A SURVEY OF IMAGE DENOISING FILTERS BASED ON BOUNDARY DISCRIMINATION NOISE DETECTION

Image denoising is an essential and complex activity that should be carried out before any other image processing because it checks for errors within the image(s) and rectifies them. There are ways to remove noise, the switching scheme is an outstanding method when equated to others, it initially segregates the noisy pixels and then filters them. Boundary Discriminative Noise Detection (BDND) is a type of algorithm that uses the switching method and is good for impulse noise detection, many works have been presented using several enhancements to detect noise from images using BDND. In this paper, we present a detailed outline of impulse noise and noise removal techniques by looking at over a decade of research conducted to establish a fundamental understanding of the Boundary discriminative noise detector algorithm used in image denoising. We analyzed 19 relevant papers through Google Scholar, focusing on three aspects: the methods for detecting noisy pixels, the type(s) of noise, and the major challenges. We found that many of the image denoising methods still use BDND and at least one algorithm is developed yearly except for 2017 to 2021, indicating the algorithm is significant in the field of image denoising. Furthermore, we wrap up the survey by highlighting some research challenges and offering a list of key recommendations to spur further research in this area.


INTRODUCTION
Noise in images can be associated to various sources like variation in detector sensitivity, environmental variation, and transmission. Noise at any level is always undesirable, hence denoising has to be employed before the image could be used for further analysis. One of such techniques for image denoising is the switching technique where noisy pixels are detected in advance then filtered.
Boundary Discrimination Noise Detection (BDND) Algorithm is one of the methods that use the switching technique, where every pixel belonging to an image is subjected to a process of detection. A kernel of 21×21 dimension is centered on the target pixel, the pixel intensity values will be grouped into three clusters (the upper, middle, and the lower cluster) and the binary decision map is formed using "0s" to denote the locations of non-noisy, and "1s" denoting the noisy pixels. As a result, two essential boundaries are formed. If the pixel in question falls within the middle cluster, it will be considered uncorrupted, given that its intensity value is neither relatively low nor relatively high, else, the pixel may be corrupted by impulse noise. The accuracy of clustering results ultimately depends on how accurate the identified boundaries are (Pei-Eng Ng & Kai-Kuang Ma, 2006). The contribution of this paper is to provide a clear outlook of recent advances of BDND algorithm so as to enhance the understanding of researchers on the basis of image denoising algorithm using BDND.
The rest of this paper is structured as follows: first, an explanation of the impulse noise models is given; then a description of the two steps of original BDND; additionally an outline of the works related to BDND are presented.

Figure 1 Study Selection process
Contributions: 1. We present an updated descriptive literature review on BDND techniques used in image denoising. 2. We provide open research problem and opportunities for future research 3. We also reviewed the evaluation parameters by the research papers in the area of Image processing using BDND. Impulse Noise Model Fixed valued impulse noise or Salt-and-pepper noise: -the corrupted pixels takes either of the two extreme values (i.e. 0 and 255) leading to white and black spots in the image. For this noise model the distribution p of noise N is defined as in (Pei-Eng Ng & Kai-Kuang Ma, 2006): Random Valued Impulse Noise/ Uniform Impulse Noise: The noisy pixels are corrupted with values within range of [0, 255] for gray-scale images. "Removal of Random valued impulse noise is more complicated due to the random distribution of the noise pixels (Nadeem et al., 2020a). The distribution of the impulse noise is equally distributed. This is also presented in (Nadeem et al., 2020b).
Mixed Impulse Noise or Universal impulse noise: -The contamination is equivalently influenced by the two most prevalent impulse noise models, which are the Random Valued Impulse Noise (RVIN) and Salt and pepper Impulse Noise (SPIN). The Universal impulse noise model is more realistic. This noise can be described by the following equation from (Pei-Eng Ng & Kai-Kuang Ma, 2006

The Filtration Stage
In the filtration stage, the Noise Adaptive Switching Median (NASM) (Eng & Ma, 2001) was exploited to replace only the noisy pixels identified by the BDND. It was developed to solve the problem of replacing the identified noisy pixel with a wrong pixel value, which could occur when using a smaller window size due to increase in the number of corrupted pixels in the window. Therefore, the window is enlarged in four directions until the total of uncorrupted pixels in the window is more than half the pixels or reaches the final size of the window.

