characterizing completable fuzzy metric spaces recently we showed the existence of a fuzzy metric space in the sense of george and veeramani which is not completable fuzzy sets and systems 130 2002 399 here we present an internal characterization of those fuzzy metric spaces that are completable some applications are derived and some illustrative examples are given

on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

nonlocal discrete regularization on weighted graphs a framework for image and manifold processing we introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing the approach considers the problem as a variational one which consists of minimizing a weighted sum of two energy terms a regularization one that uses a discrete weighted dirichlet energy and an approximation one this is the discrete analogue of recent continuous euclidean nonlocal regularization functionals the proposed formulation leads to a family of simple and fast nonlinear processing methods based on the weighted laplace operator parameterized by the degree of regularity the graph structure and the graph weight function these discrete processing methods provide a graph based version of recently proposed semi local or nonlocal processing methods used in image and mesh processing such as the bilateral filter the tv digital filter or the nonlocal means filter it works with equal ease on regular 2 d and 3 d images manifolds or any data we illustrate the abilities of the approach by applying it to various types of images meshes manifolds and data represented as graphs

rapid and brief communication the solutions of equation based noise detector for an adaptive median filter techniques of noise detection have been widely applied in impulse noise reduction however the phenomenon of pixel misclassification is very obvious in high noise density in order to improve pixel identification in this paper the new noise detector is proposed based on solutions of equations an estimated block of every 8x8 block of a noise image is generated then according to relationships between these noise blocks and their estimated blocks corrupted and uncorrupted pixels are identified during image filtering a noise detection based adaptive median algorithm is presented experimental results show that the proposed filter can well reduce the impulse noise and preserve more details of original images

ends of maps ii versions of the finiteness obstruction and simple homotopy theory within e overx are developed this provides a setting for obstructions to the map analogs of the end ands cobordism theorems for manifolds these are applied to study equivariant mapping cylinder neighborhoods in topological group actions triangulations of locally triangulable spaces and block bundle structures on approximate fibrations

median filter based on fuzzy rules and its application to image restoration abstract a novel median type filter controlled by fuzzy rules is proposed in order to remove impulsive noises on signals such as images median filter is well known for removing impulsive noises but this filter distorts the fine structure of signals as well the filter proposed here is obtained as a weighted sum of the input signal and the output of the median filter and the weight is set based on fuzzy rules concerning the states of the input signal sequence moreover this weight is obtained optimally by a learning method so that the mean square error of the filter output for some training signal data can be the minimum some results of image processing show the high performance of this filter moreover the influence of the training signal on the filter performance is shown

a robust structure adaptive hybrid vector filter for color image restoration a robust structure adaptive hybrid vector filter is proposed for digital color image restoration in this paper at each pixel location the image vector i e pixel is first classified into several different signal activity categories by applying a modified quadtree decomposition to luminance component image of the input color image a weight adaptive vector filtering operation with an optimal window is then activated to achieve the best tradeoff between noise suppression and detail preservation through extensive simulation experiments conducted using a wide range of test color images the filter has demonstrated superior performance to that of a number of well known benchmark techniques in terms of both standard objective measurements and perceived image quality in suppressing several distinct types of noise commonly considered in color image restoration including gaussian noise impulse noise and mixed noise

alpha trimmed means and their relationship to median filters suppose that x is a finite set of n numbers the trimmed mean of x is obtained by sorting x into ascending order removing trimming a fixed fraction alpha 0 leq alpha leq 0 5 from the high and low ends of the sorted set and computing the average of the remaining values when applied to a sliding window of length lw the trimming process is called trim filtering for 0 5 the trimmed mean of a set is the median of the set and the filtering operation is called median filtering repeated application of a median filter to the output of a previous median filter of the same length lw eventually produces a signal which is invariant to median filtering this final signal is called the root signal this paper explains the relationship between trimmed means and median filters derives a simple straightforward and fast algorithm for applying a median filter and provides a new explanation of the convergence of repeated median filtering to the root signal the latter result incorporates an approach which permits generalization of the associated concepts to a larger class of index map filters

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

optimal median type filtering under structural constraints this paper presents a method for the design of median type filters that achieve the maximum noise attenuation under structural constraints imposed by the requirement of preserving certain signal or image features as compared with the design of optimal weighted median wm filters that calls for solving a set of linear inequalities this method is extremely simple yet general enough the filter is obtained by modifying directly the boolean function of a median filter and an analytic closed form representation of its boolean function can be obtained furthermore it is proven theoretically that under the same set of structural constraints the filter designed in this way will never do worse in removing i i d noise with any distribution than the optimal wm filter improvements as high as 41 46 and 52 have been achieved in simulations in a 2 d case for the uniform gaussian and double exponential distributions respectively also the improvement in the impulsive noise environment is very significant as is demonstrated by an image enhancement application

weighted centroid neural network for edge preserving image compression an edge preserving image compression algorithm based on an unsupervised competitive neural network is proposed the proposed neural network the called weighted centroid neural network wcnn utilizes the characteristics of image blocks from edge areas the mean residual vector quantization m rvq scheme is utilized in this proposed approach as the framework of the proposed algorithm the edge strength of image block data is utilized as a tool to allocate the proper code vectors in the proposed wcnn the wcnn successfully allocates more code vectors to the image block data from edge area while it allocates less code vectors to the image black data from shade or non edge area when compared to conventional neural networks based on vq algorithm as a result a simple application of wcnn to an image compression problem gives improved edge characteristics in reconstructed images over conventional neural network based on vq algorithms such as self organizing map som and adaptive som

identification of time delays using a polynomial identification method abstract an algorithm for the exact least squares identification of an approximate continuous time time delay system is derived and its operation verified by simulation

