multiple window parallel adaptive boundary finding in computer vision the problem considered in this paper is the estimation of highly variable object boundaries in noisy images boundaries may be those of a tank in an ir image a spinal canal in a cat scan a cloud in a visible light image etc or they may be internal to an object such as the boundary between a spherical surface and a cylindrical surface in a manufactured object the focus of the paper is on parallel multiple window boundary estimation algorithms here the image field is parti tioned into an array of rectangular windows and boundary finders are run simultaneously within the windows the boundary segments found within the windows are then seamed together to obtain meaningful global boundaries the entire procedure is treated within a maximum likelihood estimation framework that we have developed for boundary finding although our multiple window estimation approach can be used with a number of local boundary finding algorithms we concen trate on one which is based on dynamic programming and will produce the true maximum likelihood boundary some theoretical considera tions for boundary model design and boundary finding runtime are covered included is the use of a low computational cost f test for test ing whether a window contains a boundary and an analytical treatment which shows that use of coarse pixels with a chi square test or an f test improves the probability of correctly recognizing whether a boundary is present in a window

a wavelet or lifting scheme based imputation method summary the paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis our method incorporates a bayesian mixture prior for these wavelet coefficients into a gibbs sampler to generate a complete posterior distribution for the variable of interest intuitively the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites we demonstrate the strong performance of our estimator in both one and two dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines

approximate random variate generation from infinitely divisible distributions with applications to bayesian inference summary stochastic processes with independent increments play a central role in bayesian nonparametric inference the distributions of the increments of these processes aside from fixed points of discontinuity are infinitely divisible and their laplace and or fourier transforms in the levy representation are usually known conventional bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest although markov chain monte carlo methods have been used to obtain a fuller analysis in the context of dirichlet process priors in this paper we propose and implement a general method for simulating infinitely divisible random variates when their fourier or laplace transforms are available in the levy representation theoretical justification is established by proving a convergence theorem that is a sampling form of a classical theorem in probability the results provide a method for implementing bayesian nonparametric inference by using a wide range of stochastic processes as priors

blind deconvolution using a variational approach to parameter image and blur estimation following the hierarchical bayesian framework for blind deconvolution problems in this paper we propose the use of simultaneous autoregressions as prior distributions for both the image and blur and gamma distributions for the unknown parameters hyperparameters of the priors and the image formation noise we show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations we apply variational methods to approximate the posterior probability of the unknown image blur and hyperparameters and propose two different approximations of the posterior distribution one of these approximations coincides with a classical blind deconvolution method the proposed algorithms are tested experimentally and compared with existing blind deconvolution methods

nonlinear measures a new approach to exponential stability analysis for hopfield type neural networks in this paper a new concept called nonlinear measure is introduced to quantify stability of nonlinear systems in the way similar to the matrix measure for stability of linear systems based on the new concept a novel approach for stability analysis of neural networks is developed with this approach a series of new sufficient conditions for global and local exponential stability of hopfield type neural networks is presented which generalizes those existing results by means of the introduced nonlinear measure the exponential convergence rate of the neural networks to stable equilibrium point is estimated and for local stability the attraction region of the stable equilibrium point is characterized the developed approach can be generalized to stability analysis of other general nonlinear systems

discrete vector potentials for nonsimply connected three dimensional domains in this paper we focus on the representation of a divergence free vector field defined on a connected nonsimply connected domain omega subset r 3 with a connected boundary gamma by its curl and its normal component on the boundary the considered problem is discretized with h curl and h div conforming finite elements in order to ensure the uniqueness of the vector potential we propose a spanning tree methodology to identify the independent edges the topological features of the domain under consideration are analyzed here by means of the homology groups of first and second order

