Trimmed Median Filters for Salt and Pepper Noise Removal

Transcription

1 Trimmed Median Filters for Salt and Pepper Noise Removal S. Athi Narayanan, G. Arumugam, Prof. Kamal Bijlani Amrita E-Learning Research Lab, Amrita University, Kollam, Kerala, India Abstract: With this paper we propose an iterative trimmed median filter and an adaptive window trimmed median filter for effective suppression of salt and pepper noise. The iterative trimmed median filter works in a way that, when a selected neighborhood window of a noise pixel is completely noisy, such pixels will be left unchanged in the current iteration and will be processed in the next iteration. The adaptive window trimmed median filter works in a way, when a selected neighborhood window of a noise pixel is completely noisy, the size of the neighborhood window is adaptively increased till an image pixel is found in the neighborhood. The visual quality of the denoised image using the proposed methods outperforms the Trimmed Median Filter (TMF) in terms of Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) values. At high noise densities, the proposed iterative filter outperforms the proposed adaptive window filter. Keywords: Adaptive Window Filter, Impulse noise, Median Filter, Trimmed Median Filter colors (or false intensities in the case of grayscale images) in the denoised image, which is not desirable. Thus, trimmed median filter fails when all the pixels in the selected neighborhood window are noisy (TMF failing scenario), Figure.1 shows the trimmed median filtering [1] output of an 80% corrupted lena image. In Figure.1, we could easily notice the false colors introduced by TMF. We overcome this drawback by i) unchanging such center pixels in the current iteration and processing them in the next iteration ii) adaptively increasing the selected window size at TMF failure locations to obtain an image pixel within the selected window. In this work, we extensively compare the performance of TMF with our proposed methods. 1. INTRODUCTION Impulse noise is a special type of noise which can have many different causes. Thus, in the case of satellite or TV images it can be caused through atmospheric disturbances. In other applications it can be caused by strong electromagnetic fields, transmission errors, etc. Impulse noise is characterized by short, abrupt alterations of the color values in the image. There are two major impulse noise models used in contemporary literature: 1) salt-and-pepper noise model, where noise pixels can have only two values the highest and the lowest value within the dynamic range, and 2) uniform impulse noise model where noisy pixels can have any value from the dynamic range with equal probability. In this work, we proposed two trimmed median filters for restoring images corrupted by salt-and-pepper noise. 2. LITERATURE SURVEY To remove impulse noise, many filters based on median filters have been proposed in the literature. Very recently it has been proved that trimmed median filtering (TMF) [1] outperforms many of the variants of median filters [2-8] available in the literature. TMF has the drawback that, when a 3 X 3 window is completely corrupted by saltand-pepper noise, TMF replaces the center pixel with the mean of the pixels in the window. It introduces false Figure 1 TMF output of 80% corrupted lena image 3. TRIMMED MEDIAN FILTER (TMF) Trimmed Median Filter (TMF) [1] is a decision based unsymmetric filter. TMF is a two stage filter. First it detects the noisy pixels and then restores them. TMF considers all saturated pixels (0 or 255) as noisy pixels. If a pixel value lies within the dynamic range then it is considered a noise free pixel. Noise free pixels are left unchanged in the restoration stage. For each noisy pixel, the neighboring pixels within the 3X3 window are analyzed in the restoration stage. If all the pixels of the selected 3X3 window are deemed to be noisy, then the center pixel is replaced by the mean of the 3X3 window in the restored image. If the selected 3X3 window contains both the noisy pixels and noise free pixels, then the center pixel is replaced by the median of the noise free pixels in the 3X3 window. 4. ITERATIVE TRIMMED MEDIAN FILTER (ITMF) In [1], the TMF failure scenario is handled by replacing the center pixel with the mean value of all the pixels within the selected window. This will introduce false Volume 2, Issue 1 January - February 2013 Page 35

