Vector median filters

Median filters (MF) are used both to filter ‘salt and pepper’ noise from signals and images and in other signal processing applications. In this paper, an extension of the MF, the vector median filter (VMF), is introduced. As opposed to the MF, the VMF outputs for each window location a number of data elements. By adjusting the VMF parameters, the MF is obtained as a VMF special case. Just like the MF, the VMF filters impulses while simultaneously preserving step changes in a signal. The VMF's principal advantage is that it reduces the total stored data signal computation time while it produces visual outputs comparable to that of an MF. Deterministic and statistical properties of the VMF are examined. Computer-generated experimental results are also presented.     

Vector median filters

Two nonlinear algorithms for processing vector-valued signals are introduced. The algorithms, called vector median operations, are derived from two multidimensional probability density functions using the maximum-likelihood-estimate approach. The underlying probability densities are exponential, and the resulting operations have properties very similar to those of the median filter. In the vector median approach, the samples of the vector-valued input signal are processed as vectors. The operation inherently utilizes the correlation between the signal components, giving the filters some desirable properties. General properties as well as the root signals of the vector median filters are studied. The vector median operation is combined with linear filtering, resulting in filters with improved noise attenuation and filters with very good edge response. An efficient algorithm for implementing long vector median filters is presented. The noise attenuation of the filters is discussed, and an application to velocity filtering is shown     

Topological median filters

This paper describes the definition and testing of a new type of median filter for images. The topological median filter implements some existing ideas and some new ideas on fuzzy connectedness to improve, over a conventional median filter, the extraction of edges in noise. The concept of alpha-connectivity is defined and used to create an algorithm for computing the degree of connectedness of a pixel to all the other pixels in an arbitrary neighborhood. The resulting connectivity map of the neighborhood effectively disconnects peaks in the neighborhood that are separated from the center pixel by a valley in the brightness topology. The median of the connectivity map is an estimate of the median of the peak or plateau to which the center pixel belongs. Unlike the conventional median filter, the topological median is relatively unaffected by disconnected features in the neighborhood of the center pixel. Four topological median filters are defined. Qualitative and statistical analyses of the four filters are presented. It is demonstrated that edge detection can be more accurate on topologically median filtered images than on conventionally median filtered images.     

Convergence properties of median and weighted median filters

It has been shown that assuming the first and last value carry-on appending strategy, a finite number of passes of the same median filter to an arbitrary signal of finite length results in a root signal that will be invariant to additional filtering passes. This so-called convergence property is reproven using an extremely simple approach. In addition, the well-known idempotent property (i.e., where convergence is achieved with only one filtering pass) of a recursive median filter is reproven similarly, and the convergence behavior of weighted median filters is studied     

Sharpening vector median filters

A sharpening vector median (VM) filter for simultaneous denoising and enhancing vector-valued signals is introduced. This filter uses the trimmed aggregated distance minimization concept and robust vector order statistics to enhance edges and image details while retaining the noise removal characteristics of the standard VM operator. The procedure accommodates various design, implementation and application objectives by enhancing the vector-valued signals depending on the local image statistics and/or the user's needs. The filter properties discussed in this paper are proven and suggest that the proposed solution is a robust vector processing operator. The performance and efficiency of the filter are analyzed and commented upon. Examples from its application to color image filtering and virtual restoration of artworks are provided.     

Generalized multistage median filters.

As an extension of the multistage median filters, a class of r -filters is presented. Some properties of these filters are discussed. It is shown that the filters can smooth noise and preserve details of images efficiently.     

Deterministic properties of analog median filters

Two key deterministic properties of analog median filters are established. The first is that root signals are characterized by a special class of locally monotone functions, and the second is that the repeated application of a median filter produces a root signal which retains significant features in the original data. Both results are extensions of well known facts for discrete median filters. In addition, it is shown that these properties do not extend to a natural multidimensional version of the median filter     

二值FIR中值混合滤波

本文对传统的FIR中值混合(FMH)滤波,给出了一种二值FMH滤波的概念,并在此基础上,首次建立了VLSI实现的实时信号处理电路结构。     

Analysis of two-dimensional center weighted median filters

Center weighted median (CWM) filters, which have been recognized as detail preserving filters, are an important and the simplest subclass of weighted median (WM) filters. In this paper, we analyze the root signals of two-dimensional (2-D) CWM filters. In particular, we derive the required form for a signal to be a root of a 2-D CWM filter. The required form of signals to be roots is then used to evaluate the detail preserving properties of 2-D CWM filters. As examples, the detail preserving properties of some 2-D CWM filters are compared with other detail preserving filters, i.e. multilevel median filters. The generation of binary root signals of some 2-D CWM filters is treated in the term of the smallest surviving object (SSO). It is illustrated by some examples that CWM filters with different orientation of windows can be useful in image segmentation.     

Adding explicit content classification to nonlinear filters

Nonlinear filters are known for better edge-preserving performance in image processing applications as they can adapt to some local image content. Instead of trying to find a single optimal filter that can adapt to all the image content, some classification-based approaches first apply a pre-classification on the image content and then employ an optimal linear filter for each content class. It is interesting to extend the linear filter in such approaches to a nonlinear filter and see if the explicit content classification, can still add to such inherently adapting nonlinear filters. In this paper, we investigate several categories of nonlinear filters: order statistics filters, hybrid filters, neural filters, and bilateral filters with different forms of content classification in various image processing applications, including image de-blocking, noise reduction, and image interpolation.     