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

global exponential stability of impulsive discrete time neural networks with time varying delays this paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete time neural networks with time varying delays firstly by means of the lyapunov stability theory some inequality analysis techniques and a discrete time halanay type inequality technique sufficient conditions for ensuring global exponential stability of discrete time neural networks are derived and the estimated exponential convergence rate is provided as well the obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete time neural networks with time varying delays finally numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria

a new development for the tikhonov theorem in nonlinear singular perturbation systems abstract this paper deals with the exponential stability of nonlinear perturbation systems under a new condition a novel criterion of exponential stability of nonlinear systems is firstly given in a general form in this criterion a new kind of characteristic value is introduced which makes the exponential stability measurable based on this criterion a new development for the tikhonov theorem in nonlinear singular perturbation systems is presented

outperforming the gibbs sampler empirical estimator for nearest neighbor random fields given a markov chain sampling scheme does the standard empirical estimator make best use of the data we show that this is not so and construct better estimators we restrict attention to nearest neighbor random fields and to gibbs samplers with deterministic sweep but our approach applies to any sampler that uses reversible variable at a time updating with deterministic sweep the structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance the extra computational cost is negligible when the random field is spatially homogeneous symmetrizations of our estimator lead to further variance reduction the performance of the estimators is evaluated in a simulation study of the ising model

variational bayesian image restoration with a product of spatially weighted total variation image priors in this paper a new image prior is introduced and used in image restoration this prior is based on products of spatially weighted total variations tv these spatial weights provide this prior with the flexibility to better capture local image features than previous tv based priors bayesian inference is used for image restoration with this prior via the variational approximation the proposed restoration algorithm is fully automatic in the sense that all necessary parameters are estimated from the data and is faster than previous similar algorithms numerical experiments are shown which demonstrate that image restoration based on this prior compares favorably with previous state of the art restoration algorithms

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

about the gauge conditions arising in finite element magnetostatic problems abstract in this paper we deal with some magnetostatic models considered in vector potential formulations and solved by a finite element solver in order to ensure the uniqueness of the solution a gauge condition has to be imposed and several possibilities occur moreover the source term has to be correctly defined to ensure a physically admissible solution we show the equivalence between some of these choices for several kinds of boundary conditions moreover we highlight their characteristic behaviors on some numerical benchmarks to illustrate our theoretical results

stability analysis of dynamical neural networks in this paper we use the matrix measure technique to study the stability of dynamical neural networks testable conditions for global exponential stability of nonlinear dynamical systems and dynamical neural networks are given it shows how a few well known results can be unified and generalized in a straightforward way local exponential stability of a class of dynamical neural networks is also studied we point out that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point from this some well known and new sufficient conditions for local exponential stability of neural networks are obtained

on the equivalence of soft wavelet shrinkage total variation diffusion total variation regularization and sides soft wavelet shrinkage total variation tv diffusion tv regularization and a dynamical system called sides are four useful techniques for discontinuity preserving denoising of signals and images in this paper we investigate under which circumstances these methods are equivalent in the one dimensional case first we prove that haar wavelet shrinkage on a single scale is equivalent to a single step of space discrete tv diffusion or regularization of two pixel pairs in the translationally invariant case we show that applying cycle spinning to haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of tv diffusion we prove that space discrete tv diffusion and tv regularization are identical and that they are also equivalent to the sides system when a specific force function is chosen afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the laplacian pyramid of the signal we analyze possibilities to avoid gibbs like artifacts for multiscale haar wavelet shrinkage by scaling the thresholds finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and pde variational approaches these methods are based on iterated shift invariant wavelet shrinkage at multiple scales with scaled thresholds

augmented formulations for solving maxwell equations we consider augmented variational formulations for solving the static or time harmonic maxwell equations for that a term is added to the usual h curl conforming formulations it consists of a weighted l2 scalar product between the divergence of the em and the divergence of test fields in this respect the methods we present are h curl div conforming we also build mixed augmented variational formulations with either one or two lagrange multipliers to dualize the equation on the divergence and when applicable the relation on the tangential or normal trace of the field it is proven that one can derive formulations which are equivalent to the original static or time harmonic maxwell equations in the latter case spurious modes are automatically excluded numerical analysis and experiments will be presented in the forthcoming paper augmented formulations for solving maxwell equations numerical analysis and experiments in preparation

novel delay dependent global asymptotic stability condition of hopfield neural networks with delays in this paper the global asymptotic stability of hopfield neural networks with delays is investigated distinct differences from other analytical approaches lie in transforming to an equivalent system by using a parameterized transformation which allows free variables in an operator a novel less conservative and restrictive criterion than those established in the earlier references is given in terms of several matrix inequalities by utilizing the lyapunov theory and matrix inequality framework the results are related to the size of delays numerical examples are given to show the effectiveness of our proposed method

