new abstract hardy spaces the aim of this paper is to propose an abstract construction of spaces which keep the main properties of the already known hardy spaces h1 we construct spaces through an atomic or molecular decomposition we prove some results about continuity from these spaces into l1 and some results about interpolation between these spaces and the lebesgue spaces we also obtain some results on weighted norm inequalities finally we present partial results in order to understand a characterization of the duals of hardy spaces

transition thresholds and transition operators for binarization and edge detection the transition method for image binarization is based on the concept of t transition pixels a generalization of edge pixels and t transition sets we introduce a novel unsupervised thresholding for unimodal histograms to estimate the transition sets we also present dilation and incidence transition operators to refine the transition set afterward we propose the simple edge transition operator for detecting edges our experiments show that the new approach increases the effectiveness of ocr applications outperforming several top ranked binarization algorithms

enhancing multiple point geostatistical modeling 1 graph theory and pattern adjustment in recent years higher order geostatistical methods have been used for modeling of a wide variety of large scale porous media such as groundwater aquifers and oil reservoirs their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard quantitative data which endow them with the capability for generating realistic realizations of porous formations with very complex channels as well as features that are mainly a barrier to fluid flow one group of such models consists of pattern based methods that use a set of data points for generating stochastic realizations by which the large scale structure and highly connected features are reproduced accurately the cross correlation based simulation ccsim algorithm proposed previously by the authors is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few cpu seconds the method is however sensitive to pattern s specifications such as boundaries and the number of replicates in this paper the original ccsim algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large scale patterns of heterogeneities in porous media first an effective boundary correction method based on the graph theory is presented by which one identifies the optimal cutting path surface for removing the patchiness and discontinuities in the realization of a porous medium next a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns the original ccsim algorithm is then combined with the two methods and is tested using various complex two and three dimensional examples it should however be emphasized that the methods that we propose in this paper are applicable to other pattern based geostatistical simulation methods

new algebraic criteria for synchronization stability of chaotic memristive neural networks with time varying delays in this brief we consider the exponential synchronization of chaotic memristive neural networks with time varying delays using the lyapunov functional method and inequality technique the dynamic analysis here employs the theory of differential equations with discontinuous right hand side as introduced by filippov the designing laws in the synchronization of neural networks are proposed via state or output coupling in addition the new proposed algebraic criteria are very easy to verify and they also enrich and improve the earlier publications finally an example is given to show the effectiveness of the obtained results

minimal multi element stochastic collocation for uncertainty quantification of discontinuous functions we propose a multi element stochastic collocation method that can be applied in high dimensional parameter space for functions with discontinuities lying along manifolds of general geometries the key feature of the method is that the parameter space is decomposed into multiple elements defined by the discontinuities and thus only the minimal number of elements are utilized on each of the resulting elements the function is smooth and can be approximated using high order methods with fast convergence properties the decomposition strategy is in direct contrast to the traditional multi element approaches which define the sub domains by repeated splitting of the axes in the parameter space such methods are more prone to the curse of dimensionality because of the fast growth of the number of elements caused by the axis based splitting the present method is a two step approach firstly a discontinuity detector is used to partition parameter space into disjoint elements in each of which the function is smooth the detector uses an efficient combination of the high order polynomial annihilation technique along with adaptive sparse grids and this allows resolution of general discontinuities with a smaller number of points when the discontinuity manifold is low dimensional after partitioning an adaptive technique based on the least orthogonal interpolant is used to construct a generalized polynomial chaos surrogate on each element the adaptive technique reuses all information from the partitioning and is variance suppressing we present numerous numerical examples that illustrate the accuracy efficiency and generality of the method when compared against standard locally adaptive sparse grid methods the present method uses many fewer number of collocation samples and is more accurate

nonparametric tests for edge detection in noise abstract in this paper we describe three statistically motivated techniques for detecting edges in gray level images two similar methods based on linear rank sums are described specifically the wilcoxon and median statistics are implemented in a modified form and are found to perform effectively on both noisy and uncontaminated sample images a novel approach based on fitting order statistics to the image data is also advanced numerous examples are given and computational requirements are examined

robust image modeling techniques with an image restoration application a robust parameter estimation algorithm for a nonsymmetric half plane nshp autoregressive model where the driving noise is a mixture of a gaussian and an outlier process is presented the convergence of the estimation algorithm is proved an algorithm to estimate parameters and original image intensity simultaneously from the impulse noise corrupted image where the model governing the image is not available is also presented the robustness of the parameter estimates is demonstrated by simulation finally an algorithm to restore realistic images is presented the entire image generally does not obey a simple image model but a small portion e g 8 8 of the image is assumed to obey an nshp model the original image is divided into windows and the robust estimation algorithm is applied for each window the restoration algorithm is tested by comparing it to traditional methods on several different images

on maximal l p regularity abstract the aim of this paper is to propose weak assumptions to prove maximal l q regularity for cauchy problem d u d t t l u t f t mainly we only require off diagonal estimates on the real semigroup e t l t 0 to obtain maximal l q regularity the main idea is to use one kind of hardy space h 1 adapted to this problem and then use interpolation results these techniques permit us to prove weighted maximal regularity too

