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Faster computation of a weighted median (WM) filter is impeded by the construction of a weighted histogram for every local window of data. Since the calculated weights vary for each local window, it is difficult, using a sliding window approach, to construct the weighted histogram efficiently. In this paper, we propose a novel WM filter that overcomes the difficulty of histogram construction. Our proposed method achieves real-time processing for higher resolution images and can be applied to multidimensional, multichannel, and high precision data. The weight kernel used in our WM filter is the pointwise guided filter, which is derived from the guided filter. The use of kernels based on the guided filter avoids gradient reversal artifacts and shows a higher denoising performance than the Gaussian kernel based on the color/intensity distance. The core idea of the proposed method is a formulation that allows the use of histogram updates with a sliding window approach to find the weighted median. For high precision data we propose an algorithm based on a linked list that can reduce the memory requirements of storing histograms and the computational cost of updating them. We present implementations of the proposed method that are suitable for both CPU and GPU. Experimental results show that the proposed method indeed realizes faster computation than conventional WM filters and is capable of filtering multidimensional, multichannel, and high precision data. This is an approach which is difficult to achieve with conventional methods. [ABSTRACT FROM AUTHOR]

This paper proposes a lidar upsampling technique to obtain ultra-high resolution and omnidirectional 3D data. Obtaining a large amount of omnidirectional 3D data is expensive because of the cost of sensing and scanning systems. Instead of using expensive commercial scanning systems, we introduce a new type of low-cost 360-degree 3D scanning system to obtain 3D lidar data. The original lidar data from the system is upsampled by using the weighted median filter with novel Hue-Saturation-Depth (HSD) guide image. The proposed upsampling technique consists of two steps. The first step upsampling is performed by using linear interpolation based on pixel distance and edge-area refinement in the interpolated depth map. Thereafter, in order to reduce the saturation effect of a high-contrast RGB color guide image, we propose to add the depth information to the guide image. A novel HSD guide image is generated by replacing the intensity of the RGB image with the scaled-depth from the first-step upsampling. Finally, the second-step upsampling is performed by applying the weighted median filter to the result of the first-step upsampling. In the experiments, we present ultra-high-resolution 3D scanning results and error analysis in complex indoor environments. [ABSTRACT FROM AUTHOR]

Age-related macular degeneration is a visual disorder caused by abnormalities in a part of the eye's retina and is a leading source of blindness. The correct detection, precise location, classification, and diagnosis of choroidal neovascularization (CNV) may be challenging if the lesion is small or if Optical Coherence Tomography (OCT) images are degraded by projection and motion. This paper aims to develop an automated quantification and classification system for CNV in neovascular age-related macular degeneration using OCT angiography images. OCT angiography is a non-invasive imaging tool that visualizes retinal and choroidal physiological and pathological vascularization. The presented system is based on new retinal layers in the OCT image-specific macular diseases feature extractor, including Multi-Size Kernels ξcho-Weighted Median Patterns (MSKξMP). Computer simulations show that the proposed method: (i) outperforms current state-of-the-art methods, including deep learning techniques; and (ii) achieves an overall accuracy of 99% using ten-fold cross-validation on the Duke University dataset and over 96% on the noisy Noor Eye Hospital dataset. In addition, MSKξMP performs well in binary eye disease classifications and is more accurate than recent works in image texture descriptors. [ABSTRACT FROM AUTHOR]