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

a nodal based finite element approximation of the maxwell problem suitable for singular solutions a new mixed finite element approximation of maxwell s problem is proposed its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term which yields a very weak control on the divergence of the unknown the method is shown to be stable and convergent in the natural h rm mathbf curl 0 omega norm for this unknown in particular convergence also applies to singular solutions for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement

nonfragile h state estimation for recurrent neural networks with time varying delays on proportional integral observer design in this article a novel proportional integral observer pio design approach is proposed for the nonfragile h state estimation problem for a class of discrete time recurrent neural networks with time varying delays the developed pio is equipped with more design freedom leading to better steady state accuracy compared with the conventional luenberger observer the phenomena of randomly occurring gain variations which are characterized by the bernoulli distributed random variables with certain probabilities are taken into consideration in the implementation of the addressed pio attention is focused on the design of a nonfragile pio such that the error dynamics of the state estimation is exponentially stable in a mean square sense and the prescribed h performance index is also achieved sufficient conditions for the existence of the desired pio are established by virtue of the lyapunov krasovskii functional approach and the matrix inequality technique finally a simulation example is provided to demonstrate the effectiveness of the proposed pio design scheme

robust exponential stability of uncertain stochastic neural networks with distributed delays and reaction diffusions this paper considers the problem of stability analysis for uncertain stochastic neural networks with distributed delays and reaction diffusions two sufficient conditions for the robust exponential stability in the mean square of the given network are developed by using a lyapunov krasovskii functional an integral inequality and some analysis techniques the conditions which are expressed by linear matrix inequalities can be easily checked two simulation examples are given to demonstrate the reduced conservatism of the proposed conditions

adaptive boundary iterative learning control for an euler bernoulli beam system with input constraint this paper addresses the vibration control and the input constraint for an euler bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint a restrained adaptive boundary iterative learning control abilc law is proposed based on a time weighted lyapunov krasovskii like composite energy function in order to deal with the uncertainty of a system parameter and reject the external disturbances three adaptive laws are designed and learned in the iteration domain all the system states of the closed loop system are proved to be bounded in each iteration along the iteration axis the displacements asymptotically converge toward zero simulation results are provided to illustrate the effectiveness of the proposed abilc scheme

absolute exponential stability of a class of continuous time recurrent neural networks this paper presents a new result on absolute exponential stability aest of a class of continuous time recurrent neural networks with locally lipschitz continuous and monotone nondecreasing activation functions the additively diagonally stable connection weight matrices are proven to be able to guarantee aest of the neural networks the aest result extends and improves the existing absolute stability and aest ones in the literature

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

on the global stability of delayed neural networks lyapunov functional methods combining with some inequality techniques are employed to study the global asymptotic stability of delayed neural networks without assuming lipschitz conditions on the activation functions a new sufficient condition is established such criteria allows us to include non lipschitzian activation functions in the design of delayed neural networks the result presented here is also discussed from the point of view of its relationship to some previous results

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

global attractivity in delayed hopfield neural network models two different approaches are employed to investigate the global attractivity of delayed hopfield neural network models without assuming the monotonicity and differentiability of the activation functions liapunov functionals and functions combined with the razumikhin technique are constructed and employed to establish sufficient conditions for global asymptotic stability independent of the delays in the case of monotone and smooth activation functions the theory of monotone dynamical systems is applied to obtain criteria for global attractivity of the delayed model such criteria depend on the magnitude of delays and show that self inhibitory connections can contribute to the global convergence

global convergence and asymptotic stability of asymmetric hopfield neural networks abstract the global convergence and asymptotic stability of hopfield neural networks are known to be bases of successful applications of networks in various computing and recognition tasks however all previous studies on the networks assumed that the interconnection matrix is symmetric or antisymmetric in this paper the two fundamental properties of the networks are studied without a symmetry assumption it is proved that the networks will be globally convergent to a stable state if the interconnection matrix is weakly diagonally dominant in a sense to be defined furthermore under any one of conditions assuring global convergence of the network the maximal attraction radius of any one of stable states is found to be half of the distribution distance of the state to the network the obtained results not only generalize the existing results but also provide a theoretical foundation of performance analysis and new applications of the hopfield networks