robust modeling for image restoration using a modified reduced update kalman filter an algorithm to estimate the original image intensity from a degraded image is developed the degradation phenomena is a gaussian noise contaminated by an outlier sequence the proposed algorithm is a combination of the robust algorithm proposed by kashyap and eom 1988 and the reduced update kalman filter rukf developed by woods and radewan 1977 the proposed algorithm is compared to some commonly used techniques such as the median filter the robust algorithm and the rukf

the exponential stability and asynchronous stabilization of a class of switched nonlinear system via the t s fuzzy model in this paper we investigate the problem of exponential stability and asynchronous stabilization for a class of switched nonlinear systems the takagi and sugeno t s fuzzy model is employed to approximate the subnonlinear dynamic systems with two level functions namely crisp switching functions and local fuzzy weighting functions we introduce continuous time switched fuzzy systems which inherently contain the features of the switched hybrid systems and t s fuzzy systems by the use of delicately constructed piecewise lyapunov like functions plfs and minimum dwell time method we obtain the exponential stability of the switched fuzzy systems which allows us to have stable and unstable nonlinear subsystems in practice for the control problem it inevitably takes some time to identify the system modes and apply the matched controller the asynchronous phenomena between the system modes switching and the controllers switching generally exists based on the result of stability the fuzzy state feedback controller under asynchronous switching is proposed for switched fuzzy systems in addition the lower bound of minimum dwell time can be obtained using convex optimization such that the switched fuzzy system can be exponentially stabilized if its minimum dwell time is larger than the bound the stability results and control laws of the switched fuzzy systems are formulated in the form of linear matrix inequalities that are numerically feasible finally two illustrated numerical examples are presented to show the effectiveness of the obtained theoretical results

a class of robust image processors abstract in this paper robust recursive estimators for image restoration are developed image restoration for images corrupted by noise is carried out in two steps to preserve true edges while restoring edge detection using a 5 5 5 5 graeco latin square is carried out as a first step an edge is localized using an f test on contrasts the center pixel is then estimated as a second step the method of estimation of a center pixel uses a multiple linear regression model fitted to the noisy image part on the same side of the edge parameters of a multiple linear regression model are estimated recursively using the robbins monro stochastic approximation procedure applied to the least squares estimator when noise departs from a gaussian assumption robust techniques for restoration are sought the recursive least squares estimator is robustized using huber s maximum likelihood estimator of location parameter of the f f type where f f is approximated by an m interval polynomial approximation algorithm and f is the p d f of noise a minimax estimator based on a soft limiter is used to robustize the recursive least squares estimator as a computationally simpler but slightly less efficient alternative the theory developed in this paper was tested using computer simulations which verified the theory and evaluated the computational complexity simplicity of the methods

robust adaptive estimator for filtering noise in images provides three new methods for storing images corrupted by additive noise one is the adaptive mean median filter for preserving the details of images when restored from additive gaussian noise another is the minimum maximum method for moving outlier noise the third method the robust adaptive mean p median filter is based on a combination of the previous two methods in the past proposed restoration methods have generally proven to be inadequate for both detail preservation and noise suppression but the new adaptive mean p median filter is shown to be good at both of these tasks while the robust adaptive mean p median filter can give good performance even in the presence of outliers degraded images are processed by the proposed algorithms with the results compared with a selection of other median based algorithms that have been proposed in the literature

global exponential stability of competitive neural networks with different time scales the dynamics of cortical cognitive maps developed by self organization must include the aspects of long and short term memory the behavior of such a neural network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system we present a new method of analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance we are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the k monotone theory singular perturbation theory or those based on supervised synaptic learning we prove the existence and the uniqueness of the equilibrium a strict lyapunov function for the flow of a competitive neural system with different time scales is given and based on it we are able to prove the global exponential stability of the equilibrium point

on optimal infinite impulse response edge detection filters the authors outline the design of an optimal computationally efficient infinite impulse response edge detection filter the optimal filter is computed based on canny s high signal to noise ratio good localization criteria and a criterion on the spurious response of the filter to noise an expression for the width of the filter which is appropriate for infinite length filters is incorporated directly in the expression for spurious responses the three criteria are maximized using the variational method and nonlinear constrained optimization the optimal filter parameters are tabulated for various values of the filter performance criteria a complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented the approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions the implementation is very simple and computationally efficient has a constant time of execution for different sizes of the operator and is readily amenable to real time hardware implementation

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data

robust parametric approach for impulse response estimation a parametric technique for estimating the impulse response of a linear system using input output observations in an outlier and distributionally uncertain environment is presented the use of various cost functions for fitting the chosen output error model are discussed by simulation it is shown that the parametric approach based on the use of huber s function as a criterion for fitting the model is robust it is also shown that even though the parametric model for the impulse response is only an approximation to the true impulse response the estimates from this approach still outperform the nonparametric approach in the presence of contaminated noise and low snr