Stereo matching, which is conventionally used for three-dimensional (3D) information acquisition through cameras, is the most actively studied subject in computer vision. To obtain sophisticated 3D information, refining the disparity map in stereo vision is important. The weighted median filter (WMF) is extensively used to eliminate outliers in post-processing. To this end, various studies have implemented WMFs in hardware for real-time processing. Among them, the separable weighted median filter (sWMF) vertically and horizontally separates a two-dimensional WMF into two one-dimensional WMFs to reduce hardware resource usage. Herein, we propose a hardware architecture that can reduce the hardware resource usage of the sWMF by applying the sparse-window approach, which is a method of creating a window by selecting pixels sparsely. This approach makes it possible to reduce drastically the number of elements to be computed. Although the proposed architecture has an insignificant disparity error rate, similar to that of the sWMF, it saves 33% slice lookup tables (LUTs) and 69% slice registers when using a window size of 37 × 37 pixels as the synthesis result on the Xilinx XC7K325T FPGA. When a window size of 49 × 13 pixels with the best performance is used, the proposed architecture uses 7335 slice LUTs, 4126 slice registers, and 21 block RAMs. The proposed architecture operates at frequencies of up to 167.95 MHz; hence, it can operate in real time. The proposed WMF architecture is suitable for application in embedded systems and low-resource environments as it is hardware-friendly. [ABSTRACT FROM AUTHOR]

Abstract Because there is no temporal information available, rain removal with a single image is more challenging than that with a video. In this paper, we present a weighted median guided filtering method for rain removal with a single image. It consists of two filtering operations. Firstly, a weighted median filter is convoluted with an input rainy image to obtain a coarse rain-free image; then, guided filter is employed to obtain a refined rain-free image, where the coarse rain-free image is used as a guided image and convoluted with the input rainy image via guided filter. Experimental results show that the proposed method generated comparable results to the state-of-the-art algorithms with low computation cost.

Edge detection via anisotropic average directional ratio (AADR) for synthetic aperture radar (SAR) images produces unwanted and fragmentized edge pixels due to the speckle noise and sporadic highlight pixels from isolated strong scatterers in real scenes. In this paper, a novel robust edge detector is developed for SAR images. Anisotropic morphological directional ratio (AMDR) is proposed to describe the intensity variation in SAR images by combining rotated biwindows and the weighted median filter (WMF). Then, multiplicative spatial and directional matched filters are presented to improve edge localization and direction estimation of the AMDR. Based on the enhanced AMDR, the edge strength map (ESM) and the edge direction map (EDM) are embedded into the route of Canny detector to extract thin edges. Moreover, an edge remedy processing is given to improve the connectivity of edges near junctions. Finally, performance comparison is conducted with the existing AADR-based detectors on synthetic and real SAR images using the receiver-operating-characteristic (ROC) curves, which shows that the proposed AMDR-based detector possesses evidently more robust ability to counteract sporadic isolated highlight pixels in SAR images than the existing AADR-based detectors do. Moreover, in the case without sporadic isolated highlight pixels, its performance is also comparable with those of existing competitive AADR-based ones.

Abstract A new impulsive noise removal filter, adaptive dynamically weighted median filter (ADWMF), is proposed. A popular method for removing impulsive noise is a median filter whereas the weighted median filter and center weighted median filter were also investigated. ADWMF is based on weighted median filter. In ADWMF, instead of fixed weights, weightages of the filter are dynamically assigned with the results of noise detection. A simple and efficient noise detection method is also used to detect noise candidates and dynamically assign zero or small weights to the noise candidates in the window. This paper proposes an adaptive method which increases the window size according to the amounts of impulsive noise. Simulation results show that the AMWMF works better for both images with low and high density of impulsive noise than existing methods work.

A new impulsive noise removal filter, adaptive dynamically weighted median filter (ADWMF), is proposed. A popular method for removing impulsive noise is a median filter whereas the weighted median filter and center weighted median filter were also investigated. ADWMF is based on weighted median filter. In ADWMF, instead of fixed weights, weightages of the filter are dynamically assigned with the results of noise detection. A simple and efficient noise detection method is also used to detect noise candidates and dynamically assign zero or small weights to the noise candidates in the window. This paper proposes an adaptive method which increases the window size according to the amounts of impulsive noise. Simulation results show that the AMWMF works better for both images with low and high density of impulsive noise than existing methods work. [ABSTRACT FROM AUTHOR]