event triggered state estimation for discrete time multidelayed neural networks with stochastic parameters and incomplete measurements in this paper the event triggered state estimation problem is investigated for a class of discrete time multidelayed neural networks with stochastic parameters and incomplete measurements in order to cater for more realistic transmission process of the neural signals we make the first attempt to introduce a set of stochastic variables to characterize the random fluctuations of system parameters in the addressed neural network model the delays among the interconnections are allowed to be different which are more general than those in the existing literature the incomplete information under consideration includes randomly occurring sensor saturations and quantizations for the purpose of energy saving an event triggered state estimator is constructed and a sufficient condition is given under which the estimation error dynamics is exponentially ultimately bounded in the mean square it is worth noting that the ultimate boundedness of the error dynamics is explicitly estimated the characterization of the desired estimator gain is designed in terms of the solution to a certain matrix inequality finally a numerical simulation example is presented to illustrate the effectiveness of the proposed event triggered state estimation scheme

image reconstruction and restoration overview of common estimation structures and problems developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined particular attention is paid to common estimation structures and to practical problems not properly solved yet the problem of image reconstruction and restoration is first formulated some of the current regularization approaches used to solve the problem are then described the concepts of a priori information and compound criterion are introduced a bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated the practical aspects of computing the solution first when the hyperparameters are known and second when they must be estimated are then considered conclusions are drawn and points that still need to be investigated are outlined

genetic algorithms for ambiguous labelling problems abstract consistent labelling problems frequently have more than one solution most work in the field has aimed at disambiguating early in the interpretation process using only local evidence this paper starts with a review of the literature on labelling problems and ambiguity based on this review we propose a strategy for simultaneously extracting multiple related solutions to the consistent labelling problem in a preliminary experimental study we show that an appropriately modified genetic algorithm is a robust tool for finding multiple solutions to the consistent labelling problem these solutions are related by common labellings of the most strongly constrained junctions we have proposed three run time measures of algorithm performance the maximum fitness of the genetic algorithm s population its shannon entropy and the total hamming distance between its distinct members the results to date indicate that when the shannon entropy falls below a certain threshold new solutions are unlikely to emerge and that most of the diversity in the population disappears within the first few generations

stability and synchronization of discrete time markovian jumping neural networks with mixed mode dependent time delays in this paper we introduce a new class of discrete time neural networks dnns with markovian jumping parameters as well as mode dependent mixed time delays both discrete and distributed time delays specifically the parameters of the dnns are subject to the switching from one to another at different times according to a markov chain and the mixed time delays consist of both discrete and distributed delays that are dependent on the markovian jumping mode we first deal with the stability analysis problem of the addressed neural networks a special inequality is developed to account for the mixed time delays in the discrete time setting and a novel lyapunov krasovskii functional is put forward to reflect the mode dependent time delays sufficient conditions are established in terms of linear matrix inequalities lmis that guarantee the stochastic stability we then turn to the synchronization problem among an array of identical coupled markovian jumping neural networks with mixed mode dependent time delays by utilizing the lyapunov stability theory and the kronecker product it is shown that the addressed synchronization problem is solvable if several lmis are feasible hence different from the commonly used matrix norm theories such as the m matrix method a unified lmi approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation where the lmis can be easily solved by using the available matlab lmi toolbox two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained

iterative reweighted total generalized variation based poisson noise removal model total generalized variation tgv regularization model is one of the most effective methods for denoising and eliminating staircase effect however the tgv regularization model tends to blur edges as the existence of high order derivative in order to avoid the staircase effect while alleviating the edge blurring an iterative reweighted tgv based poisson noise removal model is presented under the assumption that each pixel of noisy image follows a poisson distribution the weight function incorporated in the tgv regularization term is derived from the expectation maximization em algorithm we design a new iterative weighted primal dual algorithm which is an improvement of the classic iterative reweighted algorithm numerical experimental results show the better performance of our model in removing noise effectively while preserving edges and eliminating staircase effect

