There are several steps to describe this algorithm which are:
1) By assuming that Cx,y is the current pixel, then select a two-dimensional
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Case1: If Cx,y is 0 or 255 and the pixels around it are not 0 ҆s or 255 ҆s, then eliminates 255 ҆s and 0 ҆s. Calculate the median value of neighboring pixels and replace it with median value.
Case2: If all pixels in the filtering window are 0 ҆s and 255 ҆s, then there
will be four possibilities: very high, very low, high, and low. Based on salt-and-pepper intensity one of the possibilities will be selected.
4) Repeat the process from (1) to (3) until all pixels in the image will be processed.
The following three cases will define the threshold values for t2 and t1 which are:
Case1: If the filtering window 33 is used, then the number of elements inside the window will be 9. However, t2 will be 4 if the 0 ҆s occurs more than 255 ҆s.
The same logic will be used when the number of 255 ҆s is greater than zeros.
Case2: The value of t2 is 6 if in the selected window the occurrence of 255 and 0 has occurred 6 times.
Case3: If all the pixels inside the filtering window are either 0 ҆s or 255 ҆s, then
the processing pixel is replaced with the value 128, which is the arithmetic mean of the two extremes gray levels.
This method uses two kinds of approaches to compare the results of this method with other different types of median filters. They are the Peak Signal to Noise Ratio (PSNR) and Image Enhancement factor (IEF).
Another work was done by Rai et al. (2015). The goal of this work is to distinguish between the local variations and image structure when the filter process the edge of the noisy image. In order to understand how to implement this method, Rai et
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al. Had divided their method into two main stages. In the first stage, a window of size 33 pixels had been used to process the noisy image. This window is used to determine the noisy pixel inside the filtering window. A simple derivative has been used with respect to the central pixel (x,y) for all the eight directions (E, W, N, S, NW, NE, SW, SE) as shown in Figure 2.2.
Here, Figure 2.2 represents the filtering window for this method. After this, fuzzy filtering was used to calculate the fuzzy derivatives. Based on this, the central pixel is considered as not an edge element if any two values from the rules are small.
In the second stage, the method will use other fuzzy rule for smoothing the image. For particular adaptive parameter value K, the fuzzy logic was repeated until the desired value of PSNR is reached. This method is performed well in removing high density of salt and pepper noise and Gaussian noise with less processing time, better output quality, and less hardware requirements when comparing it with Wiener filter.
Another proposed method had been tested on ultrasound images. Ultrasound is used for capturing images that contain internal body structures such as muscle and blood vessels. The most important reason for using ultrasound for capturing images of the internal body is because of its safety and cost effectiveness. However, the physicians may have difficulties when they try to diagnose the ultrasound images because of speckle noise, which reduce the image quality. Saadia and Rashdi (2016) proposed fuzzy weighted mean and fractional integration filter to remove the speckle
NW N NE
W (x,y) E
SW S SE
Figure 2.2: The filtering window for Rai et al., (2015)
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noise and enhanced the image quality. To implement this method, Saadia and Rashdi divide this method into two main stages.
In the first stage, echo sounder images will be processed by using 33 pixel filter. Instated of replacing it with the mean value, weights had been assigned to current pixel and all pixels in the neighborhood. By calculating the intensity differences between the processed pixel and the pixels around, this will lead to better results.
Moreover, fuzzy logic is being used to assign weights for each pixel inside the filter.
Then the pixel will change with center weighted mean value. The second stage, the resulting image from stage one will be enhanced by using fraction order integration filter. This method ensures noise suppression and preserving edge and other important features of the image.
Some researchers use machine learning to differentiate between the noisy pixel and noise-free pixel as the work proposed by Roy et al., (2016). Support Vector Machine (SVM) classification based fuzzy filter (FF) was proposed for removing impulse noise and enhance the quality of grayscale images. In order to ensure better performance for SVM classification, a set of the optimal feature was used in the training phase, where the pixels of the grayscale images were classified into noisy class and noise-free class. This will make the system highly trained to detect the noisy pixels in the corrupted image. After training the system, another set of test images will be applied. In the testing phase, the system will test the pixels of the corrupted image one by one and classified it into noisy class and noise-free class.
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The feature vector per pixel has to be of the same size as taken in the training phase. Fuzzy filtering will be performed based on the classification result from testing phase. This method performs well in removing low and high-density salt and pepper noise pixels from grayscale images. In addition to this, this method provides 98.5%
true-recognition at the time of classifying noisy class and free-noise class when the density of impulse noise level is 90%. There are many advantages of using this method like preserving of more image details, less blurring and more homogeneity for the reconstructed images.