gradient estimation using wide support operators one of the fastest methods of localizing edges in images is based on small gradient kernels such as sobel prewitt and roberts although small gradient kernels provide a fast way of computing the gradients they have little control over noise edge location and edge orientation they are known to be only sensitive to step edges and fail to detect smooth boundaries on the other hand large kernels provide superior noise suppression characteristics but they suffer from wide response area around edges they cause edges of neighboring objects to merge due to their wide support problems associated with large gradient kernels prevent their widespread usage this paper presents a fuzzy topology based method to facilitate the use of larger gradient kernels the new method effectively limits the response area around the edge and prevents neighboring objects to affect each other synthetic images are used to show the superior noise suppression properties and response characteristics to both step and ramp edges natural images are also used to assess the performance of the newly proposed topological gradient estimation qualitatively

application of partition based median type filters for suppressing noise in images an adaptive median based filter is proposed for removing noise from images specifically the observed sample vector at each pixel location is classified into one of m mutually exclusive partitions each of which has a particular filtering operation the observation signal space is partitioned based an the differences defined between the current pixel value and the outputs of cwm center weighted median filters with variable center weights the estimate at each location is formed as a linear combination of the outputs of those cwm filters and the current pixel value to control the dynamic range of filter outputs a location invariance constraint is imposed upon each weighting vector the weights are optimized using the constrained lms least mean square algorithm recursive implementation of the new filter is then addressed the new technique consistently outperforms other median based filters in suppressing both random valued and fixed valued impulses and it also works satisfactorily in reducing gaussian noise as well as mixed gaussian and impulse noise

fuzzy peer groups for reducing mixed gaussian impulse noise from color images the peer group of an image pixel is a pixel similarity based concept which has been successfully used to devise image denoising methods however since it is difficult to define the pixel similarity in a crisp way we propose to represent this similarity in fuzzy terms in this paper we introduce the fuzzy peer group concept which extends the peer group concept in the fuzzy setting a fuzzy peer group will be defined as a fuzzy set that takes a peer group as support set and where the membership degree of each peer group member will be given by its fuzzy similarity with respect to the pixel under processing the fuzzy peer group of each image pixel will be determined by means of a novel fuzzy logic based procedure we use the fuzzy peer group concept to design a two step color image filter cascading a fuzzy rule based switching impulse noise filter by a fuzzy average filtering over the fuzzy peer group both steps use the same fuzzy peer group which leads to computational savings the proposed filter is able to efficiently suppress both gaussian noise and impulse noise as well as mixed gaussian impulse noise experimental results are provided to show that the proposed filter achieves a promising performance

a switching median filter with boundary discriminative noise detection for extremely corrupted images a novel switching median filter incorporating with a powerful impulse noise detection method called the boundary discriminative noise detection bdnd is proposed in this paper for effectively denoising extremely corrupted images to determine whether the current pixel is corrupted the proposed bdnd algorithm first classifies the pixels of a localized window centering on the current pixel into three groups lower intensity impulse noise uncorrupted pixels and higher intensity impulse noise the center pixel will then be considered as uncorrupted provided that it belongs to the uncorrupted pixel group or corrupted for that two boundaries that discriminate these three groups require to be accurately determined for yielding a very high noise detection accuracy in our case achieving zero miss detection rate while maintaining a fairly low false alarm rate even up to 70 noise corruption four noise models are considered for performance evaluation extensive simulation results conducted on both monochrome and color images under a wide range from 10 to 90 of noise corruption clearly show that our proposed switching median filter substantially outperforms all existing median based filters in terms of suppressing impulse noise while preserving image details and yet the proposed bdnd is algorithmically simple suitable for real time implementation and application

wavelet thresholding of multivalued images in this paper a denoising technique for multivalued images exploiting interband correlations is proposed a redundant wavelet transform is applied and denoising is applied by thresholding wavelet coefficients specific functions of the wavelet coefficients are defined that exploit interscale and or interband correlation of the signal three functions are studied the square of the wavelet coefficients products of coefficients at adjacent scales and products of coefficients from different bands for these functions the signal and noise probability density functions pdf become more separated the high signal correlation between bands is exploited by summing these products over all bands in this way separating noise and signal pdfs even more the noise pdf of the proposed quantities is derived analytically and from this a wavelet threshold is derived the technique is demonstrated to outperform single band wavelet thresholding on multispectral remote sensing images and on multimodal mri images

stack filters the median and other rank order operators possess two properties called the threshold decomposition and the stacking properties the first is a limited superposition property which leads to a new architecture for these filters the second is an ordering property which allows an efficient vlsi implementation of the threshold decomposition architecture motivated by the success of rank order filters in a wide variety of applications and by the ease with which they can now be implemented we consider in this paper a new class of filters called stack filters they share the threshold decomposition and stacking properties of rank order filters but are otherwise unconstrained they are shown to form a very large class of easily implemented nonlinear filters which includes the rank order operators as well as all compositions of morphological operators the convergence properties of these filters are investigated using techniques similar to those used to determine root signal behavior of median filters the results obtained include necessary conditions for a stack filter to preserve monotone regions or edges in signals the output distribution for these filters is also found all the stack filters of window width 3 are determined along with their convergence properties among these filters are found two which we have named asymmetric median filters they share all the properties of median filters except that they remove impulses of one sign only that is one removes only positive going edges the other removes only negative going edges while the median filter removes impulses of both signs this investigation of the properties of stack filters thus produces several new useful and easily implemented filters