the measure on the original space from a product measure abstract the measurability problems can arise in gaussian and empirical processes underlying nonparametric and semiparametric problems critical in modern statistics and machine learning the usual applications are high dimensional data in random fields to ensure the validity of recovering a true original complex object from its observed images treated in a product space that appears in existing high dimensional data applications widely arising in physical biological and social sciences and engineering we begin with the results on the algebra of the original space induced by a given map f t mapping from to a product measure space t f t t we study the certain measurability issues on with the induced measure from the image measure t of the product space by establishing the outer measure restricted to the trace algebra we further investigate the measure on under the map f t to obtain the conditions for the identifiability equality t f t 1 to hold so that a practical and rigorous foundation is provided for the nontrivial applications to work meaningfully

estimating the granularity coefficient of a potts markov random field within a markov chain monte carlo algorithm this paper addresses the problem of estimating the potts parameter jointly with the unknown parameters of a bayesian model within a markov chain monte carlo mcmc algorithm standard mcmc methods cannot be applied to this problem because performing inference on requires computing the intractable normalizing constant of the potts model in the proposed mcmc method the estimation of is conducted using a likelihood free metropolis hastings algorithm experimental results obtained for synthetic data show that estimating jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of on the other hand choosing an incorrect value of can degrade estimation performance significantly to illustrate the interest of this method the proposed algorithm is successfully applied to real bidimensional sar and tridimensional ultrasound images

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

fast sampling of gaussian markov random fields this paper demonstrates how gaussian markov random fields conditional autoregressions can be sampled quickly by using numerical techniques for sparse matrices the algorithm is general and efficient and expands easily to various forms for conditional simulation and evaluation of normalization constants we demonstrate its use by constructing efficient block updates in markov chain monte carlo algorithms for disease mapping

phase unwrapping of mr phase images using poisson equation the authors have developed a technique based on a solution of the poisson equation to unwrap the phase in magnetic resonance mr phase images the method is based on the assumption that the magnitude of the inter pixel phase change is less than spl pi per pixel therefore the authors obtain an estimate of the phase gradient by wrapping the gradient of the original phase image the problem is then to obtain the absolute phase given the estimate of the phase gradient the least squares ls solution to this problem is shown to be a solution of the poisson equation allowing the use of fast poisson solvers the absolute phase is then obtained by mapping the ls phase to the nearest multiple of 2 k from the measured phase the proposed technique is evaluated using mr phase images and is proven to be robust in the presence of noise an application of the proposed method to the 3 point dixon technique for water and fat separation is demonstrated

object based estimation of dense motion fields motion estimation belongs to key techniques in image sequence processing segmentation of the motion fields such that ideally each independently moving object uniquely corresponds to one region is one of the essential elements in object based image processing this paper is concerned with unsupervised simultaneous estimation of dense motion fields and their segmentations it is based on a stochastic model relating image intensities to motion information based on the analysis of natural images a region based model of motion compensated prediction error is proposed in each region the error is modeled by a white stationary generalized gaussian random process the motion field and its segmentation are themselves modeled by a compound gibbs markov random field accounting for statistical bindings in spatial direction and along the direction of motion trajectories the a posteriori distribution of the motion field for a given image sequence is formulated as an objective function such that its maximization results in the map estimate a deterministic multiscale relaxation technique with regular structure is employed for optimization of the objective function simulation results are in a good agreement with human perception for both the motion fields and their segmentations