The paper presents an efficient approach for suppressing salt-and-pepper (S & P) noise under adaptive switching weighted median filter (ASWMF) framework. The ASWMF includes noise detection and noise removal stages. The proposed method first classifies a pixel into either “noise-free pixel” or “noise pixel” by checking noise candidate with the local mean value using noise detection stage. Then, the detected noisy pixels are replaced by their weighted median values using adaptive weighted median filter within a window size of 3 × 3 or 5 × 5. The proposed method is compared to several denoising schemes in terms of key performance indicators. Test results demonstrated superiority and efficiency over other methods in removing S & P noise up to percentage of 90%. [ABSTRACT FROM AUTHOR]

We propose a novel post-processing algorithm and its very-large-scale integration architecture that simultaneously uses the passive and active stereo vision information to improve the reliability of the threedimensional disparity in a hybrid stereo vision system. The proposed architecture consists of four steps -- leftright consistency checking, semi-2D hole filling, a tiny adaptive variance checking, and a 2D weighted median filter. The experimental results show that the error rate of the proposed algorithm (5.77%) is less than that of a raw disparity (10.12%) for a real-world camera image having a 1,280 × 720 resolution and maximum disparity of 256. Moreover, for the famous Middlebury stereo image sets, the proposed algorithm's error rate (8.30%) is also less than that of the raw disparity (13.7%). The proposed architecture is implemented on a single commercial fieldprogrammable gate array using only 13.01% of slice resources, which achieves a rate of 60 fps for 1,280 × 720 stereo images with a disparity range of 256. [ABSTRACT FROM AUTHOR]

Low-rank tensor factorization (LRTF) provides a useful mathematical tool to reveal and analyze multi-factor structures underlying data in a wide range of practical applications. One challenging issue in LRTF is how to recover a low-rank higher-order representation of the given high dimensional data in the presence of outliers and missing entries, i.e., the so-called robust LRTF problem. The L-norm LRTF is a popular strategy for robust LRTF due to its intrinsic robustness to heavy-tailed noises and outliers. However, few L-norm LRTF algorithms have been developed due to its non-convexity and non-smoothness, as well as the high order structure of data. In this paper we propose a novel cyclic weighted median (CWM) method to solve the L-norm LRTF problem. The main idea is to recursively optimize each coordinate involved in the L-norm LRTF problem with all the others fixed. Each of these single-scalar-parameter sub-problems is convex and can be easily solved by weighted median filter, and thus an effective algorithm can be readily constructed to tackle the original complex problem. Our extensive experiments on synthetic data and real face data demonstrate that the proposed method performs more robust than previous methods in the presence of outliers and/or missing entries. [ABSTRACT FROM AUTHOR]

This paper proposed a fuzzy-based switching technique that aims at detection and filtering of impulse noises from digital images. Two types of noise models are used to obtain the noisy images. In this two-step process, the noise-free pixels are remained unchanged. The proposed detection algorithm uses 5 $$\times $$ 5 window, based on all neighboring pixels on the center of the window of a noisy pixel. Two weighted median filters are devised, and a particular one is applied selectively to the noisy pixel based on the characteristics of the neighboring pixels within the window. Instead of a single threshold, two threshold values are used in the proposed fuzzy membership function to partition the noise level, and accordingly, a filtering method is applied to restore the corrupted pixel. Experimental results show that the proposed technique outperforms the existing impulse denoising methods in terms of peak signal-to-noise ratio and visual effects, with a comparable time complexity with the existing methods. [ABSTRACT FROM AUTHOR]

We present a new upsampling method to enhance the spatial resolution of depth images. Given a low-resolution depth image from an active depth sensor and a potentially high-resolution color image from a passive RGB camera, we formulate it as an adaptive cost aggregation problem and solve it using the bilateral filter. The formulation synergistically combines the median and bilateral filters thus it better preserves the depth edges and is more robust to noise. Numerical and visual evaluations on a total of 37 Middlebury data sets demonstrate the effectiveness of our method. A real-time high-resolution depth capturing system is also developed using commercial active depth sensor based on the proposed upsampling method. [ABSTRACT FROM AUTHOR]