feature based wavelet shrinkage algorithm for image denoising a selective wavelet shrinkage algorithm for digital image denoising is presented the performance of this method is an improvement upon other methods proposed in the literature and is algorithmically simple for large computational savings the improved performance and computational speed of the proposed wavelet shrinkage algorithm is presented and experimentally compared with established methods the denoising method incorporated in the proposed algorithm involves a two threshold validation process for real time selection of wavelet coefficients the two threshold criteria selects wavelet coefficients based on their absolute value spatial regularity and regularity across multiresolution scales the proposed algorithm takes image features into consideration in the selection process statistically most images have regular features resulting in connected subband coefficients therefore the resulting subbands of wavelet transformed images in large part do not contain isolated coefficients in the proposed algorithm coefficients are selected due to their magnitude and only a subset of those selected coefficients which exhibit a spatially regular behavior remain for image reconstruction therefore two thresholds are used in the coefficient selection process the first threshold is used to distinguish coefficients of large magnitude and the second is used to distinguish coefficients of spatial regularity the performance of the proposed wavelet denoising technique is an improvement upon several other established wavelet denoising techniques as well as being computationally efficient to facilitate real time image processing applications

on second moment properties of median filtered sequences of independent data in this paper we present the derivation of the bivariate distribution function for median filtered sequences of independent arbitrary second order random variables this result is then used to qualitatively analyze second moment properties of median filtered data the results hint towards a low pass characteristic of the median filters and a low dependency of the output spectrum on input alphabet size and distribution

using uncorrupted neighborhoods of the pixels for impulsive noise suppression with anfis in this paper a novel adaptive network based fuzzy inference system anfis based filter abf is presented for the restoration of images corrupted by impulsive noise in the abf is performed in two steps in the first step impulse detection is realized by using statistical tools in the second step a nonlinear filtering scheme based on anfis is performed for only the corrupted pixels detected in the first step to demonstrate the effectivity of abf at the removal of high level in extensive simulations were realized for abf and nine different comparison filters empirical results indicate that the proposed filter achieves a better performance than the comparison filters in terms of noise suppression and detail preservation even when the images are highly corrupted by in

a simple neuro fuzzy impulse detector for efficient blur reduction of impulse noise removal operators for digital images a new impulse noise detector based on neuro fuzzy methods is presented the proposed detector comprises two identical neuro fuzzy subdetectors combined with a decision maker the internal parameters of the subdetectors are adaptively adjusted by training training of the subdetectors is accomplished by using a simple computer generated artificial image the detector can be combined with any impulse noise removal operator the operation of the detector is completely independent of the noise removal operator and it has no influence on the filtering behavior of the operator experimental results show that the proposed detector significantly reduces the distortion effects of any impulse noise removal operator even if the operator already has its own noise detector

self adaptive algorithm of impulsive noise reduction in color images in this paper a new approach to the problem of impulsive noise reduction in color images is presented the basic idea behind the new image filtering technique is the maximization of the similarities between pixels in a predefined filtering window the improvement introduced to this technique lies in the adaptive establishing of parameters of the similarity function and causes that the new filter adapts itself to the fraction of corrupted image pixels the new method preserves edges corners and fine image details is relatively fast and easy to implement the results show that the proposed method outperforms most of the basic algorithms for the reduction of impulsive noise in color images

a hybrid neuro fuzzy filter for edge preserving restoration of images corrupted by impulse noise a new operator for restoring digital images corrupted by impulse noise is presented the proposed operator is a hybrid filter obtained by appropriately combining a median filter an edge detector and a neuro fuzzy network the internal parameters of the neuro fuzzy network are adaptively optimized by training the training is easily accomplished by using simple artificial images that can be generated in a computer the most distinctive feature of the proposed operator over most other operators is that it offers excellent line edge detail and texture preservation performance while at the same time effectively removing noise from the input image extensive simulation experiments show that the proposed operator may be used for efficient restoration of digital images corrupted by impulse noise without distorting the useful information in the image

adaptive two pass rank order filter to remove impulse noise in highly corrupted images in this paper we present an adaptive two pass rank order filter to remove impulse noise in highly corrupted images when the noise ratio is high rank order filters such as the median filter for example can produce unsatisfactory results better results can be obtained by applying the filter twice which we call two pass filtering to further improve the performance we develop an adaptive two pass rank order filter between the passes of filtering an adaptive process is used to detect irregularities in the spatial distribution of the estimated impulse noise the adaptive process then selectively replaces some pixels changed by the first pass of filtering with their original observed pixel values these pixels are then kept unchanged during the second filtering in combination the adaptive process and the second filter eliminate more impulse noise and restore some pixels that are mistakenly altered by the first filtering as a final result the reconstructed image maintains a higher degree of fidelity and has a smaller amount of noise the idea of adaptive two pass processing can be applied to many rank order filters such as a center weighted median filter cwmf adaptive cwmf lower upper middle filter and soft decision rank order mean filter results from computer simulations are used to demonstrate the performance of this type of adaptation using a number of basic rank order filters

an adaptive control algorithm for linear systems having unknown time delay abstract this paper presents an algorithm for adaptive control of linear systems having unknown time delay a rational approximation is used for the delay and it is argued that within this framework the analysis of the properties of the corresponding adaptive control algorithm essentially reduces to the issue of robustness to unmodelled dynamics a global convergence theory is presented using recent methods for analyzing robustness properties of adaptive control algorithms the analysis is supported by simulation results

paper decoupled delay estimation in the identification of differential delay systems based on the variable projection functional in nonlinear least squares theory the estimation of pure time delay is decoupled from the determination of the remaining system parameters for a class of differential delay models the approach utilizes input output data on a fixed finite time interval and avoids estimating unknown initial conditions results of a simulation study are summarized for several examples