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

3 d contextual bayesian classifiers we extend a series of multivariate bayesian two dimensional 2 d contextual classifiers to three dimensional 3 d by specifying a simultaneous gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its six nearest 3 d neighbors

bayesian lasso for semiparametric structural equation models there has been great interest in developing nonlinear structural equation models and associated statistical inference procedures including estimation and model selection methods in this paper a general semiparametric structural equation model ssem is developed in which the structural equation is composed of nonparametric functions of exogenous latent variables and fixed covariates on a set of latent endogenous variables a basis representation is used to approximate these nonparametric functions in the structural equation and the bayesian lasso method coupled with a markov chain monte carlo mcmc algorithm is used for simultaneous estimation and model selection the proposed method is illustrated using a simulation study and data from the affective dynamics and individual differences adid study results demonstrate that our method can accurately estimate the unknown parameters and correctly identify the true underlying model

the indian buffet process an introduction and review the indian buffet process is a stochastic process defining a probability distribution over equivalence classes of sparse binary matrices with a finite number of rows and an unbounded number of columns this distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features or that involve bipartite graphs in which the size of at least one class of nodes is unknown we give a detailed derivation of this distribution and illustrate its use as a prior in an infinite latent feature model we then review recent applications of the indian buffet process in machine learning discuss its extensions and summarize its connections to other stochastic processes

bayesian estimation for optimized structured illumination microscopy structured illumination microscopy is a recent imaging technique that aims at going beyond the classical optical resolution by reconstructing high resolution hr images from low resolution lr images acquired through modulation of the transfer function of the microscope the classical implementation has a number of drawbacks such as requiring a large number of images to be acquired and parameters to be manually set in an ad hoc manner that have until now hampered its wide dissemination here we present a new framework based on a bayesian inverse problem formulation approach that enables the computation of one hr image from a reduced number of lr images and has no specific constraints on the modulation moreover it permits to automatically estimate the optimal reconstruction hyperparameters and to compute an uncertainty bound on the estimated values we demonstrate through numerical evaluations on simulated data and examples on real microscopy data that our approach represents a decisive advance for a wider use of hr microscopy through structured illumination

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

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

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

some generalized sufficient convergence criteria for nonlinear continuous neural networks a reason for applying the direct method of lyapunov to artificial neural networks anns is to design dynamical neural networks so that they exhibit global asymptotic stability lyapunov functions that frequently appear in the ann literature include the quadratic function the persidskii function and the lure postnikov function this contribution revisits the quadratic function and shows that via krasovskii like stability criteria it is possible to have a very simple and systematic procedure to obtain not only new and generalized results but also well known sufficient conditions for convergence established recently by non lyapunov methods such as the matrix measure and nonlinear measure

exponential stability and oscillation of hopfield graded response neural network both exponential and stochastic stabilities of the hopfield neural network are analyzed the results are especially useful for analyzing the stabilities of asymmetric neural networks a constraint on the connection matrix has been found under which the neural network has a unique and exponentially stable equilibrium given any connection matrix this constraint can be satisfied through the adjustment of the gains of the amplifiers and the resistances in the neural net circuit a one to one and smooth map between input currents and the equilibria of the neural network can be set up the above results can be applied to the master slave net to prove that the master net can find the best connection matrix for the slave net for the neural network disturbed by some noise the stochastic stability of the network is also analyzed a special asymmetric neural network formed by a closed chain of formal neurons is also studied for its stability and oscillation both stable and oscillatory dynamics are obtained in the closed chain network through the adjustment of the gains and resistances of the amplifiers

frustration stability and delay induced oscillations in a neural network model the effect of time delays on the linear stability of equilibria in an artificial neural network of hopfield type is analyzed the possibility of delay induced oscillations occurring is characterized in terms of properties of the not necessarily symmetric connection matrix of the network such oscillations are possible exactly when the network is frustrated equivalently when the signed digraph of the matrix does not require the perron property nonlinear analysis centre manifold computation of a three unit frustrated network is presented giving the nature of the bifurcations taking place a supercritical hopf bifurcation is shown to occur and a codimension two bifurcation is unfolded