a theory of automatic parameter selection for feature extraction with application to feature based multisensor image registration this paper generalizes the previously developed automated edge detection parameter selection algorithm of yitzhaky and peli we generalize the approach to arbitrary multidimensional continuous or discrete parameter spaces and feature spaces this generalization enables use of the parameter selection approach with more general image features for use in feature based multisensor image registration applications we investigate the problem of selecting a suitable parameter space sampling density in the automated parameter selection algorithm a real valued sensitivity measure is developed which characterizes the effect of parameter space sampling on feature set variability closed form solutions of the sensitivity measure for special feature set relationships are derived we conduct an analysis of the convergence properties of the sensitivity measure as a function of increasing parameter space sampling density for certain parameter space sampling sequence types closed form expressions for the sensitivity measure limit values are presented we discuss an approach to parameter space sampling density selection which uses the sensitivity measure convergence behavior we provide numerical results indicating the utility of the sensitivity measure for selecting suitable parameter values

lagrange stability for t s fuzzy memristive neural networks with time varying delays on time scales the existed results of lagrange stability for neural networks nns are scale free and hence conservativeness appears naturally a class of takagi sugeno t s fuzzy memristive nns fmnns with time varying delays is considered on time scales first a class of fmnns is formulated using characteristics of memristors and t s fuzzy rules then some new scale limited criteria of global exponential stability in lagrange sense are obtained for fmnns with bounded feedback functions on the basis of inequalities on time scales and inequality scaling techniques also novel criteria for lurie type feedback functions are given which mainly employ the constructed scale limited generalized halanay inequality moreover by matrix norm strategies some matrix norm based scale limited criteria are derived for bounded and lurie type feedback functions respectively it also can be seen that the matrix norm based criteria are in accordance with the matrix measure based conditions provided the time scale is specified as real set all scale limited criteria for lagrange stability not only include continuous time criteria and its discrete time analogues but also contain more complex cases such as the arbitrary combination of them in the end some numerical simulations exhibit the validity of the obtained results

besov spaces with variable smoothness and integrability abstract in this article we introduce besov spaces with variable smoothness and integrability indices we prove independence of the choice of basis functions as well as several other basic properties we also give sobolev type embeddings and show that our scale contains variable order holder zygmund spaces as special cases we provide an alternative characterization of the besov space using approximations by analytic functions

image enhancement based on a nonlinear multiscale method an image enhancement method that reduces speckle noise and preserves edges is introduced the method is based on a new nonlinear multiscale reconstruction scheme that is obtained by successively combining each coarser scale image with the corresponding modified interscale image simulation results are included to demonstrate the performance of the proposed method

novel adaptive strategies for synchronization of linearly coupled neural networks with reaction diffusion terms in this paper two types of linearly coupled neural networks with reaction diffusion terms are proposed we respectively investigate the adaptive synchronization of these two types of complex network models with local information of node dynamics some novel adaptive strategies to tune the coupling strengths among network nodes are designed by constructing appropriate lyapunov functionals and using inequality techniques several sufficient conditions are given for reaching synchronization by using the designed adaptive laws finally two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results

robust estimation approach for blind denoising this work develops a new robust statistical framework for blind image denoising robust statistics addresses the problem of estimation when the idealized assumptions about a system are occasionally violated the contaminating noise in an image is considered as a violation of the assumption of spatial coherence of the image intensities and is treated as an outlier random variable a denoised image is estimated by fitting a spatially coherent stationary image model to the available noisy data using a robust estimator based regression method within an optimal size adaptive window the robust formulation aims at eliminating the noise outliers while preserving the edge structures in the restored image several examples demonstrating the effectiveness of this robust denoising technique are reported and a comparison with other standard denoising filters is presented

classes of hardy spaces associated with operators duality theorem and applications let l be the infinitesimal generator of an analytic semigroup on l 2 r n with suitable upper bounds on its heat kernels in auscher duong and mcintosh 2005 and duong and yan 2005 a hardy space h1 l r n and a bmo l r n space associated with the operator l were introduced and studied in this paper we define a class of h p l r n spaces associated with the operator l for a range of p 1 acting on certain spaces of morrey campanato functions defined in new morrey campanato spaces associated with operators and applications by duong and yan 2005 and they generalize the classical h p r n spaces we then establish a duality theorem between the h p l r n spaces and the morrey campanato spaces in that same paper as applications we obtain the boundedness of fractional integrals on h p l r n and give the inclusion between the classical h p r n spaces and the h p l r n spaces associated with operators

abstract hardy spaces with variable exponents abstract in this paper we introduce the definition of abstract hardy spaces with variable exponents via the atomic decomposition and molecular decomposition we prove the continuity from our variable hardy space h a t o p into l p where p r n 0 1 0 p p 1 moreover we investigate the bilinear theory finally we give an application of the abstract hardy spaces with variable exponents

synchronization of competitive neural networks with different time scales abstract in this paper the exponential synchronization problem for a class of competitive neural networks is investigated moreover without assuming the active functions to be differentiable and bounded some exponential synchronization criteria are devised by lyapunov functionals linear matrix inequality lmi approach the leibniz newton formula the conditions are less conservative than existing ones reported in the literature for delayed neural networks the applicability of the conditions are validated by an illustrative example

b spline snakes a flexible tool for parametric contour detection we present a novel formulation for b spline snakes that can be used as a tool for fast and intuitive contour outlining we start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal curvature constrained snake is a cubic spline irrespective of the form of the external energy field unfortunately such regularized snakes suffer from slow convergence speed because of a large number of control points as well as from difficulties in determining the weight factors associated to the internal energies of the curve we therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies i e the regularization term in other words we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots the theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments validation results are presented comparing the traditional snake using internal energies and the proposed approach without internal energies showing the similar performance of the latter several biomedical examples of applications are included to illustrate the versatility of the method

