 2.6. The denoised Boat images using different denoising alogirthms is illustrated in Figure 2.7. From this figure, it is clear that the visual quality of the proposed ADBMF alogorithm is far better than the existing algorithms. 2.4.3 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%. Table 2.5 PSNR comparison for Bridge image Noise Density in % PSNR in db SMF PSMF AMF DBA MDBA ADBMF (Proposed) 10 26.9554 29.5534 21.3538 34.0164 33.9993 35.9466 20 24.9388 27.5035 21.2769 31.0863 31.0797 32.6234 30 21.5672 25.2521 21.1226 28.8205 28.8188 30.1839 40 18.0220 22.7321 20.8214 26.9719 26.9653 28.2664 50 14.6657 19.4582 19.8534 25.1620 25.2018 26.4665 60 11.9772 15.7890 17.6543 23.4344 23.4650 24.5909 70 9.7442 9.7122 14.4672 21.6547 21.7322 22.7892 80 7.9092 7.8833 11.1058 19.5827 19.6497 20.5332 90 6.4303 6.4162 7.9614 17.0129 17.1527 17.7092 The PSNR value of the proposed ADBMF algorithm and existing denoising algorithms is tabulated in Table 2.5. From this table, it shows that the proposed ADBMF algorithm gives better PSNR than the existing algorithms. The proposed ADBMF algorithm claims more than 1 db PSNR greater than the other denoising algorithms.

36 The proposed ADBMF algorithm is tested with Bridge image and the corresponding IEF result is shown in Figure 2.8. From the figure, it is clear that the IEF value of the proposed ADBMF algorithm is far better than the existing algorithms from low to medium noise densities. At high noise densities the performance of the ADBMF algorithm is similar to that of the existing algorithms. 120 100 80 SMF PSMF AMF DBA MDBA ADBMF 60 40 20 0 10 20 30 40 50 60 70 80 90 Noise Density in % Figure 2.8 IEF curves for Bridge image The correlation factor is one of the quantitaive measure for denoising algorithms. The performance comparison of the proposed algorithm with the existing algorithms with respect to correlation factor is given in Table 2.6.

37 Table 2.6 Correlation factor for Bridge image Noise Density in % Correlation Factor SMF PSMF AMF DBA MDBA ADBMF (Proposed) 10 0.9774 0.9877 0.9175 0.9956 0.9956 0.9972 20 0.9641 0.9803 0.9161 0.9913 0.9913 0.9939 30 0.9239 0.9675 0.9131 0.9854 0.9854 0.9893 40 0.8406 0.9437 0.9072 0.9776 0.9775 0.9834 50 0.7021 0.8888 0.8858 0.9659 0.9662 0.9747 60 0.5446 0.7765 0.8212 0.9492 0.9495 0.9608 70 0.3828 0.4029 0.6803 0.9234 0.9246 0.9402 80 0.2354 0.2511 0.4702 0.8770 0.8782 0.8980 90 0.1076 0.1164 0.2308 0.7791 0.7837 0.7977 (a) Original image (b) Noisy image (70%) Figure 2.9 Original and Noisy Bridge image

38 (a) SMF (b) PSMF (c) AMF (d) DBA (e) MDBA (f) ADBMF Figure 2.10 Denoised images for Bridge image

39 The correlation factor varies with the noise density. If the noise density goes high, then the correlation factor of denoised image goes low. From the Table 2.6, it is clear that at low noise density the correlation factor is almost 1, which indicates the denoised image very close to the original image. At high noise density the correlation factor of ADBMF algorithms almost 0.8, which indicates the 80% of denoised image matched with the original image. The original, 70% of noisy Bridge image is shown in Figure 2.9. The denoised images for different denoising algorithms are shown in Figure 2.10. From this figures, it is illustrated that the denoised image of ADBMF algorithm is better than the other algorithms. Hence, the proposed ADBMF algorithm performs well for both low and high frequency images. 2.4.4 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 Figure 2.11. From the figure, it shows that the proposed algorithm perform well than the other denoising algorithms. Hence, the proposed algorithm can able to denoise colour images also. The IEF value of different denoising algorithms for Barbara (colour) image is illustrated in Figure 2.12. From the figure, it is clearly observed that the proposed ADBMF algorithm gives 2 to 3 IEF values better than the other denoising algorithms.

40 35 30 25 20 15 10 SMF PSMF AMF DBA MDBA ADBMF 5 10 20 30 40 50 60 70 80 90 Noise Density in % Figure 2.11 PSNR plot for Barbara (colour) image 70 60 50 40 30 20 SMF PSMF AMF DBA MDBA ADBMF 10 0 10 20 30 40 50 60 70 80 90 Noise Density in % Figure 2.12 IEF for Barbara (colour) image

41 The correlation factor for the ADBMF algorithm and existing algorithms for Barbara (colour) image is given in Table 2.7. From the Table 2.7, it is evident that the performance of the ADBMF algorithm gives better result than the performance of the existing algorithms. Table 2.7 Correlation factor for Barbara (colour) image Noise Density in % Correlation Factor SMF PSMF AMF DBA MDBA ADBMF 10 0.9542 0.9665 0.8835 0.9936 0.9936 0.9945 20 0.9399 0.9586 0.8805 0.9863 0.9863 0.9885 30 0.8964 0.9453 0.8789 0.9779 0.9779 0.9819 40 0.8065 0.9187 0.8753 0.9683 0.9683 0.9749 50 0.6690 0.8636 0.8573 0.9565 0.9568 0.9668 60 0.5063 0.6031 0.7923 0.9402 0.9409 0.9572 70 0.3538 0.3767 0.6507 0.9200 0.9216 0.9430 80 0.2196 0.2375 0.4465 0.8828 0.8861 0.9134 90 0.0987 0.1083 0.2196 0.8002 0.8066 0.8128 (a) Original image (b) Noisy image (75%) Figure 2.13 Original and Noisy Barbara (colour) image