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

rigid body segmentation and shape description from dense optical flow under weak perspective we present an algorithm for identifying and tracking independently moving rigid objects from optical flow some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field while discontinuities do indicate a change in scene depth they do not in general signal a boundary between two separate objects the proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion thus motion discontinuities based on self occlusion can be distinguished from those due to separate objects the use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object the algorithm assumes an affine camera where perspective effects are limited to changes in overall scale no camera calibration parameters are required a kalman filter based approach is used for tracking motion parameters with time

an integrated approach for scene understanding based on markov random field model in this paper we propose a markov random field model based approach as a unified and systematic way for modeling encoding and applying scene knowledge to the image understanding problem in our proposed scheme we formulate the image segmentation and interpretation problem as an integrated scheme and solve it through a general optimization algorithm more specifically the image is first segmented into a set of disjoint regions by a conventional region based segmentation technique which operates on image pixels and a region adjacency graph rag is then constructed from the resulting segmented regions based on the spatial adjacencies between regions our scheme then proceeds on the rag by defining the region merging and labeling problem based on the mrf models in the mrf model we specify the a priori knowledge about the optimal segmentation and interpretation in the form of clique functions and those clique functions are incorporated into the energy function to be minimized by a general optimization technique in the proposed scheme the image segmentation and interpretation processes cooperate in the simultaneous optimization process such that the erroneous segmentation and misinterpretation due to incomplete knowledge about each problem domain can be compensately recovered by continuous estimation of the single unified energy function we exploit the proposed scheme to segment and interpret natural outdoor scene images

relation between optimal nonlinearity and non gaussian noise enhancing a weak signal in a nonlinear system in the study of stochastic resonance it is often mentioned that nonlinearity can enhance a weak signal embedded in noise in order to give a systematic proof of the signal enhancement in nonlinear systems we derive an optimal nonlinearity that maximizes a signal to noise ratio snr the obtained optimal nonlinearity yields the maximum unbiased signal estimation performance which is known in the context of information theory it is found that a linear system is optimal for a gaussian noise but for a non gaussian noise there exist nonlinear systems that can achieve an snr higher than that obtained from linear systems this analysis refers to a system subjected to an additive non gaussian noise with a small signal input

bayes inference in the tobit censored regression model we consider the bayes estimation of the tobit censored regression model with normally distributed errors a simple condition for the existence of posterior moments is provided suitable versions of monte carlo procedures based on symmetric multivariate t distributions and laplacian approximations in a certain parametrization are developed and illustrated ideas involving data augmentation and gibbs sampling cf tanner and wong 1987 and gelfand and smith 1990 are also developed the methods are compared in two examples with diffuse priors and various combinations of sample sizes and degrees of censoring

selecting the number of classes under latent class regression a factor analytic analogue recently the regression extension of latent class analysis rlca model has received much attention in the field of medical research the basic rlca model summarizes shared features of measured multiple indicators as an underlying categorical variable and incorporates the covariate information in modeling both latent class membership and multiple indicators themselves to reduce complexity and enhance interpretability one usually fixes the number of classes in a given rlca often goodness of fit methods comparing various estimated models are used as a criterion to select the number of classes in this paper we propose a new method that is based on an analogous method used in factor analysis and does not require repeated fitting two ideas with application to many settings other than ours are synthesized in deriving the method a connection between latent class models and factor analysis and techniques of covariate marginalization and elimination a monte carlo simulation study is presented to evaluate the behavior of the selection procedure and compare to alternative approaches data from a study of how measured visual impairments affect older persons functioning are used for illustration

the effect of source amplitude and phase in matched field source localization traditional matched field processing is typically employed for localization of a source with unknown amplitude and phase at transmission the spectral information of the source is estimated via maximum likelihood and is used for localization with the bartlett processor maximum a posteriori estimation of the spectrum of the source is here proposed along with the estimation of source location and noise variance where the joint posterior probability distribution of all parameters is computed with gibbs sampling it is shown that the proposed method has a higher probability of correct localization than the traditional approach

voxel based bayesian lesion symptom mapping most existing voxel based lesion symptom mapping methods are based on the same statistical foundation null hypothesis significance testing nhst the two major limitations of these methods are the inability to infer that there is no difference in lesion proportions and a requirement for multiple comparison correction we propose a bayesian approach that directly models the posterior distribution of lesion proportion difference and makes decisions based on inference on this posterior distribution compared to nhst based approaches our bayesian approach yields inference results with clearer semantics and does not require multiple comparison correction we evaluated our bayesian method using simulated data and data from a study of acute ischemic left hemispheric stroke results of both experiments indicate that the bayesian approach is sensitive in detecting regions that characterize group differences