The new method based on fuzzy logic was presented by Xiao et al. (2016), and it is focused on x-ray images. This method proposed a new scheme of enhancement for x-ray images. However, this method was divided into two main stages known as noise reduction and homomorphic filtering. Moreover, the noise reduction stage was divided into two subsections; the detection method and filtering method. In addition to that, the detection method itself has two subunits known as region detection and degree detection. This method uses fuzzy rules for the detection of the noisy pixels, and the membership function of the fuzzy rules had been calculated in the region detection. On the other hand, for degree detection, the central pixel in the filtering window was surrounded by four neighboring pixels crosspoint to directions {North (N), East (E), south (S), and West (W)} as it shown in Figure 2.3.
Figure 2.3: The window with central pixel
N W (x,y) E
S
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These four directional values are known as central gradient values around the central pixel (x, y). However, the values for noisy pixels and edge pixels are both large.
In order to distinguish between them, two related gradient values in the same direction are calculated as the fuzzy gradient in this direction. Moreover, this method used two sets of fuzzy rules; one for noisy pixels and another one for noise-free pixels. After completing the calculations, the noisy pixels will be passed to the filtering method.
Otherwise, it will consider noise-free pixels and send directly to the output image. In addition to that, the modified weighted median filter has been used to process the noisy pixels. Then, the result from filtering process will be going through homomorphic filtering for improving the brightness and contrast of the image. This method provides more efficient detection for noisy pixels by using region detection and degree detection and then filtering the noisy pixels, especially for low-level noise of salt and pepper (i.e., for noise level 0.04).
A new adaptive fuzzy median filter is presented by Sultana et al. (2013) to provide optimum detail preservation along with very high-density noise removal. The novelty of this research work comes from two directions. Firstly, the level of corruption was determined by using a triangular fuzzy membership function for each pixel that consequently ensures the replacement of noisy pixels according to the extent of corruption. Secondly, the threshold value is fully adaptive and automatically adjustable to provide ease of computation. In this work Sultana et al. (2013) proposed a fully adaptive fuzzy based median filter that avoids the drawbacks of the standard median filter and its variants by controlling the trade-off between attenuation of high probability impulse noise and preservation of fine details and edges. The experimental results show that the proposed filter outperforms other conventional and advanced
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filters in terms of both diagnosing and fine detail preservation of highly corrupted images.
Another work was done by Mahallati et al. (2013) the method applies fuzzy logic for removing the impulse noise. The results from this method are compared to those of median filter and mean filter. A novel and efficient impulse noise reduction method has been presented by the use of the fuzzy logic approach to do filtering on the noisy pixel. This method required eight, not noisy neighborhood pixels. The value of the corrupted pixel is replaced by the average value of the noise-free neighboring pixels. By this method, any number of corrupted pixels can be improved.
Consequently, eight improved neighborhood pixels are obtained. Then the average value of the eight improved neighborhood pixels substitutes the noisy pixel. If the fuzzy median value of the eight improved neighborhood pixels substitutes the noisy pixel, the obtained result in term of noise removal is much better for higher noise densities. Experimental results validate the robustness of the proposed method in term of impulse noise reduction, especially in high levels of noise
Also, Chowdhury et al. (2007) presents an enhancement technique based on fuzzy set theory to reduce image noise and to increase the contrast of structures of interest in the image. Compared to other techniques, a fuzzy method can manage the ambiguity and vagueness in many image processing applications efficiently. The method is able to represent and process human knowledge and applies fuzzy if-then rules. The algorithm includes the following steps:
1. At first, the gray values of the neighboring pixels (n×n window) are stored in an array and then sorted in ascending or descending order.
2. Then, the fuzzy membership value is assigned to each neighbor pixels:
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I. A π-shaped membership function is used.
II. The highest and lowest gray values get the membership value 0.
III. Membership value 1 is assigned to the mean value of the gray levels of the neighboring pixels.
3. Now, we consider only 2×k+1 pixels (k/2 ≤ n2) in the sorted pixels, and they are the median gray value and k previous and forward gray values in the sorted list.
4. Now, the gray value that has the highest membership value will be selected and placed as output.
A new fuzzy switching median (FSM) filter employing fuzzy techniques in image processing done by Toh et al., (2008). The proposed filter is able to remove salt-and pepper noise in digital images while minting image details and textures very well. By incorporating fuzzy reasoning in correcting the detected noisy pixel, the low complexity FSM filter is able to outperform some well-known existing salt-and pepper noise fuzzy methods. The FSM filter is composed of two semi-dependent modules, namely the salt and pepper noise detection module and the fuzzy noise cancellation module. The fuzzy set used for noise cancellation does not require time-consuming tuning of parameters and thus no training scheme is required. This marked the simplicity of the proposed algorithm.