2 colors (or intensities in case of grayscale images) to the center pixel due to the contribution of salt & peppers within the selected window. In order to overcome this drawback, a Iterative Trimmed Median Filter (ITMF) is proposed. This ITMF considers all pixels with values 0 or 255 as noisy pixels and other pixels as image pixels. The ITMF leaves the image pixels unchanged. This method restores a noisy pixel by the median of the image pixels within the selected neighborhood of the noisy pixel. When all pixels in the selected neighborhood of a noisy center pixel are deemed noisy, then the center pixel is left unchanged in the current iteration and the noise pixel count is incremented by 1. At the end of the current iteration, the total unprocessed noise pixel count is available and a new iteration is started if this count is non zero. For the next iteration, the denoised image of the current iteration becomes the input and the unprocessed noise pixel count will be reset to zero. Thus the proposed trimmed median filter iterates until the unprocessed noise pixel count is zero at the end of a iteration. The flow diagrams of the proposed iterative trimmed median filter and the iteration control logic are shown in Figure.2 and Figure.3. In Figure.2, I represents the input (noisy image), D represents the output (denoised image), and Cnt represents the total unprocessed noise pixel count. filter is shown in Figure.4. In Figure.4, I represents the input (noisy image) and D represents the output (denoised image). Figure 2 Flow diagram of the proposed ITMF method Considering pixels with values 0 or 255 as noise pixels and replacing them with the trimmed median of its neighbor window performs well for natural images. It is based on the assumption that normally only a small portion of noise-free image pixels have these two extreme values. Even if that is the case, they will be most likely replaced by close approximations of their original values, e.g., 0 with 1 or 2, and 255 with 254 or 253 (in 8-bit images). By design, the ITMF will detect and replace all noisy pixels in an input image over time. Assuming all the intensity values are equally probable in an image, the probability that an image pixel is being considered as a noisy pixel (false detection probability) by the ITMF is very low. For a 50% salt-and-pepper noise corrupted image, the false detection probability is ADAPTIVE WINDOW TRIMMED MEDIAN FILTER (AWTMF) The Adaptive Window Trimmed Median Filter (AWTMF) handles the TMF failure scenario by adaptively increasing the selected window size to obtain an image pixel within the selected window. There is no iteration process within the AWTMF. When using the AWTMF, if the selected 3 X 3 window of a pixel is fully noisy, then a 5 X 5 window is selected and trimmed median filtering is applied. If the selected 5 X 5 window is also fully noisy, then a 7 X 7 window is selected and trimmed median filtering is applied and so forth. The flow diagram of the proposed adaptive trimmed median Figure 3 Flow diagram of the proposed Iteration Control Logic Figure 4 Flow diagram of the proposed AWTMF method Volume 2, Issue 1 January - February 2013 Page 36

3 6. EXPERIMENTAL RESULTS We have compared the performance of ITMF and AWTMF with TMF. Our test data set consists of ten standard test images [10]. The color images and their corresponding grayscale images (all size 256 X 256) were used in our experiments. Figure.5 shows our test data set. For each image in the test data set, the noise percentage is varied from 10% to 95% and the denoising performances are quantitatively compared using the PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index Measure) [9] values. The PSNR and SSIM values are calculated by the equations (1), (2) and (3). Figure 5 Input test data set images. Peak signal-to-noise ratio (PSNR) is the ratio between the maximum possible power of a signal and the power of a corrupting noise that affects the fidelity of its representation. Because many signals have a very wide dynamic range, PSNR is usually expressed in terms of the logarithmic decibel (db) scale. For an MXN image the mean squared error (MSE) between the uncorrupted original image O and the denoised image D is defined as: - (1) The PSNR is defined as: - (2), are two variables to stabilize the division with weak denominator. L the dynamic range of the pixel-values (typically this is. and by default SSIM index is a decimal value between -1 and 1, and value 1 is only reachable in the case of two identical images. In our experiments, unless otherwise mentioned, the ITMF uses 3 X 3 windowing. The PSNR and SSIM values of the proposed algorithms are compared against the TMF at different noise densities and are shown in Table.1 and Table.2. From Table.1 and Table.2, it is observed that the performance of the proposed algorithms outperforms the TMF at low and high noise densities. At low and medium noise densities, the results of the ITMF and the AWTMF are comparable. At high noise densities, the ITMF outperforms the AWTMF. A plot of PSNR and SSIM values against different noise densities for the lena image and the house image for different algorithms are shown in Figure.6 and Figure.7. Figure.8 and Figure.9 shows the results of TMF, ITMF and AWTMF applied to the lena image and the house image. From Figure.8 and Figure.9 it can be observed that the visual quality of the TMF and AWTMF denoised image is better than the TMF denoised image. Figure.10 shows the noise pixel locations and ITMF output for each iteration of a corrupted grayscale lena image. Table 1: Comparison of SSIM values of different algorithms for the lena image at different noise densities is the maximum possible pixel value of the image. The Mean Square Error (MSE) is not well-correlated with the human visual system. So, we have also used the Structural Similarity Index Measure (SSIM) as the performance measure for evaluating the proposed algorithms. We have used the SSIM [9] with default parameter settings. The SSIM is a method for measuring the similarity between two images. SSIM is calculated over local windows within the image. The SSIM metric is calculated on various windows of an image. The measure between two windows x and y of common size N N is: with the average of x the average of y the variance of x the variance of y the covariance of x and y - (3) Table 2: Comparison of PSNR values of different algorithms for the lena image at different noise densities Volume 2, Issue 1 January - February 2013 Page 37