Weighted median filters: An analog implementation

The feasibility of implementing analog CMOS VLSI weighted median filters for image and signal processing is discussed. The proposed weighted median filter uses a transconductance comparator as a basic cell, where the output saturation current is used as the weight parameter in the median filter. Experimental results of the proposed analog weighted median filter for an ON Semiconductor 0.5 μm technology through MOSIS fabricated prototype are shown.     

Weighted median filters with sigma-delta modulation encoding

Digital decimation filters play a fundamental role in oversampled sigma-delta A/D decoders. In this paper, we first show that weighted median (WM) filtering of a demodulated sequence (at the Nyquist rate) can be implemented concurrently in the A/D decoder. Through a simple modification of the binary time-series outputted by the A/D modulator, the sequence obtained after the sigma-delta modulation (SDM) decoder is shown to be equivalent to WM filtering the multilevel sequence at the Nyquist rate. Second, we show that WM filters can be used for SDM decimation filters and that these filters are readily implemented in the SDM binary domain. A very promising characteristic of SDM converters equipped with WM decimating filters is that sharp discontinuities (edges) can be preserved and acquired. Thus, the bandlimited constraint imposed on the input signals can be relaxed making SDM more attractive to A/D conversion of signals containing sharp transitions. The proposed signal processing algorithms, in essence, combine A/D sigma-delta converters and WM filters into a single programmable system     

Fast adaptive optimization of weighted vector median filters

Weighted vector median (WVM) filters are effective tools for multichannel signal processing. To obtain the desired filtering behavior and characteristic, the WVM filter weights must be determined in an appropriate manner. In this paper, we first analyze previously defined approaches for WVM filter optimization and show their drawbacks related to derivative computation and vector direction information utilization. Based on this analysis, we propose two fast adaptive algorithms for WVM filter design. Proposed Algorithm I computes locally optimal weight changes at each iteration and updates the filter weights accordingly. This algorithm does not involve derivative computation, thus eliminating the instability caused by derivative approximations utilized in previous approaches. Proposed Algorithm II extends the results from established marginal weighted median optimization methods to the vector case by error metric generalization. Both algorithms can be applied to WVM filters using the L/sub p/ norm, while Algorithm I can operate on more general distance metrics. The presented simulation results show that both algorithms are effective, fast, and stable; they perform well under a wide range of circumstances.     

Applications of rank-based median filters in power electronics

A class of robust, rank-based signal processing filters is considered, particularly with regard to its usefulness in the power electronics field. This class of nonlinear filters is characterized by the inclusion of a sorting element in the signal path. The sorting operation allows these filters to suppress impulsive noise while preserving edges and monotonic sections of signals. This introductory work concentrates primarily on the median filter, it being the most accessible filter of the class. A working knowledge of issues arising in design and implementation is developed     

Adaptive median filters: new algorithms and results

Based on two types of image models corrupted by impulse noise, we propose two new algorithms for adaptive median filters. They have variable window size for removal of impulses while preserving sharpness. The first one, called the ranked-order based adaptive median filter (RAMF), is based on a test for the presence of impulses in the center pixel itself followed by a test for the presence of residual impulses in the median filter output. The second one, called the impulse size based adaptive median filter (SAMF), is based on the detection of the size of the impulse noise. It is shown that the RAMF is superior to the nonlinear mean L(p) filter in removing positive and negative impulses while simultaneously preserving sharpness; the SAMF is superior to Lin's (1988) adaptive scheme because it is simpler with better performance in removing the high density impulsive noise as well as nonimpulsive noise and in preserving the fine details. Simulations on standard images confirm that these algorithms are superior to standard median filters.     

Criteria of convergence of median filters and perturbation theorem

Repeated application of the median filter to any finite length sequence converges to a root in a finite number of passes. This requires padding on each end of the sequence. In some applications, such padding may be inappropriate because of the overemphasis on the endpoints. However, there are some of infinite-length sequences whose median filters are not convergent. In this paper, necessary and/or sufficient conditions on infinite-length sequences are derived in order that their median filters converge to roots of category I. Moreover, we study convergence of median filters of perturbed sequences. The results obtained extend the previous theory on convergence of median filters     

Directed graph representation for root-signal set of median filters

Median filtering is a simple digital technique for smoothing signals. A root signal is defined as an invariant signal to the median filtering. We describe directed graph representation for the root-signal set of median filters. The directed graph representation allows us to obtain a set of roots and the number of roots in a straightforward manner.     

Recursive weighted median filters admitting negative weights andtheir optimization

A recursive weighted median (RWM) filter structure admitting negative weights is introduced. Much like the sample median is analogous to the sample mean, the proposed class of RWM filters is analogous to the class of infinite impulse response (IIR) linear filters. RWM filters provide advantages over linear IIR filters, offering near perfect “stopband” characteristics and robustness against noise. Unlike linear IIR filters, RWM filters are always stable under the bounded-input bounded-output criterion, regardless of the values taken by the feedback filter weights. RWM filters also offer a number of advantages over their nonrecursive counterparts, including a significant reduction in computational complexity, increased robustness to noise, and the ability to model “resonant” or vibratory behavior. A novel “recursive decoupling” adaptive optimization algorithm for the design of this class of recursive WM filters is also introduced. Several properties of RWM filters are presented, and a number of simulations are included to illustrate the advantages of RWM filters over their nonrecursive counterparts and IIR linear filters     

On the convergence and roots of order-statistics filters

We propose a comprehensive theory of the convergence and characterization of roots of order-statistics filters. Conditions for the convergence of iterations of order-statistics filters are proposed. Criteria for the morphological characterization of roots of order-statistics filters are also proposed