adaptively merging large scale range data with reflectance properties in this paper we tackle the problem of geometric and photometric modeling of large intricately shaped objects typical target objects we consider are cultural heritage objects when constructing models of such objects we are faced with several important issues that have not been addressed in the past issues that mainly arise due to the large amount of data that has to be handled we propose two novel approaches to efficiently handle such large amounts of data a highly adaptive algorithm for merging range images and an adaptive nearest neighbor search to be used with the algorithm we construct an integrated mesh model of the target object in adaptive resolution taking into account the geometric and or photometric attributes associated with the range images we use surface curvature for the geometric attributes and laser reflectance values for the photometric attributes this adaptive merging framework leads to a significant reduction in the necessary amount of computational resources furthermore the resulting adaptive mesh models can be of great use for applications such as texture mapping as we will briefly demonstrate additionally we propose an additional test for the k d tree nearest neighbor search algorithm our approach successfully omits back tracking which is controlled adaptively depending on the distance to the nearest neighbor since the main consumption of computational cost lies in the nearest neighbor search the proposed algorithm leads to a significant speed up of the whole merging process in this paper we present the theories and algorithms of our approaches with pseudo code and apply them to several real objects including large scale cultural assets

a novel particle swarm optimisation approach to detecting continuous thin and smooth edges in noisy images detection of continuous edges is a hard problem and most edge detection algorithms produce jagged and thick edges particularly in noisy images this paper firstly presents a novel constrained optimisation model for detecting continuous thin and smooth edges in such images then two particle swarm optimisation based algorithms are applied to search for good solutions these two algorithms utilise two different constraint handling methods penalising and preservation the algorithms are examined and compared with a modified version of the canny algorithm as a gaussian filter based edge detector and the robust rank order rro based algorithm as a statistical based edge detector on two sets of images with different types and levels of noise pratt s figure of merit as a measure of localisation accuracy is used for the comparison of these algorithms experimental results show that the proposed edge detectors are more robust under noisy conditions and their performances are better than the canny and rro algorithms for the images corrupted by impulsive and gaussian noise the proposed algorithm based on the penalising method is faster than the algorithm using the preservation method to handle the constraints

kalman filtering in two dimensions further results the two dimensional reduced update kalman filter was recently introduced the corresponding scalar filtering equations were derived for the case of estimating a gaussian signal in white gaussian noise and were shown to constitute a general nonsymmetric half plane recursive filter this paper extends the method to the deconvolution problem of image restoration this paper also provides a more thorough treatment of the uniquely two dimensional boundary condition problems numerical and subjective examples are presented

robust edge detection edge detection is an important issue in computer vision and image understanding systems most conventional techniques have assumed gaussian noise and their performance could decrease with the departure of noise distribution from normality in this paper we present an edge detection approach using robust statistics the edge structure is first detected by a robust one way design model and then localized by a robust contrast test finally hysteresis thresholding is applied to yield the output edge map to evaluate its performance experiments were carried out on synthetic and real images corrupted with both gaussian noise and a mixture of gaussian and impulsive noise the results show that the performance of the proposed edge detector is stable and reliable under severe impulsive noise conditions

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

maximal function characterizations of variable hardy spaces associated with non negative self adjoint operators satisfying gaussian estimates abstract let p r n 0 1 be a variable exponent function satisfying the globally log holder continuous condition and l a non negative self adjoint operator on l 2 r n whose heat kernels satisfying the gaussian upper bound estimates let h l p r n be the variable exponent hardy space defined via the lusin area function associated with the heat kernels e t 2 l t 0 in this article the authors first establish the atomic characterization of h l p r n using this the authors then obtain its non tangential maximal function characterization which when p is a constant in 0 1 coincides with a recent result by l song and l yan 2016 and further induces the radial maximal function characterization of h l p r n under an additional assumption that the heat kernels of l have the holder regularity

adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations this paper investigates the problem of adaptive lag synchronization for a kind of competitive neural network with discrete and distributed delays mixed delays as well as uncertain nonlinear external and stochastic perturbations hybrid perturbations a simple but robust adaptive controller is designed such that the response system can lag synchronize with a drive system based on the lyapunov stability theory and some suitable lyapunov krasovskii functionals several sufficient conditions ensuring the lag synchronization are developed our synchronization criteria are easily verified and do not need to solve any linear matrix inequality some existing results are improved and extended moreover the designed adaptive controller has better anti interference capacity and is more practical than the usual adaptive controller numerical simulations are exploited to show the effectiveness of the theoretical results

multistability of second order competitive neural networks with nondecreasing saturated activation functions in this paper second order interactions are introduced into competitive neural networks nns and the multistability is discussed for second order competitive nns socnns with nondecreasing saturated activation functions firstly based on decomposition of state space cauchy convergence principle and inequality technique some sufficient conditions ensuring the local exponential stability of 2n equilibrium points are derived secondly some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region thirdly the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the socnns can have r 1 n locally exponentially stable equilibrium points even if there is no second order interactions the obtained results are less restrictive than those in some recent works finally three examples with their simulations are presented to verify the theoretical analysis

