a fuzzy extension of the silhouette width criterion for cluster analysis the present paper proposes a new cluster validity measure as an additional criterion to help the decision making process in fuzzy cluster analysis this measure named fuzzy silhouette is a generalization to the fuzzy case of the average silhouette width criterion originally conceived to assess crisp non fuzzy data partitions the fuzzy silhouette is more appealing than its crisp counterpart in the context of fuzzy cluster analysis since it makes explicit use of the fuzzy partition matrix provided by the clustering algorithm in addition it has been designed to improve performance of the original silhouette criterion in detecting regions with higher data density when the data set involves overlapping clusters the performance of the fuzzy silhouette is evaluated and compared to that of five well known cluster validity measures six data sets are used to illustrate different scenarios in which the proposed fuzzy silhouette performs similar to or better than these other criteria thus becoming eligible to join a pool of measures to be used all together in fuzzy cluster analysis

autocorrelation based fuzzy clustering of time series the traditional approaches to clustering a set of time series are generally applicable if there is a fixed underlying structure to the time series so that each will belong to one cluster or the other however time series often display dynamic behaviour in their evolution over time this dynamic behaviour should be taken into account when attempting to cluster time series for instance during a certain period a time series might belong to a certain cluster afterwards its dynamics might be closer to that of another cluster in this case the traditional clustering approaches are unlikely to find and represent the underlying structure in the given time series this switch from one time state to another which is typically vague can be naturally treated following a fuzzy approach this paper proposes a fuzzy clustering approach based on the autocorrelation functions of time series in which each time series is not assigned exclusively to only one cluster but it is allowed to belong to different clusters with various membership degrees

nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising part ii adaptive algorithms we combine the main ideas introduced in part i with adaptive techniques to arrive at a powerful algorithm that estimates missing data in nonstationary signals the proposed approach operates automatically based on a chosen linear transform that is expected to provide sparse decompositions over missing regions such that a portion of the transform coefficients over missing regions are zero or close to zero unlike prevalent algorithms our method does not necessitate any complex preconditioning segmentation or edge detection steps and it can be written as a progression of denoising operations we show that constructing estimates based on nonlinear approximants is fundamentally a nonconvex problem and we propose a progressive algorithm that is designed to deal with this issue directly the algorithm is applied to images through an extensive set of simulation examples primarily on missing regions containing textures edges and other image features that are not readily handled by established estimation and recovery methods we discuss the properties required of good transforms and in conjunction show the types of regions over which well known transforms provide good predictors we further discuss extensions of the algorithm where the utilized transforms are also chosen adaptively where unpredictable signal components in the progressions are identified and not predicted and where the prediction scenario is more general

simultaneous structure and texture image inpainting an algorithm for the simultaneous filling in of texture and structure in regions of missing image information is presented in this paper the basic idea is to first decompose the image into the sum of two functions with different basic characteristics and then reconstruct each one of these functions separately with structure and texture filling in algorithms the first function used in the decomposition is of bounded variation representing the underlying image structure while the second function captures the texture and possible noise the region of missing information in the bounded variation image is reconstructed using image inpainting algorithms while the same region in the texture image is filled in with texture synthesis techniques the original image is then reconstructed adding back these two sub images the novel contribution of this paper is then in the combination of these three previously developed components image decomposition with inpainting and texture synthesis which permits the simultaneous use of filling in algorithms that are suited for different image characteristics examples on real images show the advantages of this proposed approach

context aware sparse decomposition for image denoising and super resolution image prior models based on sparse and redundant representations are attracting more and more attention in the field of image restoration the conventional sparsity based methods enforce sparsity prior on small image patches independently unfortunately these works neglected the contextual information between sparse representations of neighboring image patches it limits the modeling capability of sparsity based image prior especially when the major structural information of the source image is lost in the following serious degradation process in this paper we utilize the contextual information of local patches denoted as context aware sparsity prior to enhance the performance of sparsity based restoration method in addition a unified framework based on the markov random fields model is proposed to tune the local prior into a global one to deal with arbitrary size images an iterative numerical solution is presented to solve the joint problem of model parameters estimation and sparse recovery finally the experimental results on image denoising and super resolution demonstrate the effectiveness and robustness of the proposed context aware method