Noisy Image
Impose a 21×21 window centred on a pixel xij Obtain b2:Identify the maximum value for pixel intensity between med and 255 in VD , and mark the corresponding pixel in Vẟ as the boundary Vẟ = Sort the pixels in the window and determine the median, med, of the sorted vector.
Compute VD = intensity difference between each pair of adjacent pixels across the sorted vector and obtain the difference vector.
Obtain b1:Identify the maximum value for pixel intensity between 0 and med in VD , and mark the corresponding pixel in Vẟ as the boundary If pixel Xij belongs to the middle cluster or 2 nd iteration output Yes

No
Impose a 3×3 window centred on a pixel xij

LITERATURE SURVEY
Review of previous studies revealed that, no systematic survey was carried out, regarding the use of the BDND algorithm for image denoising. Table 1 summarizes the prominent works carried out on this area of image denoise using BDND and emphasizes their focus and weaknesses.
The work of (Ng & Ma, 2006) developed switching median filter using BDND algorithm, the detection starts with BDND using a 21×21 window, centering on the target pixel and classifying the pixels as low-intensity impulse noise (lower cluster), uncorrupted (medium cluster), and high-intensity impulse noise (higher cluster). If the target pixel falls in the lower or higher cluster, it is presumed to be noisy or corrupt, and then the procedure is repeated using a 3×3 window and in the filtration Modified Noise Adaptive Switching Median (NASM) filter. Simulation results show that the filter consistently outperforms the NASM filter by achieving a much higher output. It was able to boost noisy pixel detection, especially for salt and pepper noise. Though, the overall time consumption, false alarm, and missed detection increased at a high noise level (Chen, Hung, & Zou1, 2017) (Sarvesh et al., 2021).
In the work of (Ping et al., 2007) the modified BDND was presented to reduce the computational time of BDND, in the detection stage, the boundaries are determined by calculating the local window histogram where the bin indices are the gray levels, the first boundary b1 is determined by computing the difference of non-zero adjacent bin indices between min and med, then determining the maximum difference and mark the corresponding index, same is done from med to max for b2. For filtration, if the number of uncorrupted pixels in the filtering window exceeds 3, the extension ends. Experimentally, the system accomplished better running time and better PNSR value at higher noise density, but BDND was better at denoising at lower density. The work presented by (Hsieh et al., 2009) proposed a denoising scheme that concentrated on improving both the detection and the filtration stage. In the detection stage, if the maximum value of the absolute intensity values between min to med is 0, then adjust b1= b2. On the other hand, when the maximum value of the absolute intensity values between med to last is 0, then reset b2= b1. Increase the window to a 7 × 7 dimension and redo the steps then classify, but when there is only a single non-zero value in absolute intensity values then change b2= b1. The filtration starts with a 3 × 3 checking for uncorrupted pixels if more than one uncorrupted pixel exists then calculate the median value of all uncorrupted pixels and replace the noisy pixel with the median value, if only a single uncorrupted pixel exist then substitute the noisy pixel by it. Else expand the window and check again. The result of the experiment showed BRBDND/MFSW performed better in terms of visual quality and PNSR. However, there is an increased False alarm for unbalanced salt and pepper