3 d shape from a shaded and textural surface image a new 3d texture model is developed by considering the scene image as the superposition of a random texture image on a smooth shaded image the whole image is analyzed using a patch by patch process each patch is assumed to be a tilted and slanted texture plane a modified reflectance map function is applied to describe the deterministic part and the fractional differencing periodic model is chosen to describe the random texture because of its good performance in texture synthesis and its ability to represent the coarseness and the pattern of the surface at the same time an orthographical projection technique is developed to deal with this particular random model which has a nonisotropically distributed texture pattern for estimating the parameter a hybrid method that uses both the least square and the maximum likelihood estimates is applied directly to the given intensity function by using these parameters the synthesized image is obtained and used to reconstruct the original image

3 d image denoising by local smoothing and nonparametric regression three dimensional 3 d images are becoming increasingly popular in image applications such as magnetic resonance imaging mri functional mri fmri and other image applications observed 3 d images often contain noise that should be removed beforehand for improving the reliability of subsequent image analyses in the literature most existing image denoising methods are for 2 d images their direct extensions to 3 d cases generally cannot handle 3 d images efficiently because the structure of 3 d images is often substantially more complicated than that of 2 d images for instance edge locations are surfaces in 3 d cases which are much more challenging to handle compared to edge curves in 2 d cases in this article we propose a novel 3 d image denoising procedure based on nonparametric estimation of a 3 d jump surface from noisy data one important feature of this method is its ability to preserve edges and major edge structures such as intersections of two edge surfaces pyramids pointed corn

use of abstract hardy spaces real interpolation and applications to bilinear operators this paper can be considered as the sequel of bernicot and zhao j func anal 255 1761 1796 2008 where the authors have proposed an abstract construction of hardy spaces h1 they shew an interpolation result for these hardy spaces with the lebesgue spaces here we describe a more precise result using the real interpolation theory and we clarify the use of hardy spaces then with the help of the bilinear interpolation theory we then give applications to study bilinear operators on lebesgue spaces these ideas permit us to study singular operators with singularities similar to those of bilinear calderon zygmund operators in a far more abstract framework as in the euclidean case

a jbig based approach to the encoding of contour maps previously a new technique for the lossless encoding of contour maps was introduced based on the concept of transition points in this paper we show that by using a simple representation for the transition points i e the map of transition points the problem of encoding arbitrary contour maps can be easily converted into a problem of lossless image coding experimental results show that the joint bilevel image experts group jbig image coding standard can be used successfully for encoding maps of transition points outperforming in most cases differential chain coding moreover if we take into account that jbig codecs are available as off the shelf components then the effort required to implement the proposed method is small

the 3d line motion matrix and alignment of line reconstructions we study the problem of aligning two 3d line reconstructions in projective affine metric or euclidean space we introduce the 6 6 3d line motion matrix that acts on plucker coordinates we characterize its algebraic properties and its relation to the usual 4 4 point motion matrix and propose various methods for estimating 3d motion from line correspondences based on cost functions defined in images or 3d space we assess the quality of the different estimation methods using simulated data and real images

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

digital image restoration using spatial interaction models this paper is concerned with developing fast nonrecursive algorithms for the minimum mean squared error restoration of degraded images the degradation is assumed to be due to a space invariant periodic nonseparable known point spread function and additive white noise our basic approach is to represent the images by a class of spatial interaction models namely the simultaneous autoregressve models and the conditional markov models defined on toroidal lattices and develop minimum mean squared error restoration algorithms using these models the restoration algorithms are optimal if the parameters characterizing the interaction models are exactly known however in practice the parameters are estimated from the images by using spatial interaction models we develop restoration algorithms that do not require the availability of the original image or its prototype the specific structure of the underlying lattice enables the implementation of the filters using fast fourier transform fft computations several restoration examples are given

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

edge adaptive kalman filtering for image restoration with ringing suppression the authors extend the two dimensional 2 d linear space invariant lsi reduced update kalman filter rukf to edge adaptive space invariant restoration of noisy and blurred images using a decision directed approach the edge adaptive rukf was motivated by the need to suppress the ringing artifacts caused by lsi processing the authors show that ringing artifacts can be suppressed to a great extent by using multiple image models that provide a better match to local edge orientation the maximum a posteriori probability decision procedure developed for model selection at each pixel can be used with other 2 d kalman filtering algorithms as well

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

texture modeling by multiple pairwise pixel interactions a markov random field model with a gibbs probability distribution gpd is proposed for describing particular classes of grayscale images which can be called spatially uniform stochastic textures the model takes into account only multiple short and long range pairwise interactions between the gray levels in the pixels an effective learning scheme is introduced to recover structure and strength of the interactions using maximal likelihood estimates of the potentials in the gpd as desired parameters the scheme is based on an analytic initial approximation of the estimates and their subsequent refinement by a stochastic approximation experiments in modeling natural textures show the utility of the proposed model