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 spl 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

salt and pepper noise removal by median type noise detectors and detail preserving regularization this paper proposes a two phase scheme for removing salt and pepper impulse noise in the first phase an adaptive median filter is used to identify pixels which are likely to be contaminated by noise noise candidates in the second phase the image is restored using a specialized regularization method that applies only to those selected noise candidates in terms of edge preservation and noise suppression our restored images show a significant improvement compared to those restored by using just nonlinear filters or regularization methods only our scheme can remove salt and pepper noise with a noise level as high as 90

robust identification of continuous systems with dead time from step responses in this paper a simple yet robust method is proposed for identification of linear continuous time delay processes from step responses new linear regression equations are derived from the solution and its various order integrals of the process differential equation the regression parameters are then estimated without iterations and explicit relationship between the regression parameters and those in the process are given due to use of the process output integrals in the regression equations the resulting parameter estimation is very robust in the face of large measurement noise in the output the proposed method is detailed for a second order plus dead time model with one zero which can approximate most practical industrial processes covering monotonic or oscillatory dynamics of minimum phase or non minimum phase processes such a model can be obtained without any iteration the effectiveness of the identification method has been demonstrated through simulation and real time implementation

a generalization of median filtering using linear combinations of order statistics we consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence assuming a constant signal in white noise the coefficients in the linear combination are chosen to minimize the output mse for several noise distributions it is shown that the optimal order statistic filter osf tends toward the median filter as the noise becomes more impulsive the optimal osf is applied to an actual noisy image and is shown to perform well combining properties of both the averaging and median filters a more general design scheme for applications involving nonconstant signals is also given

nonlinear regularized reaction diffusion filters for denoising of images with textures denoising is always a challenging problem in natural imaging and geophysical data processing in this paper we consider the denoising of texture images using a nonlinear reaction diffusion equation and directional wavelet frames in our model a curvelet shrinkage is used for regularization of the diffusion process to preserve important features in the diffusion smoothing and a wave atom shrinkage is used as the reaction in order to preserve and enhance interesting oriented textures we derive a digital reaction diffusion filter that lives on graphs and show convergence of the corresponding iteration process experimental results and comparisons show very good performance of the proposed model for texture preserving denoising

a fuzzy noise reduction method for color images a new fuzzy filter is presented for the reduction of additive noise for digital color images the filter consists of two subfilters the first subfilter computes fuzzy distances between the color components of the central pixel and its neighborhood these distances determine in what degree each component should be corrected all performed corrections preserve the color component distances the goal of the second subfilter is to correct the pixels where the color components differences are corrupted so much that they appear as outliers in comparison to their environment experimental results show the feasibility of the proposed approach we compare with other noise reduction methods by numerical measures and visual observations we also illustrate the performance of the proposed method as preprocessing step for edge detection

fuzzy random impulse noise reduction method a new two step fuzzy filter that adopts a fuzzy logic approach for the enhancement of images corrupted with impulse noise is presented in this paper the filtering method entitled as fuzzy random impulse noise reduction method frinr consists of a fuzzy detection mechanism and a fuzzy filtering method to remove random valued impulse noise from corrupted images based on the criteria of peak signal to noise ratio psnr and subjective evaluations we have found experimentally that the proposed method provides a significant improvement on other state of the art methods

adaptive stack filtering under the mean absolute error criterion an adaptive filter algorithm is developed for the class of stack filters which is a class of nonlinear filters obeying a weak superposition property the adaptation algorithm can be interpreted as a learning algorithm for a group of decision making units the decisions of which are subject to a set of constraints called the stacking constraints under a rather weak statistical assumption on the training inputs the decision strategy adopted by the group which evolves according to the proposed learning algorithm is shown to converge to an optimal strategy in the sense that it corresponds to an optimal stack filter under the mean absolute error criterion this adaptive algorithm requires only increment decrement and comparison operations and only local interconnections between the learning units implementation of the algorithm in hardware is therefore very feasible an example is provided to show how the adaptive stack filtering algorithm can be used in an application in image processing

rank conditioned rank selection filters for signal restoration a class of nonlinear filters called rank conditioned rank selection rcrs filters is developed and analyzed in this paper the rcrs filters are developed within the general framework of rank selection rs filters which are filters constrained to output an order statistic from the observation set many previously proposed rank order based filters can be formulated as rs filters the only difference between such filters is in the information used in deciding which order statistic to output the information used by rcrs filters is the ranks of selected input samples hence the name rank conditioned rank selection filters the number of input sample ranks used is referred to as the order of the rcrs filter the order can range from zero to the number of samples in the observation window giving the filters valuable flexibility low order filters can give good performance and are relatively simple to optimize and implement if improved performance is demanded the order can be increased but at the expense of filter simplicity in this paper many statistical and deterministic properties of the rcrs filters are presented a procedure for optimizing over the class of rcrs filters is also presented finally extensive computer simulation results that illustrate the performance of rcrs filters in comparison with other techniques in image restoration applications are presented

geometric transfer and the homotopy type of the automorphism groups of a manifold introduction for m a compact manifold with or without boundary in one of the categories diff pl or top we denote by a m the semisimplicial ss group of automorphisms of m i e the group of diffeomorphisms pl homeomorphisms or homeomorphisms resp in this paper we describe in the stability range and localized away from two the homotopy structure of a m we do this in terms of a m the ss group of block automorphisms whose homotopy structure is a sophisticated formulation of surgery theory abk and some new homotopy functors 5 theorem c the functors 5 and 5 l here considered have already been studied in the pl category by hatcher h from a different point of view the present geometric description is appropriate to the description of the homotopy structure of a m and enables us to produce a natural map b sc x 5 x from the associative monoid of simple homotopy equivalence of x to 5 x which will be important for our study besides the geometric topology results blr two ideas partially developed in bli are basic the first is the transfer map and stability for concordances described in the pl context by hatcher and in the differentiable context in bli the second is the splitting of a z 1 weak commutative topological group with involution as a product up to homotopy of two pieces the symmetric respectively antisymmetric parts applied to our situation those parts manifest very different behavior the results of this paper have been sketched by the first author in the survey paper b there is an overlap between some but not all results of a and results of hatcher h2 published in the same volume as b the results of this paper are stated in the next section statement of results and the proofs are given in subsequent sections we continue this section with a description of the notations used