Baththama, et al, FJS
In (Nasimudeen et al., 2012) The algorithm removes all pixel values below the b1 and above b2 leaving only the middle cluster intensity values, if what is left does not contain a value, the minimum and maximum values will be set as b1 and b2, otherwise b1 and b2 will be the new minimum and maximum values of the reduced list. Only pixels contained in the middle cluster are classified as uncorrupted, this is used to form a binary map. An advanced adaptive switching filter based on the four key directions was developed in the filtration stage, using a 3 × 3 window, and expanding by two pixels outward if the quantity of uncontaminated pixels inside the window is less than half. The system achieved a reduced processing time unfortunately, the relationship between the pixel values is likely lost as the window size increases during filtration.
Another work was presented by (Haidi Ibrahim, 2011) titled modified BDND, it creates two local histograms corresponding to a 21×21 and a 3×3, it uses local cumulative density function to calculate the median, then finds the largest bin gap between 0 to med and the corresponding intensity value is b1, from med to 255 the corresponding intensity value of the largest bin gap is b2. In both the detection and the filtration stages, the global noise density estimation is used to decide the total number of local histograms used. Although it was able to reduce the computation time, it had a similar result as BDND.
Another work also presented a combination of the Local outlier factor, a density-based outlier detection method, and BDND. In the detection stage, the LOF value of each pixel is checked whether it is higher than the first threshold value, if it is higher it is considered as noise, then BDND is invoked to check using a 21×21 window if it is still assumed to be the noise it then goes through a validation stage where it is checked against the second threshold value. If it is higher, BDND is invoked using a 3×3 window. For the filtration stage, the directional weighted median filter (DWMF) is used. LOFBDND had an enhanced performance in terms of the PNSR and reduced missed detection compared to the contending methods but increased false detection compared to BDND (Wang & Lu, 2011) ABDND was presented by (Tripathi et al., 2011), the detection starts by calculating the forward difference between two adjacent histogram counts to form a difference array, t1 is the index corresponding to the negative maximum and t2 is the max index corresponding to the positive max in the difference array. The difference between the concerned pixel and the minimum intensity value in the window and the difference between the concerned pixel and the maximum intensity value in the window is checked against t1 and t2 respectively, If greater than the thresholds, it is assumed to be noise, after this the noise map refinement is invoked where final noise map is determined. Finally, an adaptive switching median filter is used for filtration. ABDND accomplished a good result but has increased false detection at very-low-density noise compared to BDND.
NBLDND was proposed by (Zuviria et al., 2012) to suppress salt and pepper noise at a very high density. It uses the same initial step of BDND in the detection stage, if the pixel is assumed as noisy, the noise density is determined and the detection window based on the noise density is placed around the pixel and the steps of BDND are repeated. In the filtration stage of NBLDND, the algorithm initiates an extra vertical window size and a horizontal window, these windows are checked until a noise-free pixel is found within the neighborhood to replace the noisy pixel. NBLDND accomplished an improved visual quality and decreased processing time. However, artifacts are introduced in some cases.
In (Jafar et al., 2013) the work improved the accuracy of filtration stage by considering the sum of uncorrupted pixels inside the filtering window. A simple change to the condition was made, only expanding the window when the total number of uncorrupted pixels within the filtering window is zero or less than half the pixels and maximum window size has not been reached and during the calculation of the approximated pixel values, the spatial relationship between the noisy pixel and the uncorrupted pixels in the window and the relationship between the values of the uncorrupted pixels and the central pixel is considered. An enhanced performance was shown on the visual quality of the filtered image.
"Non-local means filter for removal of high-density RVIN and Salt and pepper noise was introduced by (Nasri et al., 2013). For the latter, the original BDND and simple detection were used in the detection stage. In the filtration stage, two different windows are considered the bigger window called the search window and the smaller is known as the patch window, the repaired value of the pixel in concern is gotten as the weighted sum of all non-noisy pixels which are based on a similar patch in the search window. A non-adaptive window was used in the filtration, and this made the method non-responsive to highdensity noise.
The method in (Verma & Singh, 2013), was developed with the aid of three membership functions, fuzzification is integrated into BDND noise identification, each rule is given a weight for verifying whether a pixel is distorted by noise or not, therefore forming a binary map. Later, a confirmation is done using a 5×5 window. Noisy pixels are then filtered using the median of nonnoisy intensity value in the window, based on the requirement that the number of uncorrupted pixels should be greater than or equal to half of the total number of pixels in that particular window the size of the window is raised from 3x3 to 7x7. Showed a significant improvement but blurs the image at above 50% noise density.
The paper by (Huang et al., 2013) MABDND is an improved ABDND that aims to eliminate random-value noise of high density. There are two components for the detection stage, noise detection and non-noise detection. For noise detection, it utilizes the same process as ABDND. The non-noise detection step is a verification component using histogram statistics from the first stage to classify pixels of false detection as corrupted or uncorrupted pixels. MABDND results show a decreased false detection and low MD when compared to ABDND.
The work of (Shalimettilsha & Kumar, 2014) In this work, the estimated noise density, total number of pixels in the filtering window are calculated, if the total sum of uncorrupted intensity value is below half of the percentage of noisy pixels in the filtering window is expanded outward by one pixel in all directions. The median of the uncorrupted pixels in the window is calculated and adjusted according to the spatial value using the Cubic interpolation.