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

edge sensitive image restoration using order constrained least squares methods in this paper we consider a novel technique for the restoration of noise corrupted images using order constrained least squares methods the restoration process uses a moving cross shaped filter window within which two operations are combined the first operation consists of simple hypothesis tests for the presence of an edge of some minimal height crossing the center of the window the second operation computes the window output as the order constrained least squares fit of the windowed values if an edge is deemed to be present or simply the average if no edge is present the new technique is applied to some actual noise corrupted images and the results are compared to the results of applying similarly configured median and averaging filters some computational considerations and comparisons are discussed at the end of the paper

fast computation of a contrast invariant image representation this paper sets out a new representation of an image which is contrast independent the image is decomposed into a tree of shapes based on connected components of level sets which provides a full and nonredundant representation of the image a fast algorithm to compute the tree the fast level lines transform fllt is explained in detail some simple and direct applications of this representation are shown

a global sparse gradient based coupled system for image denoising abstract we consider a coupled system for image denoising which consists of an anisotropic diffusion equation and a global sparse gradient model gsg the global sparse gradient model is used to estimate the edge map from the noisy image accurately and robustly the anisotropic diffusion process is guided by the edge map furthermore we prove the existence and uniqueness of the solutions of the coupled system with dirichlet initial boundary value problem finally comparing with the edge indicators based on local methods experimental results demonstrate that our proposed method has the state of the art performance among the pde based anisotropic diffusion approaches both in objective measurement and visual evaluation

suppression of salt and pepper noise based on youden designs abstract this paper presents a new class of algorithms based on youden designs to detect and restore edges present in an image imbedded by mixture or salt and pepper noise the mixture noise consists of a uncorrelated or correlated noisy background plus uncorrelated impulsive noise the objective is to restore pixels affected by the impulsive part of the mixture noise the approach is to consider that these pixels have lost their true value and their estimate is obtained via the normal equation that yields the least sum of square error lsse this procedure is known in the literature as the missing value approach problem the estimates are introduced into the image data and an anova technique based on youden design is carried out we introduce youden designs which are special symmetric balanced incomplete block sbib designs the pertinent statistical tests and estimates of the factor effects we derive the estimate of the missing value for the uncorrelated noise environment as well as for the correlated one the high level of performance of these algorithms can be evaluated visually via the input output images and objectively via the input output signal to noise ratio snr

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

function spaces of variable smoothness and integrability abstract in this article we introduce triebel lizorkin spaces with variable smoothness and integrability our new scale covers spaces with variable exponent as well as spaces of variable smoothness that have been studied in recent years vector valued maximal inequalities do not work in the generality which we pursue and an alternate approach is thus developed using it we derive molecular and atomic decomposition results and show that our space is well defined i e independent of the choice of basis functions as in the classical case a unified scale of spaces permits clearer results in cases where smoothness and integrability interact such as sobolev embedding and trace theorems as an application of our decomposition we prove optimal trace theorem in the variable indices case

stability and stabilization of takagi sugeno fuzzy systems via sampled data and state quantized controller in this paper we investigate the problem of stability and stabilization for sampled data fuzzy systems with state quantization by using an input delay approach the sampled data fuzzy systems with state quantization are transformed into a continuous time system with a delay in the state the transformed system contains nondifferentiable time varying state delay based on some integral techniques some new stability and stabilization criteria are first proposed by a modified lyapunov functional furthermore in the case of no quantization some new stability and stabilization criteria are also obtained it is shown that the new stability and stabilization criteria can provide a larger upper bound of the sampling interval than some existing ones in the literature two simulation examples are given to show the effectiveness of the proposed design method

multidimensional state space model kalman filtering with application to image restoration in this paper a set of three dimensional 3 d state space models based on roesser s model is employed to restore the degraded image by kalman filtering the 3 d models extend the regions of the correlation of image pixels and of the point spread function psf of blur to a nonsymmetric half plane nshp in addition the correlations of both models may be inseparable in vertical and horizontal directions so that these models are more compatible with the innate characters of image and blur processes furthermore these two models image process and psf of blur may be reduced to one by merging their signal flow graphs thus lowering the order of states and simplifying the computational algorithm a state space model for strip filtering can then be derived from this merged 3 d model a numerical example is presented below to illustrate this idea and a strip filtering model with two scan lines is derived from it for the image restoration as can be seen from the restored images resulting from the simulation experiment this 3 d model has been very effective

hardy spaces and divergence operators on strongly lipschitz domains of rn abstract let be a strongly lipschitz domain of r n consider an elliptic second order divergence operator l including a boundary condition on and define a hardy space by imposing the non tangential maximal function of the extension of a function f via the poisson semigroup for l to be in l1 under suitable assumptions on l we identify this maximal hardy space with h 1 r n if r n with h r 1 under the dirichlet boundary condition and with h z 1 under the neumann boundary condition