Demosaicking is an estimation process to determine missing color values when a single-sensor digital camera is used for color image capture. In this paper, we propose a number of new methods based on the application of Taylor series and cubic spline interpolation for color filter array demosaicking. To avoid the blurring of an edge, interpolants are first estimated in four opposite directions so that no interpolation is carried out across an edge. A weighted median filter, whose filter coefficients are determined by a classifier based on an edge orientation map, is then used to produce an output from the four interpolants to preserve edges. Using the proposed methods, the original color can be faithfully reproduced with minimal amount of color artifacts even at edges. [ABSTRACT FROM AUTHOR]

An efficient technique to remove periodic noise from digital images via a novel implementation of the median filter is presented and discussed within this letter. The technique is based on applying the nonlinear filter to the Fourier amplitude spectrum of the image. Since the median filter is normally used to spatially reduce spiky noise in digital images, using this filter in Fourier space is especially useful for removing periodic frequency noise. Provisional experimental results are shown that demonstrate that the proposed filter provides good performance when compared with a similar Fourier filter: the notch filter. This letter, when considering a prototype version of a Fourier-based median filter, defines the set of user-defined options that are available and also defines a possible solution to solve the distortions caused around the dc component due to natural spectrum decay. [ABSTRACT FROM AUTHOR]

Since weighted median filters effective in recovering images belong to the class of stack filters, the authors have proposed a fuzzy weighted median (FWM) filter, which is a weighted median filter defined by a fuzzy Boolean function, and have presented its design method. The design of the FWM filter can be considered in terms of the design of the weight and the design of the fuzzy Boolean function separately. In the design methods developed to date, the fuzzy Boolean functions are sigmoid-type functions and the weights are S-type functions with only the distance from the processing point as a variable, which are approximated and require derivations of four parameters, which is an easy task. Such methods, however, are restricted to the class of designable FWM filters. In this paper, the class of designable FWM filters has been significantly expanded to incorporate nearly all classes of FWM filters by establishing all weights independently and by defining the fuzzy Boolean functions by appropriate functions in addition to the sigmoid-type functions. Thus, a high-performance filter is designed by the filter weight and the fuzzy Boolean function designed for the kinds of added noise for real image processing examples, which change more flexibly as compared with the FWM filters developed in the previous design methods. In addition, a design procedure for realistic cases in which only the images which are targets of processing are known is presented and a design method for an FWM filter, which is effective in practical terms, is presented by showing its performance. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(2): 95–106, 2001 [ABSTRACT FROM AUTHOR]

The stack filter is the most systematic among the nonlinear filters, including the weighted median filter and the morphology filter. The authors undertook to expand the class of stack filters and to increase the number of degrees of freedom in the design. They employed a fuzzy Boolean function in which the output Boolean function takes a continuous value between “0” and “1,” and proposed a fuzzy stack filter defined by that function. Up to the present, the fuzzy median filter and the fuzzy center weighted median filter have been presented as the most fundamental and simplest fuzzy stack filters. This paper proposes a fuzzy weighted median filter in which the weighted median filter, which is a more general nonlinear filter, is given a fuzzy property through the stack filter. The fuzzy weighted median filter changes continuously from the weighted median filter to the weighted average filter by varying the setting of the fuzzy Boolean function. This implies that the fuzzy weighted median filter has a high noise elimination ability for both impulsive and Gaussian noise. The fuzzy weighted median filter can be designed independently for the weight function and the fuzzy Boolean function. This paper aims at a simple design for the weight function and the fuzzy Boolean function, without losing its general character. The weight is approximated by an S-shaped function with only the distance from the processed point as the parameter, and the fuzzy Boolean function is approximated by a sigmoid function. The design is reduced to the determination of four parameters, which is performed by the LMS algorithm. Through application examples, the properties and the effectiveness of the fuzzy weighted median filter are revealed. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(10): 40–49, 1999 [ABSTRACT FROM AUTHOR]