Baththama, et al, FJS
"Modified Boundary Discriminative Noise Detection" (MBDND) was presented by (Thanakumar et al., 2014)) was proposed to decrease the expansion of window size and spatial relationship should be used in the pixel replacement during filtering, to do these the window is expanded only when any of the two windows are violated (i) if number of uncorrupted pixels is ≥ half of the number of pixels in the window.
(ii)number of the uncorrupted pixel is not equal to zero and finally for the estimation of pixel. However, under high noise densities, the first condition demanding the number of uncorrupted pixels to be more than half of the number of pixels in the window is easily violated. Thus, with high noise densities, the filtering window is expected to be expanded and most likely it will reach the maximum size. However, such a requirement is hard to satisfy under high noise densities.
The work of (Sharma & Pateriya, 2015) improved BDND in the detection stage by modifying the second iteration using a 3×3 window, if the target pixel isn't an extreme value, then the pixel is uncorrupted, but if the center pixel is 0 and window contains intensity value order than the two extreme values then calculate weighted median intensity values and finally, if window contains only the two extreme values, the number of zeros and 255 will compared then the noisy pixel is replaced with the highest number i.e. (0 or 255).

Regression Based Color Noise Estimation and Removal with
Improved BDND Algorithm by (Sendhilkumar & Pandurangan, 2017) was proposed to refine Modified Boundary Discriminative Noise Detection (MBDND) by (Thanakumar et al., 2014) by relaxing the condition a bit and taking into consideration the estimated noise density which is determined from the detection step of the algorithm and the total number of pixels in the filtering window by using linear regression. The authors reported the algorithm tolerates up to 90% of the noise and high PSNR obtained of up to 30db.
Another work proposed a modified BDND algorithm to improve detection at higher impulse noise density. In the filtering stage the sum of uncontaminated pixels within a window is determined, if the sum of uncontaminated pixel is above zero, then, the Euclidean distance between the centered pixels and the uncorrupted pixels is calculated and converted to distance weight. The noisy pixel is substituted by the sum of the product of distance weight and all the uncorrupted pixels (Sangave & Jain, 2017). In (Rani & Satyanarayana, 2017)"This Boundary Discrimination Noise Detection with switching bilateral filter (BDNDSBF) was developed to be able to filter mixed noise (a combintion of Gaussian and impulse noise). It is a two stage method, the detection and the filtering stage. In the detection stage BDND is used to segregate the noisy from the non-noisy pixels then generate a two-dimensional binary decision map. The image and the output of BDND is passed to Switching Bilateral Filter is employed to detect the edges, edge information and classify noisy pixels as either impulse or gaussian. The filtration is similar to SBF(Chih-Hsing Lin et al., 2010). In the work of (Sarvesh et al., 2021) every iteration considers a local window (3 ×3) to establish b1 and b2 boundaries by determining the window's contrast value. Contrast/2 describes b1, and median + contrast/2 describes b2. If a pixel value is outside the range of b1 and b2, it is referred to as corrupted, whereas pixels that are within the bounds are referred to as uncorrupted. The binary matrix is created by assigning 1 to corrupted pixels and 0 to uncorrupted pixels. The noisy pixel's value is replaced with the window's median value in the related image, while uncorrupted pixel values remain intact. The summary of these finding are presented in Table 1, it tabulates the author of each denoising method, name of method if available or name of paper, reason for modification, filtration method, algorithms used for comparison and finally the limitation of the method.

NASM
-Execution Time is high -High false alarm and missed detection at high noise density.

Metrics of image denoising Method
i. Peak signal-to-noise ratio (PSNR) : The higher PSNR value the better quality of the image ii.
Mean Squared Error (MSE): The smaller the value the better. iii.
Mean Absolute Error (MAE): The value ranges from 0 to infinity. The Smaller the value the better. iv.
Root Mean Square Error (RSME): Ranges from 0 to infinity. The Smaller the value the better. v.
Structural Similarity Index (SSIM): The larger the SSIM value the better. vi.
Figure of Merit (FOM): The higher the value of FOM the better.

vii.
Image Enhancement Factor (IEF): The higher value of IEF the better. Table 2 shows the metric(s) used by each work to indicate its performance. Approximately, more than three-quarter (3/4) of the studies were measured using peak signal-to-noise ratio, two used the MSE, another two used the MAE, one used SSIM, two used the FOM while only one used the IEF, indicating that the PNSR is the most used metrics used at the time of this literature review, probably it is because it is one of the common and easiest error metrics. The parameters such as the SSIM, IQI, and FOM are used for measuring overall image quality, structure, and edge preservation, but they receive less attention.