4 noisy image and processed results of various algorithms for image corrupted by 80% and 95% noise densities, respectively. (a) (b) (c) (d) Figure 6 Comparison graphs of PSNR and SSIM at different noise densities for the lena image. Figure 9 Results of different algorithms for the house image. (a) Noisy image. (b) Output of TMF. (c) Output of ITMF. (d) Output of AWTMF. Row1 and Row2 show the noisy image and processed results of various algorithms for image corrupted by 80% and 95% noise densities, respectively. (a) (b) (c) Figure 10 Noise pixel and denoised image after each, iteration for 80% corrupted grayscale lena image in ITMF output. Row1 shows the Noise pixel locations a) Iteration 1, noise pixel count b) Iteration 2, noise pixel count 248. c) Iteration 3, noise pixel count 0. Row 2 shows the restored images a) Iteration 1 b) Iteration 2. c) Iteration 3. Figure 7 Comparison graphs of PSNR and SSIM at different noise densities for the house image. (a) (b) (c) (d) Figure 8 Results of different algorithms for the lena image. (a) Noisy image. (b) Output of TMF. (c) Output of ITMF. (d) Output of AWTMF. Row1 and Row2 show the We have also experimented with the ITMF by varying the window sizes. The PSNR and SSIM values of the proposed ITMF at different window sizes for grayscale lena image and grayscale house image are shown in Table.3 and Table.4. In Table.3 and Table.4, the iteration column represents the number of iterations involved in denoising through ITMF. Figure.11 shows the results of ITMF for the lena image at different window sizes. From Table.3, Table.4 and Figure.11 we observed that for a noise density of 95%, the results of ITMF using a 5X5 window outperforms the usage of 3X3 and 7X7 windows. At low and medium noise densities, the results of ITMF using a 3X3 window outperforms the usage of 5X5 and 7X7 windows Volume 2, Issue 1 January - February 2013 Page 38

5 Table 3 Comparison of noise measures of ITMF results at different window sizes for the grayscale lena image Table 4 Comparison of noise measures of ITMF results at different window sizes for the grayscale house image Figure 11 Results of ITMF for lena image at different window sizes. (a) Noisy Image. (b) 3X3. (c) 5X5. (d) 7X7. Row1 and Row2 show the noisy image and processed results for image corrupted by 80% and 95% noise densities, respectively. 7. CONCLUSION In this paper, two new algorithms (ITMF & AWTMF) are proposed to handle the failure scenario of TMF. ITMF & AWTMF produce visually better quality denoised images compared to the TMF in terms of SSIM values. The performance of the algorithms has been tested at low, medium and high noise densities on both grayscale and color images. At high noise densities, ITMF outperforms AWTMF. The proposed algorithms effectively restored the images corrupted by high density salt and pepper noise. REFERENCES [1] S. Esakkirajan, T. Veerakumar, Adabala N. Subramanyam, and C. H. PremChand, "Removal of High Density Salt and Pepper Noise Through Modified Decision Based Unsymmetric Trimmed Median Filter", IEEE Signal Process. Lett., vol. 18, no. 5, pp , May [2] J. Astola and P. Kuosmaneen, Fundamentals of Nonlinear Digital Filtering. Boca Raton, FL: CRC, [3] H. Hwang and R. A. Hadded, Adaptive median filter: New algorithms and results, IEEE Trans. Image Process., vol. 4, no. 4, pp , Apr [4] S. Zhang and M. A. Karim, A new impulse detector for switching median filters, IEEE Signal Process. Lett., vol. 9, no. 11, pp , Nov [5] P. E. Ng and K. K. Ma, A switching median filter with boundary discriminative noise detection for extremely corrupted images, IEEE Trans. Image Process., vol. 15, no. 6, pp , Jun Volume 2, Issue 1 January - February 2013 Page 39

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