brief paper identification of continuous time systems with multiple unknown time delays by global nonlinear least squares and instrumental variable methods this paper considers the identification problem of multiple input single output miso continuous time systems with unknown time delays of the inputs from sampled input output data an iterative global separable nonlinear least squares gsepnls method which estimates the time delays and transfer function parameters separably is derived to significantly reduce the possibility of convergence to a local minimum by using the stochastic global optimization techniques furthermore the gsepnls method is modified to a novel global separable nonlinear instrumental variable gsepniv method to remove the biases of the estimates in the presence of high measurement noise simulation results show that the proposed algorithms work quite well

the fuzzy transformation and its applications in image processing the spatial and rank sr orderings of samples play a critical role in most signal processing algorithms the recently introduced fuzzy ordering theory generalizes traditional or crisp sr ordering concepts and defines the fuzzy spatial samples fuzzy order statistics fuzzy spatial indexes and fuzzy ranks here we introduce a more general concept the fuzzy transformation fzt which refers to the mapping of the crisp samples order statistics and sr ordering indexes to their fuzzy counterparts we establish the element invariant and order invariant properties of the fzt these properties indicate that fuzzy spatial samples and fuzzy order statistics constitute the same set and under commonly satisfied membership function conditions the sample rank order is preserved by the fzt the fzt also possesses clustering and symmetry properties which are established through analysis of the distributions and expectations of fuzzy samples and fuzzy order statistics these properties indicate that the fzt incorporates sample diversity into the ordering operation which can be utilized in the generalization of conventional filters here we establish the fuzzy weighted median fwm fuzzy lower upper middle flum and fuzzy identity filters as generalizations of their crisp counterparts the advantage of the fuzzy generalizations is illustrated in the applications of dct coded image deblocking impulse removal and noisy image sharpening

on connectivity properties of grayscale pictures abstract a grayscale digital picture is called connected if it has only one connected component of constant gray level that is maximal i e not adjacent to any component of higher gray level this note establishes some equivalent conditions for connectedness and also defines a grayscale generalization of the genus in terms of sums of local property values

efficient impulse noise reduction via local directional gradients and fuzzy logic this paper proposes an efficient noise reduction method for image restoration a novel pixel classification method by using fuzzy logic and local gradients is first introduced to discriminate noise and noise free pixels from corrupted images then a switching filtering scheme is employed to noisy images the noise pixels will be filtered by a weighted median filter with adaptive weights when the noise free pixels are preserved in the filtered images both numerical comparisons and perceptual observations are demonstrated in the experimental simulations it is found that the proposed method achieves a fairly better performance than a number of other existing methods in noise reduction and image restoration

some topological properties of kahler manifolds and homogeneous spaces on donne des calculs explicites des groupes d homotopie rationnels du monoide topologique de toutes les auto equivalences d homotopie d une variete de kahler homogene

estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising we develop three novel wavelet domain denoising methods for subband adaptive spatially adaptive and multivalued image denoising the core of our approach is the estimation of the probability that a given coefficient contains a significant noise free component which we call signal of interest in this respect we analyze cases where the probability of signal presence is 1 fixed per subband 2 conditioned on a local spatial context and 3 conditioned on information from multiple image bands all the probabilities are estimated assuming a generalized laplacian prior for noise free subband data and additive white gaussian noise the results demonstrate that the new subband adaptive shrinkage function outperforms bayesian thresholding approaches in terms of mean squared error the spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity the performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding

a new efficient approach for the removal of impulse noise from highly corrupted images a new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank ordered pixels in a sliding window as part of this framework several algorithms are examined each of which is applicable to fixed and random valued impulse noise models first a simple two state approach is described in which the algorithm switches between the output of an identity filter and a rank ordered mean rom filter the technique achieves an excellent tradeoff between noise suppression and detail preservation with little increase in computational complexity over the simple median filter for a small additional cost in memory this simple strategy is easily generalized into a multistate approach using weighted combinations of the identity and rom filter in which the weighting coefficients can be optimized using image training data extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as 40 impulse noise corruption moreover the method can effectively restore images corrupted with gaussian noise and mixed gaussian and impulse noise finally the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise

noise adaptive soft switching median filter existing state of the art switching based median filters are commonly found to be nonadaptive to noise density variations and prone to misclassifying pixel characteristics at high noise density interference this reveals the critical need of having a sophisticated switching scheme and an adaptive weighted median filter we propose a novel switching based median filter with incorporation of fuzzy set concept called the noise adaptive soft switching median nasm filter to achieve much improved filtering performance in terms of effectiveness in removing impulse noise while preserving signal details and robustness in combating noise density variations the proposed nasm filter consists of two stages a soft switching noise detection scheme is developed to classify each pixel to be uncorrupted pixel isolated impulse noise nonisolated impulse noise or image object s edge pixel no filtering or identity filter standard median sm filter or our developed fuzzy weighted median fwm filter will then be employed according to the respective characteristic type identified experimental results show that our nasm filter impressively outperforms other techniques by achieving fairly close performance to that of ideal switching median filter across a wide range of noise densities ranging from 10 to 70

a new fuzzy color correlated impulse noise reduction method a new impulse noise reduction method for color images is presented color images that are corrupted with impulse noise are generally filtered by applying a grayscale algorithm on each color component separately or using a vector based approach where each pixel is considered as a single vector the first approach causes artefacts especially on edge and texture pixels vector based methods were successfully introduced to overcome this problem nevertheless they tend to cluster the noise and to receive a lower noise reduction performance in this paper we discuss an alternative technique which gives a good noise reduction performance while much less artefacts are introduced the main difference between the proposed method and other classical noise reduction methods is that the color information is taken into account to develop 1 a better impulse noise detection method and 2 a noise reduction method that filters only the corrupted pixels while preserving the color and the edge sharpness experimental results show that the proposed method provides a significant improvement on other existing filters