Nonlinear filters are known to be effective for restoration of image signals subject to additive noise. Among them, the most typical are median filters, and particularly popular are stack filters. Signal processing in the stack filters involves the following three stages: threshold value decomposition, calculation of the Boolean function output at each level, and signal synthesis. The Boolean function is defined by the binary input/output. However, to achieve better filter characteristics and design diversity, the authors considered using fuzzy Boolean functions defined by continuous output values from 0 to 1, rather than conventional Boolean functions. In the current study, the authors performed fuzzification of such common stack filters as the median filter and center weighted median (CWM) filter. Fuzzification was performed by using fuzzy Boolean functions to define the median filter or the CWM filter. The fuzzy Boolean function is derived from fuzzy inference. As a next step, the authors developed a method for fuzzy inference optimization (tuning method). © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(2): 83–94, 1999 [ABSTRACT FROM AUTHOR]

The authors have previously proposed a fuzzy stack filter that is defined by a fuzzy Boolean function. We have also presented a specific design method (called the fuzzy Boolean function determination method) for the most fundamental fuzzy stack filter, the FCWM (fuzzy center weighted median). By varying the fuzzy Boolean function, we can achieve both an arbitrary CWM filter and a weighted average value filter in which only the weights at arbitrary processing points are varied. Hence, in comparison with the CWM filter, our filter is better at eliminating Gaussian noise. In this paper, to improve the reconstruction accuracy of nonsteady state signals, such as the image signals, a data-dependent FCWM (DD-FCWM) is proposed anew. The data-dependent filter is an adaptive filter in which the filter parameters are varied in response to the nature of the data near the processing point (local information). In a DD-FCWM filter, the fuzzy Boolean function is varied by using local information. We demonstrate that the proposed DD-FCWM filter uses the local signal information to appropriately vary, not only the weights of the processing points, but also the filter mode (average value type or median type). Furthermore, by use of image processing examples, we demonstrate that highly accurate signal reconstruction can be attained. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(8): 27–40, 1998 [ABSTRACT FROM AUTHOR]

Radioactive pollution detection plays a key role in nuclear technology application. In this paper, an array-type of nuclear pollution detection system is designed for the detection scenario of complex surfaces. Firstly, to get the three-dimensional point cloud of the surface, a complex surface was modeled based on the geometric ranging model of a two-dimensional laser profilometer and the motion model of a two-degree-of-freedom displacement platform. Secondly, an 'S' type scanning scheme of profilometer was developed to overcome the problem of limited scanning area of the profilometer. Thirdly, Euclidean distance weighted median filtering was used to solve the impulsive noise that may occur during the point cloud acquisition process. Finally, the 3D point cloud information of the complex surface was used for controlling the movement of the 6 × 6 array channel pollution detector to complete the α and β particle measurement tasks. A mechanical platform was constructed for experiments, the results are as follows. The working range of this system is from −5 cm to 5 cm in elevation difference of surfaces, and the accuracy is 12 μm in surface height measuring. It takes 26.13 s to perform a detection task including surface scanning and the detector moving, and scanning accuracy is 0.35 × 0.35 mm2. The maximum control error of the surface contamination detector is 0.4 mm. Specifically, the detection area of the system reaches 240 × 240 mm2. The results show that the system acquires three-dimensional terrain information, and realizes control over the movement of the pollution detector accurately and then completes the detection of α and β particles effectively. [ABSTRACT FROM AUTHOR]

The rank ordering of samples is widely used in robust nonlinear signal processing. Recent advances in nonlinear filtering algorithms have focused on combining spatial and rank (SR) order information into the filtering process to allow spatial correlations to be exploited while retaining the robust characteristics of strict rank order methods. Further generalization can be achieved by replacing the crisp, or binary, SR information utilized by most methods with more general fuzzy SR information. Indeed, by exploiting fuzzy methodologies real valued SR orderings can be defined that not only relate the spatial and rank orderings of samples, but also includes information on sample spread. This paper utilizes this approach to define fuzzy ranking and fuzzy order statistics. Properties of these concepts are discussed and several previously defined filters are generalized by including fuzzy concepts. Specifically, the fuzzy median, fuzzy rank conditioned rank selection, and fuzzy weighted median filters are defined. Optimization of the parameters for these filters are discussed. Simulation results are presented to show the advantages of these fuzzy filters over their crisp counterparts.