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.     

基于颜色分量单独噪声检测的混合中值滤波器

为了进一步提高开关型矢量中值滤波器滤除脉冲噪声尤其是细微噪声的能力,提出了一种基于颜色分量单独噪声检测的开关型标量和矢量混合中值滤波器(SVHMF)。与其它经典矢量滤波器相比,SVHMF最大的不同在于它是根据对像素点各个颜色单独进行噪声检测的结果,采用与之相适应的标量和矢量混和滤波方法。新滤波器可以最大限度地保护彩色图像图像像素中未被噪声干扰的颜色分量数据,从而可以进一步提高滤波效果。实验数据表明:SVHMF的滤波效果明显优于其它各类在彩色图像降噪中得到广泛应用的矢量中值滤波器。     

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.     

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     

Analysis of weighted median filters based on inequalities relating the weights

By considering all orderings of the input samples, which are discrete-time continuous-valued, it is shown here that a weighted median (WM) filter of spanN can be specified unambiguously by 2^N–1 consistent linear inequalities relating the weights. This specification is identical to that of a self-dual threshold function with the same weights. It is also shown that WM filters with symmetric weights can be specified by ternary threshold functions. Based on these inequalities, properties of WM filters which can be used to check equivalence of some WM filters are derived.This work was supported in part by the National Science Foundation under Grant DCI-8611859. A portion of this work was presented at the IEEE International Symposium on Circuits and Systems, Portland, Oregon, May 1989.     

Fuzzy repairable reliability based on fuzzy gert

Military equipment and weapon systems have become more advanced, precise and complex. Requirements of threat and readiness have been raised. Nowadays, the advance of weapon systems and their logistic support places the emphasis on the life cycle in the initial design. However, reliability analysis is the main work of logistic engineering. Its aim is to develop the best design for weapon systems operating in a special operation environment. Accordingly, there are many factors to consider in the reliability of weapon systems. Generally, those factors are of an uncertain nature. Traditionally, we use probability theory to treat the reliability of a weapon system. The probabilistic approach can only represent the randomness of a success or failure event, and requires complete data and predetermined conditions. Fuzzy sets theory can efficiently treat the above characteristics and shortcomings. Therefore we will propose a method and technology of fuzzy system reliability to solve the above problems.In this paper we first formulate the building membership functions of component reliability based on the α-cut method. Secondly, when the membership functions of the components are built, we can propose some fuzzy mathematic models for solving fuzzy system reliability. Different models and approaches have been studied and proposed in this research. In an unrepairable system, we have built two methods. In a repairable system, we will propose a fuzzy GERT (graphical evaluation and review technique) method to calculate the fuzzy reliability. For a simple and efficient computation, we have developed systematic and practical algorithms to calculate and analyze fuzzy system reliability. We have also presented an example of a military operation mission to demonstrate our proposed methods.     

基于神经网络与模糊理论的模糊自编码器

自编码器是深度学习中广泛使用的一种网络,许多深度网络都以其为基础构建特定的网络结构。对于传统自编码器及其变体,不同层单元之间的参数被限定为普通实数,这在某种程度限制了自编码器的能力,为了克服这种问题,文中以模糊理论为基础,通过将自编码器的参数设置为模糊数,构建了模糊自编码器模型,并引入了相应的学习算法。基于MINIST手写数字数据集的实验表明,模糊自编码器在表示能力和鲁棒性方面都要优于普通自编码器。     

A new approach to vector median filtering based on space fillingcurves

The availability of a wide set of multidimensional information sources in different application fields (e.g., color cameras, multispectral remote sensing imagery devices, etc.) is the basis for the interest of image processing research on extensions of scalar nonlinear filtering approaches to multidimensional data filtering. A new approach to multidimensional median filtering is presented. The method is structured into two steps. Absolute sorting of the vectorial space based on Peano space filling curves is proposed as a preliminary step in order to map vectorial data onto an appropriate one-dimensional (1-D) space. Then, a scalar median filtering operation is applied. The main advantage of the proposed approach is the computational efficiency of the absolute sorting step, which makes the method globally faster than existing median filtering techniques. This is particularly important when dealing with a large amount of data (e.g., image sequences). Presented results also show that the filtering performances of the proposed approach are comparable with those of vector median filters presented in the literature.     