cluster differences scaling with a within clusters loss component and a fuzzy successive approximation strategy to avoid local minima cluster differences scaling is a method for partitioning a set of objects into classes and simultaneously finding a low dimensional spatial representation ofk cluster points to model a given square table of dissimilarities amongn stimuli or objects the least squares loss function of cluster differences scaling originally defined only on the residuals of pairs of objects that are allocated to different clusters is extended with a loss component for pairs that are allocated to the same cluster it is shown that this extension makes the method equivalent to multidimensional scaling with cluster constraints on the coordinates a decomposition of the sum of squared dissimilarities into contributions from several sources of variation is described including the appropriate degrees of freedom for each source after developing a convergent algorithm for fitting the cluster differences model it is argued that the individual objects and the cluster locations can be jointly displayed in a configuration obtained as a by product of the optimization finally the paper introduces a fuzzy version of the loss function which can be used in a successive approximation strategy for avoiding local minima a simulation study demonstrates that this strategy significantly outperforms two other well known initialization strategies and that it has a success rate of 92 out of 100 in attaining the global minimum

fuzzy clustering for data time arrays with inlier and outlier time trajectories in many knowledge discovery and data mining tasks fuzzy clustering is one of the most common tools for data partitioning in this paper dynamic fuzzy clustering models for classifying a set of multivariate time trajectories time series sequences are developed in particular by adopting an exploratory approach based on a geometric algebraic formulation of the data time array different kinds of dynamic fuzzy clustering models based on cross sectional and longitudinal aspects are suggested furthermore a modified version of the previous clustering models that can be seen as a generalization of these models is proposed by utilizing these models we can obtain beneficial effects in the clustering process when anomalous trajectories trajectories with anomalous positions and slopes are present in the dataset in fact the models are suitable for detecting structures of time trajectories with anomalous patterns that are not uniformly distributed over the structure s domains and are characterized by strange slopes in these models the disruptive effect of the anomalous trajectories is neutralized and smoothed and the information on the influence of individual time trajectories on the detected groups is given furthermore some remarks on dynamic three way extensions of a few robust fuzzy clustering models for two way data are suggested demonstrative examples are shown and a comparison assessment based on artificial multivariate time varying data is carried out

quantile autocovariances a powerful tool for hard and soft partitional clustering of time series abstract a key issue in cluster analysis is determining a proper dissimilarity measure between two data objects and many pairwise dissimilarities have been proposed to deal with time series assuming that the clustering purpose is to group series according to the underlying dependence structures a detailed study of the behavior in clustering of a dissimilarity based on comparing estimated quantile autocovariance functions qaf is carried out quantile autocovariances provide information about the serial dependence structure that other conventional features are not able to capture which suggests great potential to perform clustering of series the asymptotic behavior of the sample quantile autocovariances is studied and an algorithm to determine optimal combinations of lags and pairs of quantile levels to perform clustering is introduced the proposed metric is used to perform hard and soft partitioning based clustering first a broad simulation study examines the behavior of the proposed metric in crisp clustering with the pam procedure a novel fuzzy c medoids algorithm based on the qaf dissimilarity is then proposed and compared with other fuzzy procedures in a new simulation study conducted to cluster fuzzy scenarios involving ar and garch models in all cases the qaf based procedures outperform or are highly competitive with a range of dissimilarities reported in the literature particularly exhibiting high capability to cluster conditionally heteroskedastic time series and robustness to the distributional form of the errors two specific applications involving air quality data and financial time series illustrate the usefulness of the proposed procedures

color sparse representations for image processing review models and prospects sparse representations have been extended to deal with color images composed of three channels a review of dictionary learning based sparse representations for color images is made here detailing the differences between the models and comparing their results on the real and simulated data these models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering transformation of the color channels moreover this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix based color filtering which highlights the filtering implicitly applied through this model based on this reformulation the new color filtering model is introduced using unconstrained filters in this model spatial morphologies of color images are encoded by atoms and colors are encoded by color filters color variability is no longer captured in increasing the dictionary size but with color filters this gives an efficient color representation

fuzzy clustering of time series using extremes abstract in this study we explore the grouping together of time series with similar seasonal patterns using extreme value analysis with fuzzy clustering input features into the fuzzy clustering methods are parameter estimates of time varying location scale and shape obtained from fitting the generalised extreme value gev distribution to annual maxima or the r largest order statistics per year of the time series an innovative contribution of the study is the development of new generalised fuzzy clustering procedures taking into account weights and the derivation of iterative solutions based on the gev parameter estimators simulation studies conducted to evaluate the methods reveal good performance an application is made to a set of daily sea level time series from around the coast of australia where the identified clusters are well validated and they can be meaningfully interpreted

