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1001 Solutions
Published in Jaakko Astola, Pauli Kuosmanen, Fundamentals of Nonlinear Digital Filtering, 2020
Jaakko Astola, Pauli Kuosmanen
Thus, the output of the LUM smoother is X(s) (some lower order statistic) if the center sample satisfies X* < X(s). If X* > X(N−s+1) the output of the LUM smoother is X(N−s+1) (some higher order statistic). Otherwise the output is simply the center sample, X*. The parameter s defines the range of the accepted order statistics. If X* lies in the range it is not modified. If X* lies outside this range, it is replaced by a sample lying closer to the median. Impulses are typically such values. The parameter value s enables tuning between detail preservation and noise suppression. If s = 1 the LUM smoother is an identity filter: if s = k + 1 it is the median filter. In fact the LUM smoother is identical to the Winsorized smoother proposed by Mallows [73, 74]. Furthermore, it is identical to the center weighted median filter (Exercise).
Noise reduction of retinal image for diabetic retinopathy assessment
Published in Ahmad Fadzil Mohamad Hani, Dileep Kumar, Optical Imaging for Biomedical and Clinical Applications, 2017
Ahmad Fadzil Mohamad Hani, Toufique Ahmed Soomro, Ibrahima Faye, Nidal Kamel, Norashikin Yahya
In retinal fundus imaging, image denoising problem is still a challenge for the researchers because removal of noise causes the artefacts and image blurring. Image denoising is classified into two types, that is, spatial domain filtering and transform domain filtering methods. A spatial filter is an image operation where each pixel value I(x,y) is changed by a function of the intensities of pixels in a neighbourhood of (x,y). Spatial filters can be further ordered into non-linear and linear filters. A filtering method is linear when the output is a weighted sum of the input pixels such as mean filter, average filter, Wiener and Lee filter. Non-linear spatial filters cannot be calculated using just a weighted sum. Other operations (e.g. square root, log, sorting and selection) are involved in calculation of non-linear filters. Examples of non-linear filters are median filter and weighted median filters. Non-linear filters are not easy to implement as compared to linear spatial filters such as non-linear Lee filter, Roberts filter and Kirsch's template filter. Non-linear filters can smooth with less blurring edges compared to linear filters and can detect edges at all orientations simultaneously, but can be slow to compute.
Qualitative performance analysis of greyscale image denoising techniques
Published in Rajesh Singh, Anita Gehlot, Intelligent Circuits and Systems, 2021
Amandeep Singh, Gaurav Sethi, G.S. Kalra
Images captured by a digital camera can have various sources of noise, i.e. compression, environment effect on transmission, dust on camera lenses and damaged memory locations. This dilutes the details and information present in the image. So, image denoising plays an important role to maintain the image quality and details of the image. Image denoising is required to remove the noise without affecting the details of image like texture, edges [1–4]. In certain images, it is very difficult to identify the difference between objects and their boundaries. It is important to understand that the solution of every noise cannot be the same as denoising is the inverse problem. There are different types of noises playing roles in image distortion. But impulse noise plays a major role in image distortion. So, it becomes important to detect and remove impulse noise. Impulse noise is also known as salt and pepper noise, which affects the image pixel with minimum or maximum value of intensity possible in the image i.e., 0 or 255. This noise can affect the image at any location, which makes it hard to identify the noise location and it is further difficult to remove the impulse noise or restore the original value [5]. In the field of greyscale image denoising, various algorithms are available for denoising but it is hard to find a desirable one. In this paper, we will compare three existing denoising algorithms on the basis of their performance on different noise levels. The performance evaluation is made in the form of peak signal to noise ratio (PSNR) [6]. These three denoising algorithms are median filter (MF), progressive switching median filter (PSMF) and centred weighted median filter (CWMF). We have no intention to give you a detailed review of these methods. More focus in this paper is on the qualitative result-based comparison. This manuscript is systematized as follows. In Section 2, the process of comparative analysis is presented. Section 3 is dedicated to results and discussion (denoising noise of greyscale images). The concluding remarks are drawn in Section 4.
Colour-weighted rank transform and improved dynamic programming for fast and accurate stereo matching
Published in The Imaging Science Journal, 2023
Mohamed Hallek, Randa Khemiri, Ali Aseere, Abdellatif Mtibaa, Mohamed Atri
The filtering is the next process in the disparity refinement step. This stage is performed using the Weighted Median Filter (WMF). As implemented in [9,13,42], the WMF is utilized to eliminate the existing noise and smooth the hole-filled disparity map. Using a support window with , the WMF replaces each central pixel with the weighted median value of its neighbouring pixels. The weight of each pixel is calculated based on spatial and colour distances between the pixel of interest and its neighbouring pixels. The WMF performs edge-preserving filters many times using weighted histograms. Similar to the approach in [9,13], the WMF implementation is given by Equations (22) and (23) to obtain the filtered disparity map.
Robust optimization model for medical staff rebalancing problem with data contamination during COVID-19 pandemic
Published in International Journal of Production Research, 2022
Xuehong Gao, Guozhong Huang, Qiuhong Zhao, Cejun Cao, Huiling Jiang
Next, we consider the weighted median for the observations, with corresponding weights, . Note that the weighted median with equal weights (i.e. ) becomes the conventional median. Let be the order statistics of such that ; then, the breakdown point for the weighted median is defined by In what follows, we consider the best and worst cases to explore the upper and lower bounds of the breakdown point for the weighted median in Cases I and II, respectively. Case INow, we consider the best case, where the upper bound of the breakdown point for the weighted median can be obtained. Let be the order statistics of such that and . If considering the best case that when all the contaminated values have smaller weights, then we have Obviously, the breakdown point can be increased to . Thus, the upper bound is given by
A random-valued impulse noise removal algorithm via just noticeable difference threshold detector and weighted variation method
Published in International Journal of Computers and Applications, 2022
In order to suppress RVIN in images, a large number of techniques have been proposed in the past few decades. The median filter and its variations [2–8], such as adaptive switching median filter [2], adaptive center weighted median filter [3], four phase detector median filter [4], optimal direction based median filter [5], and adaptive dual threshold median filter [6], Difference based median filter method [7], are widely used techniques for RVIN removal. The mean-based filters [9–14] are another shared impulse removal mechanisms frequently mentioned in the literature, including, the multitexton noise identification and local dissimilarity-based noise removal (MNI-LDNR) method [9], the fuzzy mean filters [10], weighted mean filter [11], the peer group concept mean filter [12], the fuzzy weighted nonlocal mean filter [13], the rank-ordered difference of rank-ordered absolute difference based weighted mean filter [14]. Owing to the effectiveness and high computational efficiency, most of the above filters receive extensive concern in recent years. However, the median filter, the mean filter, and their variations are difficult to restore the noise candidates on image details accurately. Therefore, the restoration results by these filters may often blur image details.