42 (a) SMF (b) PSMF (c) AMF (d) DBA (e) MDBA (f) ADBMF Figure 2.14 Denoised images for Barbara (colour) image

43 The original and 75% of noisy Barbara (colour) image is given in Figure 2.13. The denoised images for different denoising algorithms are shown in Figure 2.14. From the figure, it is illustrated that the denoised image of ADBMF algorithm is better than the other algorithms. Hence, the proposed ADBMF algorithm performs well for colour image. 2.5 GLOBAL TRIMMED MEAN FILTER The ADBMF algorithm replaces the noisy pixel with mean value of the selected window, when all the pixels in the selected window are 0 and 255. If all the pixels in the selected window are 0 or 255, then the mean value of the selected window is also noisy (i.e., either 0 or 255). This drawback is overcome by global trimmed mean filter with ADBMF algorithm. In this method, the global trimmed mean value replaces the noisy pixel, when all surrounding pixels in the selected window are 0s or 255s. 2.5.1 Computation of Global Trimmed Mean Let f(x,y) represent a noisy image, the processing pixel is marked as yellow colour as shown in Figure 2.15. The processing pixel takes a value of 255 which is noisy. It is also possible to observe that all the elements within the processing window take a gray value of 255. The mean value of the selected window is 255. This reveals the fact that noise impact is not minimized. In such cases, it would be better to replace the processing pixel by trimmed global mean value of the noise free pixel in the image. The method to obtain trimmed global mean is summarized below:

44 (a) The image g(x,y) is obtained from f(x,y) by removing all the noisy pixel which is shown in Figure 2.15 (b). (a) Noisy Image (f(x,y) ) (b) Noise free Image ( g(x,y)) (c) Denoised pixel Figure 2.15 Computation of Trimmed Global Mean value

45 (b) The trimmed global mean (M) of the noise free image g(x,y) is calculated from the equation (2.1) 1 M gˆ( i) N i N (2.1) where N is the number of noise free pixel in an image and ĝ is the noise free element in an image. (c) Replace the noisy pixel by the trimmed global mean value. In this illustration, the trimmed global mean value is 100. Hence the noisy pixel value 255 is replaced by 100. Simulation Results and Discussions The PSNR value of the proposed algorithm (TMF) is compared against the existing methods by varying the noise densities from 10 to 90% and is shown in Table 2.8. From the table, it is evident that the performance of the proposed algorithm is better than the existing algorithms at high noise densities. Apparently, the performance of the proposed method is marginally better than the existing methods at high noise densities. The IEF value of the proposed algorithm is compared against the existing methods by varying the noise densities from 10 to 90% and the results are shown in Table 2.9. From the table, it is possible to conclude that the proposed algorithm outperforms the existing algorithms at high noise densities.

46 Table 2.8 PSNR values for Lena image Noise Density in % PSNR in db MF AMF DBA MDBA ADBMF TMF (Proposed) 10 31.5103 25.1800 40.2130 40.2438 41.4942 41.4942 20 28.3274 25.1529 36.3012 36.3069 37.8086 37.8086 30 23.3061 25.0050 33.8097 33.8134 35.5357 35.5357 40 18.8983 24.4354 31.4999 31.5337 33.2160 33.2160 50 15.2538 22.6663 29.6288 29.7376 31.6803 31.6803 60 12.3081 19.3930 27.6333 27.6942 29.5470 29.5470 70 10.0260 15.2828 25.3394 25.4633 27.2607 27.6607 80 8.1611 11.5756 22.8589 22.9872 24.2479 24.8479 90 6.6248 8.2278 19.6312 19.8991 20.3747 20.9851 Table 2.9 IEF values for Lena image Noise Density in % IEF MF AMF DBA MDBA ADBMF TMF (Proposed) 10 40.4264 9.4047 299.8705 301.9992 402.7603 402.7603 20 39.0382 18.7757 244.8320 245.1567 346.4227 346.4227 30 18.3712 27.1476 206.3024 206.4781 306.9720 306.9720 40 8.8723 31.7728 161.5099 162.7716 239.7761 239.7761 50 4.7844 26.3643 131.0163 134.3404 210.1279 210.1279 60 2.9157 14.8885 99.3729 100.7745 154.3955 154.3955 70 2.0082 6.7323 68.2579 70.2322 106.2373 108.5371 80 1.4937 3.2805 44.0595 45.3798 60.6641 64.6945 90 1.1814 1.7084 23.6068 25.1091 28.0145 32.4817

47 2.6 SUMMARY The summary of the chapter as follows: 1. The experimental results in this chapter reveal the fact that ADBMF algorithm gives better denoised image quality for different noise densities of salt and pepper noise. IEF values are higher (by 3 to 100) than the existing algorithms for Lena image. 2. The correlation factor of the proposed algorithm around 1 to 2 % higher than the existing algorithms for Barbara (colour) image at high noise density. 3. The performance of ADBMF is better than that of existing algorithms but in high noise densities trimmed mean filter much better PSNR than the ADBMF algorithm. 4. The major drawback of ADBMF algorithm is all the pixels in the selected window are 0s or 255s then the replacement pixel is also noisy. 5. The major drawback of TMF algorithm the single global trimmed mean value replaces the noisy pixel when the pixels are in selected window all or noisy (i.e., either 0 or 255 ). The calculation of global trimmed mean value is computational cost when compared to ADBMF algorithm. To overcome this difficulty, fuzzy logic is introduced in the next chapter.