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

image inpainting by patch propagation using patch sparsity this paper introduces a novel examplar based inpainting algorithm through investigating the sparsity of natural image patches two novel concepts of sparsity at the patch level are proposed for modeling the patch priority and patch representation which are two crucial steps for patch propagation in the examplar based inpainting approach first patch structure sparsity is designed to measure the confidence of a patch located at the image structure e g the edge or corner by the sparseness of its nonzero similarities to the neighboring patches the patch with larger structure sparsity will be assigned higher priority for further inpainting second it is assumed that the patch to be filled can be represented by the sparse linear combination of candidate patches under the local patch consistency constraint in a framework of sparse representation compared with the traditional examplar based inpainting approach structure sparsity enables better discrimination of structure and texture and the patch sparse representation forces the newly inpainted regions to be sharp and consistent with the surrounding textures experiments on synthetic and natural images show the advantages of the proposed approach

silhouettes a graphical aid to the interpretation and validation of cluster analysis a new graphical display is proposed for partitioning techniques each cluster is represented by a so called silhouette which is based on the comparison of its tightness and separation this silhouette shows which objects lie well within their cluster and which ones are merely somewhere in between clusters the entire clustering is displayed by combining the silhouettes into a single plot allowing an appreciation of the relative quality of the clusters and an overview of the data configuration the average silhouette width provides an evaluation of clustering validity and might be used to select an appropriate number of clusters

a decoupled method for image inpainting with patch based low rank regulariztion abstract in this paper we propose a decoupled variational method for image inpainting in both image domain and transform domain including wavelet domain and fourier domain the original image inpainting problem is decoupled as two minimization problems with different energy functionals one is image denoising with low rank regularization method i e the patch based weighted nuclear norm minimization pwnnm the other is linear combination in image domain or transform domain an iterative algorithm is then obtained by minimizing the two problems alternatingly in particular we derive the variational formulas for pwnnm and reformulate the denoising process into three steps image decomposition patch matrix denoising and image reconstruction the convergence of the numerical algorithm is proved under some assumptions the numerical experiments and comparisons on various images demonstrate the effectiveness of the proposed methods

correspondence map aided neighbor embedding for image intra prediction this paper describes new image prediction methods based on neighbor embedding ne techniques neighbor embedding methods are used here to approximate an input block the block to be predicted in the image as a linear combination of k nearest neighbors however in order for the decoder to proceed similarly the k nearest neighbors are found by computing distances between the known pixels in a causal neighborhood called template of the input block and the co located pixels in candidate patches taken from a causal window similarly the weights used for the linear approximation are computed in order to best approximate the template pixels although efficient these methods suffer from limitations when the template and the block to be predicted are not correlated e g in non homogenous texture areas to cope with these limitations this paper introduces new image prediction methods based on ne techniques in which the k nn search is done in two steps and aided at the decoder by a block correspondence map hence the name map aided neighbor embedding mane method another optimized variant of this approach called omane method is also studied in these methods several alternatives have also been proposed for the k nn search the resulting prediction methods are shown to bring significant rate distortion performance improvements when compared to h 264 intra prediction modes up to 44 75 rate saving at low bit rates

linear worst case estimators for denoising quantization noise in transform coded images transform coded images exhibit distortions that fall outside of the assumptions of traditional denoising techniques in this paper we use tools from robust signal processing to construct linear worst case estimators for the denoising of transform compressed images we show that while standard denoising is fundamentally determined by statistical models for images alone the distortions induced by transform coding are heavily dependent on the structure of the transform used our method thus uses simple models for the image and for the quantization error with the latter capturing the transform dependency based on these models we derive optimal linear estimators of the original image that are optimal in the mean squared error sense for the worst case cross correlation between the original and the quantization error our construction is transform agnostic and is applicable to transforms from block discrete cosine transforms to wavelets furthermore our approach is applicable to different types of image statistics and can also serve as an optimization tool for the design of transforms quantizers through the interaction of the source and quantizer models our work provides useful insights and is instrumental in identifying and removing quantization artifacts from general signals coded with general transforms as we decouple the modeling and processing steps we allow for the construction of many different types of estimators depending on the desired sophistication and available computational complexity in the low end of this spectrum our lookup table based estimator which can be deployed in low complexity environments provides competitive psnr values with some of the best results in the literature