impulse noise removal from digital images by a detail preserving filter based on type 2 fuzzy logic a novel image filter based on type 2 fuzzy logic techniques is proposed for detail preserving restoration of digital images corrupted by impulse noise the performance of the proposed filter is evaluated for different test images corrupted at various noise densities and also compared with representative conventional as well as state of the art impulse noise filters from the literature experimental results show that the proposed filter exhibits superior performance over the competing operators and is capable of efficiently suppressing the noise in the image while at the same time effectively preserving thin lines edges texture and other useful information within the image

a detection statistic for random valued impulse noise this paper proposes an image statistic for detecting random valued impulse noise by this statistic we can identify most of the noisy pixels in the corrupted images combining it with an edge preserving regularization we obtain a powerful two stage method for denoising random valued impulse noise even for noise levels as high as 60 simulation results show that our method is significantly better than a number of existing techniques in terms of image restoration and noise detection

tri state median filter for image denoising a novel nonlinear filter called tri state median tsm filter is proposed for preserving image details while effectively suppressing impulse noise we incorporate the standard median sm filter and the center weighted median cwm filter into a noise detection framework to determine whether a pixel is corrupted before applying filtering unconditionally extensive simulation results demonstrate that the proposed filter consistently outperforms other median filters by balancing the tradeoff between noise reduction and detail preservation

on the identifiability of the time delay with least squares methods this paper investigates the presence and the effects of multiple minima in the loss function to be minimized in time delay estimation methods based on least squares it is shown how in most cases a low pass filtering action is required on data used in the identification phase in order to estimate the proper delay value the results presented are derived by means of a frequency domain interpretation of the least squares technique the paper does not focus on a specific estimation algorithm rather it presents a scenario to accommodate many recently published identification methods some numerical examples illustrate the main results

generalized multichannel image filtering structures recent works in multispectral image processing advocate the employment of vector approaches for this class of signals vector processing operators that involve the minimization of a suitable error criterion have been proposed and shown appropriate for this task in this framework two main classes of vector processing filters have been reported in the literature astola et al 1990 introduce the well known class of vector median filters vmf which are derived as maximum likelihood ml estimates from exponential distributions trahanias et al see ibid vol 2 no 4 p 528 34 1993 and vol 5 no 6 p 868 80 1996 study the processing of color image data using directional information considering the class of vector directional filters vdf we introduce a new filter structure the directional distance filters ddf which combine both vdf and vmf in a novel way we show that ddf are robust signal estimators under various noise distributions they have the property of chromaticity preservation and finally compare favorably to other multichannel image processing filters

stack filter design a structural approach a new approach is developed for finding the optimal stack filter that minimizes noise subject to constraints on its structural behavior based on the output moments of stack filters it is proven that the optimal stack filter is a combination of the median filter which has the same window width as the stack filter and a set of maximum and minimum filters which are attributed to the structural constraints design examples for 1 d signal processing and image processing are provided

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

polynomial weighted median filtering this paper extends weighted median wm filters to the class of polynomial weighted median pwm filters traditional polynomial filtering theory based on linear combinations of polynomial terms is able to approximate important classes of nonlinear systems the linear combination of polynomial terms however yields poor performance in environments characterized by heavy tailed distributions weighted median filters in contrast are well known for their outlier suppression and detail preservation properties the weighted median sample selection methodology is naturally extended to the polynomial sample case yielding a filter structure that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers moreover the pwm filter class is well motivated by an analysis of cross and square term statistics a presented probability density function analysis shows that these terms have heavier tails than the observed samples indicating that robust combination methods should be utilized to avoid undue influence of outliers further analysis shows weighted median processing of polynomial terms is justified from a maximum likelihood perspective the established pwm filter class is statistically analyzed through the determination of the filter output distribution and breakdown probability filter parameter optimization procedures are also presented finally the effectiveness of pwm filters is demonstrated through simulations that include temporal spectrum and bispectrum analysis

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

a new class of chromatic filters for color image processing theory and applications this paper advances a new framework for chromatic filtering of color images the chromatic content of a color image is encoded in the cie u v chromaticity coordinates whereas the achromatic content is encoded as cie y tristimulus value within the u v chromaticity diagram colors are added according to the well known center of gravity law of additive color mixtures which is generalized here into a nonlinear filtering scheme for processing the two chromatic signals u and v the achromatic channel y can be processed with traditional filtering schemes either linear or nonlinear depending on the specific task at hand the most interesting characteristics of the new filtering scheme are 1 the elimination of color smearing effects along edges between bright and dark areas 2 the possibility of processing chromatic components in a noniterative fashion through linear convolution operations and 3 the consequent amenability to computationally efficient implementations with fast fourier transform the paper includes several examples with both synthetic and real images where the performance of the new filtering method is compared with that of other color image processing algorithms

design of weighted order statistic filters using the perceptron algorithm we observe that the design of optimal weighted order statistic wos filters under the mean absolute error criterion can be thought of as a two class linear classification problem based on this observation the perceptron algorithm is applied to designing wos filters it is shown experimentally that the perceptron algorithm can find optimal or near optimal wos filters in practical situations

digital parameter adaptive control of processes with unknown dead time simultaneous estimation of process parameters and process time delay is achieved by applying a modification of the recursive least squares method for an extended process model the order of the numerator polynomial is increased by an upper limit of the time delay the estimation of the actual time delay email protected and the calculation of the final process model is done in every step by fitting the impulse response of a model with an assumed order email protected and time delay email protected to the impulse response of the estimated extended process model by combining this method with a feedback control algorithm parameter adaptive control algorithms result and they can be applied to processes with unknown parameters and unknown constant or time varying time delays