基于模糊中值的IRFPA自适应盲元检测与补偿

红外焦平面阵列(IRFPA)的盲元既包括因材料与制造工艺的缺陷而导致的固定盲元,也包括因环境温度的漂移而出现的随机盲元.基于场景的盲元检测与补偿算法是去除这两种盲元,提高IRFPA 成像质量的有效手段.针对目前滤波类场景检测算法无法有效区分弱小点目标和随机盲元的缺陷,重点研究了随机盲元的响应特性和噪声特性,并提出了一种基于模糊中值与时域累积的盲元自适应检测与补偿算法.首先利用模糊中值滤波器从场景中提取出潜在的盲元,并通过多帧累积确定固定盲元和随机盲元的正确分布,最后对盲元进行实时补偿.实验结果证明:该算法可以有效地实现对盲元的校正,同时避免对弱小点目标的误判别.     

EMCCD图像自适应模糊中值滤波算法研究

针对电子倍增CCD（EMCCD）图像噪声密度随着增益的变化而变化,提出了一种基于噪声点检测的自适应模糊中值滤波算法。该算法由模糊滤波模块和自适应模块两部分组成。首先,该算法对滤波窗口内的中心点进行噪声检测;然后对检测为噪声的像素点引入双阈值,并根据引入的阈值和滤波窗口内的中值建立噪声点的模糊隶属函数,根据模糊隶属函数对噪声点进行滤波处理后输出;最后采用自适应模块调整待处理图像的像素。仿真及实验结果表明,新算法不仅能够有效地将图像中的噪声去除,而且很好地保护了图像中的细节和边缘,PSNR比传统的自适应中值滤波算法平均提高了15 dB以上;该算法在低噪声密度情况下性能明显好于其他中值滤波器,在高噪声密度情况下性能也比较稳定。     

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.     

General expressions for vector and scalar potentials

This paper derives general expressions for the vector and scalar potentials in a bounded region. The necessary conditions for a vector function to be, respectively, the curl of another vector function and the gradient of a scalar function are first presented. Then with the help of Helmholtz's theorem, general expressions for the vector and scalar potentials are derived. The results are summarized in two theorems. Three corollaries are presented. The first one indicates that a vector function in a simply bounded space is the curl of another vector function, if and only if, its divergence is equal to zero. The second one indicates that a vector function in a simply connected space is the gradient of a scalar function, if and only if, its curl is equal to zero. The last one indicates that the magnetic induction is the curl of a vector potential. The classical textbook by Jeans (1915) presents the same conclusion about the magnetic induction using an erroneous discussion. The point where the discussion breaks down is indicated. Applications to antenna theory as well as four simple examples are shown to facilitate the understanding of the present discussion     

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     

Image distortions produced by mean, median and mode filters

The paper reviews earlier continuum models of image distortions produced by mean, median and mode filters, and shows that rigorous discrete calculations are required to give predictions that agree accurately with experimental measurements in the median case. In addition, the paper describes what is believed to be the first discrete model of the distortions produced by median filters that is able to predict essentially exact numerical values of relevant boundary shifts. Not only does it take proper account of the actual discrete processes that are involved in the median computation, but also it reveals important intricacies about the operation of median filters and demonstrates clearly the unexpectedly large anisotropy that this type of filtering produces     

On root structures and convergence properties of weighted median filters

A weighted median filter is a nonlinear digital filter consisting of a window of length 2N + 1 and a weight vector W=(W_? N,..., W₀,..., W_N). A root signal of a median type filter is a signal that is invariant to the filter. However, not all weighted median filters possess the convergence property. In this paper, we shall study the root structures and the convergence behavior of a subclass of weighted median filters, calledclass- 1 filters, which is symmetric in its weight vector. We shall introduce an important parameter, calledfeature value, and show that any one-dimensional unappended signal of lengthL will converge to a root signal in at most $$3\left\lceil {\frac{{L - 2}}{{2(2N + 2 - p)}}} \right\rceil$$ passes of aclass ?1 filter with window width 2N + 1 and thefeature value p.     

V-l scalar circuits based on CCIIs

CCII-based electronic circuits which allow independent scaling of the voltage and current in the terminals of electronic elements are presented. The proposed circuits can compensate the non-idealities inherent in the V-I characteristics of an electronic element, thus improving the performance of the circuit in which the element is employed. An illustrative example by PSPICE simulation shows satisfactory results     

基于噪声估计和双加权的彩色图像矢量中值滤波

针对彩色图像椒盐噪声滤除中保护色彩和细节这个关键问题,提出了一种基于噪声估计和双加权的滤波新算法.噪声估计采用二级估计策略,第1级基于灰度最大、最小值进行粗估计,第2级采用加权方向算子进行精估计.对非噪声点保持像素灰度不变,对噪声点设计了空间和灰度双加权的矢量中值滤波算法(VMF).实验结果表明,新算法对低、中密度的彩...