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

mixed h infinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays in this brief the problems of the mixed h infinity and passivity performance analysis and design are investigated for discrete time delay neural networks with markovian jump parameters represented by takagi sugeno fuzzy model the main purpose of this brief is to design a filter to guarantee that the augmented markovian jump fuzzy neural networks are stable in mean square sense and satisfy a prescribed passivity performance index by employing the lyapunov method and the stochastic analysis technique applying the matrix decomposition techniques sufficient conditions are provided for the solvability of the problems which can be formulated in terms of linear matrix inequalities a numerical example is also presented to illustrate the effectiveness of the proposed techniques

impulsive synchronization of reaction diffusion neural networks with mixed delays and its application to image encryption this paper presents a new impulsive synchronization criterion of two identical reaction diffusion neural networks with discrete and unbounded distributed delays the new criterion is established by applying an impulse time dependent lyapunov functional combined with the use of a new type of integral inequality for treating the reaction diffusion terms the impulse time dependent feature of the proposed lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction diffusion neural networks than the conventional impulse time independent lyapunov functions functionals while the new integral inequality which is derived from wirtinger s inequality overcomes the conservatism introduced by the integral inequality used in the previous results numerical examples demonstrate the effectiveness of the proposed method later the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image the experimental results verify that the proposed image encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks

duality of hardy and bmo spaces associated with operators with heat kernel bounds the introduction and development of hardy and bmo spaces on euclidean spaces r in the 1960s and 1970s played an important role in modern harmonic analysis and applications in partial differential equations these spaces were studied extensively in 32 22 18 19 31 and many others an l function f on r is in the hardy spaceh r if the area integral function of the poisson integral e t f satisfies

novel stability criteria for t s fuzzy systems in this paper novel stability conditions for takagi sugeno t s fuzzy systems are presented the so called nonquadratic membership dependent lyapunov function is first proposed which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature then new membership dependent stability conditions are developed by the new lyapunov function approach it is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical results

artistic edge and corner enhancing smoothing two important visual properties of paintings and painting like images are the absence of texture details and the increased sharpness of edges as compared to photographic images painting like artistic effects can be achieved from photographic images by filters that smooth out texture details while preserving or enhancing edges and corners however not all edge preserving smoothers are suitable for this purpose we present a simple nonlinear local operator that generalizes both the well known kuwahara filter and the more general class of filters known in the literature as ldquocriterion and value filter structure rdquo this class of operators suffers from intrinsic theoretical limitations which give rise to a dramatic instability in presence of noise especially on shadowed areas such limitations are discussed in the paper and overcome by the proposed operator a large variety of experimental results shows that the output of the proposed operator is visually similar to a painting comparisons with existing techniques on a large set of natural images highlight conditions on which traditional edge preserving smoothers fail whereas our approach produces good results in particular unlike many other well established approaches the proposed operator is robust to degradations of the input image such as blurring and noise contamination

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

a robust nonlinear filter for image restoration a class of nonlinear regression filters based on robust estimation theory is introduced the goal of the filtering is to recover a high quality image from degraded observations models for desired image structures and contaminating processes are employed but deviations from strict assumptions are allowed since the assumptions on signal and noise are typically only approximately true the robustness of filters is usually addressed only in a distributional sense i e the actual error distribution deviates from the nominal one in this paper the robustness is considered in a broad sense since the outliers may also be due to inappropriate signal model or there may be more than one statistical population present in the processing window causing biased estimates two filtering algorithms minimizing a least trimmed squares criterion are provided the design of the filters is simple since no scale parameters or context dependent threshold values are required experimental results using both real and simulated data are presented the filters effectively attenuate both impulsive and nonimpulsive noise while recovering the signal structure and preserving interesting details

3d object classification using multi object kohonen networks the problem of three dimensional planar faced opaque object recognition from one single perspective view is addressed in this paper a view parameterization based on hough transform is described classification is accomplished by multiple multi object kohonen networks a new object grouping criterion has been investigated to assign disjoint subsets of objects to each kohonen network of the system on the basis of input space topology recognition tests are presented on both synthetic and real world 3d objects even in the presence of partial occlusion

hardy spaces with variable exponents and generalized campanato spaces in the present paper we define hardy spaces with variable exponents on rn by the grand maximal function and then investigate their several properties the present paper will connect harmonic analysis with function spaces with variable exponents we obtain the atomic decomposition and the molecular decomposition with these decomposition proved we investigate the littlewood paley characterization also we specify the dual spaces of hardy spaces with variable exponents they will turn out to be campanato spaces with variable growth conditions the present paper covers local hardy spaces with variable exponents

robust reweighted map motion estimation this paper proposes a motion estimation algorithm that is robust to motion discontinuity and noise the proposed algorithm is constructed by embedding the least median squares lmeds of robust statistics into the maximum a posteriori map estimator difficulties in accurate estimation of the motion field arise from the smoothness constraint and the sensitivity to noise to cope robustly with these problems a median operator and the concept of reweighted least squares rls are applied to the map motion estimator resulting in the reweighted robust map rrmap the proposed rrmap motion estimation algorithm is also generalized for multiple image frame cases computer simulation with various synthetic image sequences shows that the proposed algorithm reduces errors compared to three existing robust motion estimation algorithms that are based on m estimation total least squares tls and hough transform it is also observed that the proposed algorithm is statistically efficient and robust to additive gaussian noise and impulse noise furthermore the proposed algorithm yields reasonable performance for real image sequences

a robust approach for high resolution frequency estimation a robust estimation method for frequencies of received signals is considered the influence function of a robust estimate is derived for the sinusoidal signals the variance of the robust estimate is also derived using the influence function it is found that the robust estimate attains the cramer rao lower bound crlb for the contaminated gaussian distribution it is of order o n sup 3 and is close to the crlb for the perfect gaussian distribution the authors introduce some basic definitions for the high resolution frequency estimation method and prove that the robust estimate has the high resolution property this property is also confirmed by numerical simulations