wavelets ridgelets and curvelets for poisson noise removal in order to denoise poisson count data we introduce a variance stabilizing transform vst applied on a filtered discrete poisson process yielding a near gaussian process with asymptotic constant variance this new transform which can be deemed as an extension of the anscombe transform to filtered data is simple fast and efficient in very low count situations we combine this vst with the filter banks of wavelets ridgelets and curvelets leading to multiscale vsts ms vsts and nonlinear decomposition schemes by doing so the noise contaminated coefficients of these ms vst modified transforms are asymptotically normally distributed with known variances a classical hypothesis testing framework is adopted to detect the significant coefficients and a sparsity driven iterative scheme reconstructs properly the final estimate a range of examples show the power of this ms vst approach for recovering important structures of various morphologies in very low count images these results also demonstrate that the ms vst approach is competitive relative to many existing denoising methods

fusion of median and bilateral filtering for range image upsampling 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

geometric features based filtering for suppression of impulse noise in color images a geometric features based filtering technique named as the adaptive geometric features based filtering technique agff is presented for removal of impulse noise in corrupted color images in contrast with the traditional noise detection techniques where only 1d statistical information is used for noise detection and estimation a novel noise detection method is proposed based on geometric characteristics and features i e the 2 d information of the corrupted pixel or the pixel region leading to effective and efficient noise detection and estimation outcomes a progressive restoration mechanism is devised using multipass nonlinear operations which adapt to the intensity and the types of the noise extensive experiments conducted using a wide range of test color images have shown that the agff is superior to a number of existing well known benchmark techniques in terms of standard image restoration performance criteria including objective measurements the visual image quality and the computational complexity

stack filters and the mean absolute error criterion a method to determine the stack filter which minimizes the mean absolute error between its output and a desired signal given noisy observations of this desired signal is presented specifically an optimal window width b stack filter can be determined with a linear program with o b2 sup b variables this algorithm is efficient since the number of different inputs to a window width b filter is m sup b if the filter has m valued input and the number of stack filters grows faster than 2 raised to the 2 sup b 2 power it is shown that optimal stack filtering under the mean absolute error criterion is analogous to optimal linear filtering under the mean squared error criterion both linear filters and stack filters are defined by superposition properties both classes are implementable and both have tractable procedures for finding the optimal filter under an appropriate error criterion

directional processing of color images theory and experimental results the processing of color image data using directional information is studied the class of vector directional filters vdf which was introduced by the authors in a previous work is further considered the analogy of vdf to the spherical median is shown and their relation to the spatial median is examined moreover their statistical and deterministic properties are studied which demonstrate their appropriateness in image processing vdf result in optimal estimates of the image vectors in the directional sense this is very important in the case of color images where the vectors direction signifies the chromaticity of a given color issues regarding the practical implementation of vdf are also considered in addition efficient filtering schemes based on vdf are proposed which include adaptive and or double window structures experimental and comparative results in image filtering show very good performance measures when the error is measured in the l a b space l a b is known as a space where equal color differences result in equal distances and therefore it is very close to the human perception of colors moreover an indication of the chromaticity error is obtained by measuring the error on the maxwell triangle the results demonstrate that vdf are very accurate chromaticity estimators

an adaptive neuro fuzzy system for automatic image segmentation and edge detection an autoadaptive neuro fuzzy segmentation and edge detection architecture is presented the system consists of a multilayer perceptron mlp like network that performs image segmentation by adaptive thresholding of the input image using labels automatically pre selected by a fuzzy clustering technique the proposed architecture is feedforward but unlike the conventional mlp the learning is unsupervised the output status of the network is described as a fuzzy set fuzzy entropy is used as a measure of the error of the segmentation system as well as a criterion for determining potential edge pixels the proposed system is capable to perform automatic multilevel segmentation of images based solely on information contained by the image itself no a priori assumptions whatsoever are made about the image type features contents stochastic model etc such an universal algorithm is most useful for applications that are supposed to work with different and possibly initially unknown types of images the proposed system can be readily employed as is or as a basic building block by a more sophisticated and or application specific image segmentation algorithm by monitoring the fuzzy entropy relaxation process the system is able to detect edge pixels

switching based filter based on dempster s combination rule for image processing in this work a two pass switching rank ordered arithmetic mean tsram filter that preserves image details while effectively suppressing impulse noise is proposed to improve the performance of switching based median filters the proposed filter mechanism includes an efficient impulse detector based on the dempster shafer d s evidence theory and a rank ordered arithmetic mean filter that works by estimating the noise free ordered mean values excluding the current pixel a modified dempster s combination rule is applied to the impulse detector to improve filtering performance a simple switching median filter is included to perform second pass filtering experimental results show that the proposed filter outperforms many well accepted switching based median filters in terms of both noise suppression and detail preservation providing excellent robustness at various percentages of impulse noise

partition fuzzy median filter based on fuzzy rules for image restoration in this paper a novel adaptive median based filter called the partition fuzzy median pfm filter is proposed for improving the median based filter to preserve image details while effectively suppressing impulsive noises the proposed filter achieves its effect through a summation of the weighted output of the median filter and the related weighted input signal the weights are set in accordance with the fuzzy rules in order to design this weight function a method to partition of the observation vector space and a learning approach are proposed so that the mean square error of the filter output can be minimum based on the constrained least mean square algorithm an iterative learning procedure is derived and its convergence property is investigated as for the noise suppressing on both fixed and random valued impulses without degrading the quality of fine details extensive experimental results demonstrate that the proposed filter outperforms the other median based filters in the literature the new filter also provides excellent robustness with respect to various percentages of impulse noise in our testing examples