sparsity based image error concealment via adaptive dual dictionary learning and regularization in this paper we propose a novel sparsity based image error concealment ec algorithm through adaptive dual dictionary learning and regularization we define two feature spaces the observed space and the latent space corresponding to the available regions and the missing regions of image under test respectively we learn adaptive and complete dictionaries individually for each space where the training data are collected via an adaptive template matching mechanism based on the piecewise stationarity of natural images a local correlation model is learned to bridge the sparse representations of the aforementioned dual spaces allowing us to transfer the knowledge of the available regions to the missing regions for ec purpose eventually the ec task is formulated as a unified optimization problem where the sparsity of both spaces and the learned correlation model are incorporated experimental results show that the proposed method outperforms the state of the art techniques in terms of both objective and perceptual metrics

on the importance of combining wavelet based nonlinear approximation with coding strategies this paper provides a mathematical analysis of transform compression in its relationship to linear and nonlinear approximation theory contrasting linear and nonlinear approximation spaces we show that there are interesting classes of functions random processes which are much more compactly represented by wavelet based nonlinear approximation these classes include locally smooth signals that have singularities and provide a model for many signals encountered in practice in particular for images however we also show that nonlinear approximation results do not always translate to efficient compress on strategies in a rate distortion sense based on this observation we construct compression techniques and formulate the family of functions stochastic processes for which they provide efficient descriptions in a rate distortion sense we show that this family invariably leads to besov spaces yielding a natural relationship among besov smoothness linear nonlinear approximation order and compression performance in a rate distortion sense the designed compression techniques show similarities to modern high performance transform codecs allowing us to establish relevant rate distortion estimates and identify performance limits

modal data are insufficient for identification of both mass and stiffness matrices simutaneous changes in the mass and stiffness matrices cannot be identified by using modal data only the mode shapes cannot provide a reference basis

solving inverse problems with piecewise linear estimators from gaussian mixture models to structured sparsity a general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper the approach is based on gaussian mixture models which are estimated via a maximum a posteriori expectation maximization algorithm a dual mathematical interpretation of the proposed framework with a structured sparse estimation is described which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques we demonstrate that in a number of image inverse problems including interpolation zooming and deblurring of narrow kernels the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art

nonlocal image restoration with bilateral variance estimation a low rank approach simultaneous sparse coding ssc or nonlocal image representation has shown great potential in various low level vision tasks leading to several state of the art image restoration techniques including bm3d and lssc however it still lacks a physically plausible explanation about why ssc is a better model than conventional sparse coding for the class of natural images meanwhile the problem of sparsity optimization especially when tangled with dictionary learning is computationally difficult to solve in this paper we take a low rank approach toward ssc and provide a conceptually simple interpretation from a bilateral variance estimation perspective namely that singular value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular value thresholding saist for noise data saist generalizes the celebrated bayesshrink from local to nonlocal models for incomplete data saist extends previous deterministic annealing based solution to sparsity optimization through incorporating the idea of dictionary learning in addition to conceptual simplicity and computational efficiency saist has achieved highly competent often better objective performance compared to several state of the art methods in image denoising and completion experiments our subjective quality results compare favorably with those obtained by existing techniques especially at high noise levels and with a large amount of missing data

a universal variational framework for sparsity based image inpainting in this paper we extend an existing universal variational framework for image inpainting with new numerical algorithms given certain regularization operator and denoting u the latent image the basic model is to minimize the l p p 0 1 norm of u preserving the pixel values outside the inpainting region utilizing the operator splitting technique the original problem can be approximated by a new problem with extra variable with the alternating minimization method the new problem can be decomposed as two subproblems with exact solutions there are many choices for in our approach such as gradient operator wavelet transform framelet transform or other tight frames moreover with slight modification we can decouple our framework into two relatively independent parts 1 denoising and 2 linear combination therefore we can take any denoising method including bm3d filter in the denoising step the numerical experiments on various image inpainting tasks such as scratch and text removal randomly missing pixel filling and block completion clearly demonstrate the super performance of the proposed methods furthermore the theoretical convergence of the proposed algorithms is proved

a parametric texture model based on joint statistics of complex wavelet coefficients we present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform the model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations orientations and scales we develop an efficient algorithm for synthesizing random images subject to these constraints by iteratively projecting onto the set of images satisfying each constraint and we use this to test the perceptual validity of the model in particular we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set we also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures

passive error concealment for wavelet coded i frames with an inhomogeneous gauss markov random field model in video communication over lossy packet networks e g the internet packet loss errors can severely damage the transmitted video the damaged video can largely be repaired with passive error concealment where neighboring information is used to estimate missing information we address the problem of passive error concealment for wavelet coded data with dispersive packetization the reported techniques of this kind have many problems and usually fail in the reconstruction of high frequency content this paper presents a novel locally adaptive error concealment method for subband coded i frames based on an inhomogeneous gaussian markov random field model we estimate the parameters of this model from a local context of each lost coefficient and we interpolate the lost coefficients accordingly the results demonstrate a significant improvement over the reported related methods both in terms of objective performance measures and visually the biggest improvement of the proposed method compared to the state of the art in the field is the correct reconstruction of high frequency information such as textures and edges

nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising part i theory we study the robust estimation of missing regions in images and video using adaptive sparse reconstructions our primary application is on missing regions of pixels containing textures edges and other image features that are not readily handled by prevalent estimation and recovery algorithms we assume that we are given a linear transform that is expected to provide sparse decompositions over missing regions such that a portion of the transform coefficients over missing regions are zero or close to zero we adaptively determine these small magnitude coefficients through thresholding establish sparsity constraints and estimate missing regions in images using information surrounding these regions unlike prevalent algorithms our approach does not necessitate any complex preconditioning segmentation or edge detection steps and it can be written as a sequence of denoising operations we show that the region types we can effectively estimate in a mean squared error sense are those for which the given transform provides a close approximation using sparse nonlinear approximants we show the nature of the constructed estimators and how these estimators relate to the utilized transform and its sparsity over regions of interest the developed estimation framework is general and can readily be applied to other nonstationary signals with a suitable choice of linear transforms part i discusses fundamental issues and part ii is devoted to adaptive algorithms with extensive simulation examples that demonstrate the power of the proposed techniques

fine granularity and spatially adaptive regularization for projection based image deblurring this paper studies two classes of regularization strategies to achieve an improved tradeoff between image recovery and noise suppression in projection based image deblurring the first is based on a simple fact that r times landweber iteration leads to a fixed level of regularization which allows us to achieve fine granularity control of projection based iterative deblurring by varying the value r the regularization behavior is explained by using the theory of lagrangian multiplier for variational schemes the second class of regularization strategy is based on the observation that various regularized filters can be viewed as nonexpansive mappings in the metric space a deeper understanding about different regularization filters can be gained by probing into their asymptotic behavior the fixed point of nonexpansive mappings by making an analogy to the states of matter in statistical physics we can observe that different image structures smooth regions regular edges and textures correspond to different fixed points of nonexpansive mappings when the temperature regularization parameter varies such an analogy motivates us to propose a deterministic annealing based approach toward spatial adaptation in projection based image deblurring significant performance improvements over the current state of the art schemes have been observed in our experiments which substantiates the effectiveness of the proposed regularization strategies

color direction patch sparsity based image inpainting using multidirection features this paper proposes a color direction patch sparsity based image inpainting method to better maintain structure coherence texture clarity and neighborhood consistence of the inpainted region of an image the method uses super wavelet transform to estimate the multi direction features of a degraded image and combines with color information to construct the weighted color direction distance wcdd to measure the difference between two patches based on the wcdd the color direction structure sparsity is defined to obtain a more robust filling order and more suitable multiple candidate patches are searched then the target patches are sparsely represented by the multiple candidate patches under neighborhood consistency constraints in both the color and the multi direction spaces experimental results are presented to demonstrate the effectiveness of the proposed approach on tasks such as scratch removal text removal block removal and object removal the effects of super wavelet transforms and direction features are also investigated

automated parameter identification and order reduction for discrete time series models the estimated models are used to predict the transient response of structures subject to arbitrary input the linear structural transfer function is expressed in the form of an arma discrete time series model overspecification of the system order has proven useful in reducing the bias errors but the resulting model may be excessively large and will contain noise related modes

mixture model and least squares based packet video error concealment a gaussian mixture model gmm based spatio temporal error concealment approach has recently been proposed for packet video the method improves peak signal to noise ratio psnr compared to several famous error concealment methods and it is asymptotically optimal when the number of mixture components goes to infinity there are also drawbacks however the estimator has high online computational complexity which implies that fewer surrounding pixels to the lost area than desired are used for error concealment moreover gmm parameters are estimated without considering maximization of the error concealment psnr in this paper we propose a mixture based estimator and a least squares approach for solving the spatio temporal error concealment problem compared to the gmm scheme the new method may base error concealment on more surrounding pixels to the loss while maintaining low computational complexity and model parameters are found by an algorithm that increases psnr in each iteration the proposed method outperforms the gmm based scheme in terms of computation performance tradeoff