impulsive control and synchronization for delayed neural networks with reaction diffusion terms this paper discuss the global exponential stability and synchronization of the delayed reaction diffusion neural networks with dirichlet boundary conditions under the impulsive control in terms of p norm and point out the fact that there is no constant equilibrium point other than the origin for the reaction diffusion neural networks with dirichlet boundary conditions some new and useful conditions dependent on the diffusion coefficients are obtained to guarantee the global exponential stability and synchronization of the addressed neural networks under the impulsive controllers we assumed finally some numerical examples are given to demonstrate the effectiveness of the proposed control methods

global exponential stability of multitime scale competitive neural networks with nonsmooth functions in this paper we study the global exponential stability of a multitime scale competitive neural network model with nonsmooth functions which models a literally inhibited neural network with unsupervised hebbian learning the network has two types of state variables one corresponds to the fast neural activity and another to the slow unsupervised modification of connection weights based on the nonsmooth analysis techniques we prove the existence and uniqueness of equilibrium for the system and establish some new theoretical conditions ensuring global exponential stability of the unique equilibrium of the neural network numerical simulations are conducted to illustrate the effectiveness of the derived conditions in characterizing stability regions of the neural network

unified detection of skewed rotation reflection and translation symmetries from affine invariant contour features symmetry detection is significant for object detection and recognition since symmetries are salient cues for distinguishing geometrical structures from cluttered backgrounds this paper proposes a unified framework to detect rotation reflection and translation symmetries simultaneously on unsegmented real world images the detection is performed based on affine invariant contour features and is applicable under skewed imaging with distortions contours on a natural image are first matched to each other to find affine invariant matching pairs which are then classified into three groups using a sign change criterion corresponding to the three types of symmetries the three groups are used to vote for the corresponding symmetries the voting for rotation utilizes a scheme of short line segments the voting for reflection is based on a parameterization of axis equation and the voting for translation uses a cascade like approach experimental results of real world images are provided with quantitative evaluations validating that the proposed framework achieves desired performance

segmentation based on fusion of range and intensity images using robust trimmed methods abstract this paper proposes a segmentation algorithm based on fusion of range and intensity images using robust trimmed methods based on the bayesian theory a priori knowledge is represented using the markov random field mrf a maximum a posteriori map estimator is constructed using the edge features extracted from both range and intensity images objects are represented by a number of local planar surfaces in range images and the parametric space for surface representation is constructed with the surface parameters estimated pixel by pixel based on the least trimmed squares lts method whereas in intensity images the trimmed variance is adopted as the feature for edge extraction a final edge map is obtained by the map estimator that is constructed using the likelihood functions based on the edge information obtained from range and intensity images finally an image is segmented using the fused edge map computer simulation results show that our new segmentation algorithm effectively segments test images independent of shadow noise and lighting environment

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

a method to detect and characterize ellipses using the hough transform we describe a new technique for detecting and characterizing ellipsoidal shapes automatically from any type of image this technique is a single pass algorithm which can extract any group of ellipse parameters or characteristics which can be computed from those parameters without having to detect all five parameters for each ellipsoidal shape moreover the method can explicitly incorporate any a priori knowledge the user may have concerning ellipse parameters the method is based on techniques from projective geometry and on the hough transform this technique can significantly reduce interpretation and computation time by automatically extracting only those features or geometric parameters of interest from images and making exact use of a priori information

application of two dimensional generalized mean filtering for removal of impulse noises from images a new method for removing impulse noises from images is proposed the filtering scheme is based on replacing the central pixel value by the generalized mean value of all pixels inside a sliding window the concepts of thresholding and complementation which are shown to improve the performance of the generalized mean filter are introduced the threshold is derived using a statistical theory the actual performance of the proposed filter is compared with that of file commonly used median filter by filtering noise corrupted real images the hardware complexity of the two types of filters are also compared indicating the advantages of the generalized mean filter

synchronization of stochastic competitive neural networks with different timescales and reaction diffusion terms we propose a feedback controller for the synchronization of stochastic competitive neural networks with different timescales and reaction diffusion terms by constructing a proper lyapunov krasovskii functional as well as employing stochastic analysis theory the lashall type invariance principle for stochastic differential delay equations and a linear matrix inequality lmi technique a feedback controller is designed to achieve the asymptotical synchronization of coupled stochastic competitive neural networks a simulation example is given to show the effectiveness of the theoretical results

graph spectral image smoothing using the heat kernel a new method for smoothing both gray scale and color images is presented that relies on the heat diffusion equation on a graph we represent the image pixel lattice using a weighted undirected graph the edge weights of the graph are determined by the gaussian weighted distances between local neighboring windows we then compute the associated laplacian matrix the degree matrix minus the adjacency matrix anisotropic diffusion across this weighted graph structure with time is captured by the heat equation and the solution i e the heat kernel is found by exponentiating the laplacian eigensystem with time image smoothing is accomplished by convolving the heat kernel with the image and its numerical implementation is realized by using the krylov subspace technique the method has the effect of smoothing within regions but does not blur region boundaries we also demonstrate the relationship between our method standard diffusion based pdes fourier domain signal processing and spectral clustering experiments and comparisons on standard images illustrate the effectiveness of the method