adaptive neuro fuzzy inference systems based approach to nonlinear noise cancellation for images the adaptive neuro fuzzy inference system anfis is an effective tool that can be applied to induct rules from observations e g pattern recognition in this paper we extend the nonlinear noise cancellation method using anfis from 1 d signals to 2 d counterpart images first the image restoration contaminated with gaussian noise is investigated in nonlinear passage dynamics of order 2 we inspect eight types of membership functions mf bell mf triangle mf gaussian mf two sided gaussian mf pi shaped mf product of two sigmoidal mfs difference of two sigmoidal mfs and trapezoidal mf in addition the other parameters such as the training epochs the number of mfs for each input the optimization method the type of output mfs and the over fitting problem are investigated for comparison with the noise cancellation using anfis we simulate 22 conventional filtering techniques spatial filters optimal wiener filter frequency domain filters wavelet wavelet packet 2 d adaptive filters etc the quality in terms of mean square error mse of image restoration using the proposed noise cancellation using anfis pi shaped mf is at least 75 times better for gaussian noise than that derived using any of these conventional filtering techniques

streaking in median filtered images this paper presents a probabilistic analysis of the streaking or blotching effect commonly observed in median filtered signals in both one and two dimensions the effcts are identified as runs of equal or nearly equal values which create visual impressions that have no visual correlate for one dimensional discrete iid random signals with continuous input probability densities the probability of a streak of length l occurring is computed and shown to be independent of the input probability distribution expressions for the first and second moments of the streak length are also derived and certain asymptotic results are given as the analysis and definition of the analogous effect in two dimensions is less tractable the probability that medians taken from distinct overlapping windows will take the same value is derived for various filter geometries the analytic results are supported by examples using both one and two dimensional signals

analysis of the properties of median and weighted median filters using threshold logic and stack filter representation the deterministic properties of weighted median wm filters are analyzed threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering the authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive boolean function because the cascade of wm filters can always be expressed as a single stack filter this allows expression of the cascade of wm filters as a single wm filter a direct application is the computation of the output distribution of a cascade of wm filters the same method is used to find a nonrecursive expansion of a recursive wm filter as applications of theoretical results several interesting deterministic and statistical properties of wm filters are derived

the teichmuller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible for a smooth manifold m we define the teichmuller space 2t m of all riemannian metrics on m and the teichmuller space 2t m of pinched negatively curved metrics on m where 0 oo we prove that if m is hyperbolic the natural inclusion f m 2t m is in general not homotopically trivial in particular 2t m is in general not contractible

recursive estimation of time delay in sampled systems abstract this paper presents a new identification method based on standard recursive least squares for the estimation of time delay in linear sampled systems the algorithm relies on the fact that if the continuous time model has a delay or anticipation shorter than one sampling time then a real negative zero arises in the corresponding sampled system by inspection of the phase contribution of this zero the value of the delay is recursively updated a frequency domain analysis is also performed to examine the characteristics of the algorithm simulation results illustrate the performances of the time delay estimation algorithm

adaptive fuzzy segmentation of magnetic resonance images an algorithm is presented for the fuzzy segmentation of two dimensional 2 d and three dimensional 3 d multispectral magnetic resonance mr images that have been corrupted by intensity inhomogeneities also known as shading artifacts the algorithm is an extension of the 2 d adaptive fuzzy c means algorithm 2 d afcm presented in previous work by the authors this algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space it iteratively adapts to the intensity inhomogeneities and is completely automated in this paper the authors fully generalize 2 d afcm to three dimensional 3 d multispectral images because of the potential size of 3 d image data they also describe a new faster multigrid based algorithm for its implementation they show using simulated mr data that 3 d afcm yields lower error rates than both the standard fuzzy c means fcm algorithm and two other competing methods when segmenting corrupted images its efficacy is further demonstrated using real 3 d scalar and multispectral mr brain images

a robust approach to image enhancement based on fuzzy logic in this paper we propose a robust approach to image enhancement based on fuzzy logic that addresses the seemingly conflicting goals of image enhancement i removing impulse noise ii smoothing out nonimpulse noise and iii enhancing or preserving edges and certain other salient structures we derive three different filters for each of the above three tasks using the weighted or fuzzy least squares ls method and define the criteria for selecting each of the three filters the criteria are based on the local context and they constitute the antecedent clauses of the fuzzy rules the overall result of the fuzzy rule based system is the combination of the results of the individual filters where each result contributes to the degree that the corresponding antecedent clause is satisfied this approach gives us a powerful and flexible image enhancement paradigm results of the proposed method on several types of images are compared with those of other standard techniques

minimum mean absolute error stack filtering with structural constraint and goals a theory for the structural behavior of stack filters is developed this theory provides a test which can determine if a given stack filter has any root signals a method for classifying the root signal behavior of any stack filter found to have roots and perhaps most important a method for designing stack filters with specific root signals or other structural behavior this theory of root signals for stack filters is then combined with the theory of minimum mean absolute error stack filtering this unified theory allows the designer to pick a filter which minimizes noise subject to constraints on its structural behavior

cdna microarray image processing using fuzzy vector filtering framework this paper presents a novel filtering framework capable of processing cdna microarray images the proposed two component adaptive vector filters integrate well known concepts from the areas of fuzzy set theory nonlinear filtering multidimensional scaling and robust order statistics by appropriately setting the weighting coefficients in a generalized framework the method is capable of removing noise impairments while preserving structural information in cdna microarray images noise removal is performed by tuning a membership function which utilizes distance criteria applied to cdna vectorial inputs at each image location the classical vector representation adopted here for a two channel processing task as well as a new color ratio model representation are used simulation studies reported in this paper indicate that the proposed adaptive fuzzy vector filters are computationally attractive yield excellent performance and are able to preserve structural information while efficiently suppressing noise in cdna microarray data