contextual estimators of mixing probabilities for markov chain random fields abstract this paper discusses the estimation of proportions of classes from an image classification methods are compared with likelihood methods and the importance of contextual information is discussed the joint distribution of classes at neighbouring sites is modelled by a markov chain random field the class attributes are estimated from training sets and unclassified observations the effect of biased class means is reduced with a stochastic model of the bias contextual likelihood methods yield better results than non contextual methods

estimation of generalized multisensor hidden markov chains and unsupervised image segmentation this paper attacks the problem of generalized multisensor mixture estimation a distribution mixture is said to be generalized when the exact nature of components is not known but each of them belongs to a finite known set of families of distributions estimating such a mixture entails a supplementary difficulty one must label for each class and each sensor the exact nature of the corresponding distribution such generalized mixtures have been studied assuming that the components lie in the pearson system we propose a more general procedure with applications to estimating generalized multisensor hidden markov chains our proposed method is applied to the problem of unsupervised image segmentation the method proposed allows one to 1 identify the conditional distribution for each class and each sensor 2 estimate the unknown parameters in this distribution 3 estimate priors and 4 estimate the true class image

bayesian image restoration an application to edge preserving surface recovery bayesian methods for recovering a 2 d surface are discussed it is assumed that there is a textural image that can be modeled by a markov random field and that the original surface is composed of different surfaces each of which is associated with one textural state both parametric and nonparametric methods are used to enforce smoothness of these surfaces iterative procedures are examined for simultaneous restoration of the textural image and estimation of underlying parameters from the estimated textural image and the estimated parameters an estimate for the original surface is obtained two illustrative examples are presented

unsupervised image segmentation using markov random field models abstract we present two unsupervised segmentation algorithms based on hierarchical markov random field models for segmenting both noisy images and textured images each algorithm finds the the most likely number of classes their associated model parameters and generates a corresponding segmentation of the image into these classes this is achieved according to the maximum a posteriori criterion to facilitate this an mcmc algorithm is formulated to allow the direct sampling of all the above parameters from the posterior distribution of the image to allow the number of classes to be sampled a reversible jump is incorporated into the markov chain experimental results are presented showing rapid convergence of the algorithm to accurate solutions

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 fast algorithm for sparse multichannel blind deconvolution abstractwe have addressed blind deconvolution in a multichannel framework recently a robust solution to this problem based on a bayesian approach called sparse multichannel blind deconvolution smbd was proposed in the literature with interesting results however its computational complexity can be high we have proposed a fast algorithm based on the minimum entropy deconvolution which is considerably less expensive we designed the deconvolution filter to minimize a normalized version of the hybrid l1 l2 norm loss function this is in contrast to the smbd in which the hybrid l1 l2 norm function is used as a regularization term to directly determine the deconvolved signal results with synthetic data determined that the performance of the obtained deconvolution filter was similar to the one obtained in a supervised framework similar results were also obtained in a real marine data set for both techniques

minimum entropy deconvolution of pulse echo signals acquired from attenuative layered media in this article deconvolution of ultrasonic pulse echo data acquired from attenuative layered media is considered the problem is divided in two subproblems treating the sparse reflection sequence caused by the layered structure of the media and treating the frequency dependent attenuation the first subproblem is solved by means of joint maximum a posteriori estimation of the assumed zero mean white nonstationary reflection sequence and its corresponding sequence of unknown standard deviations this approach leads to an algorithm that seeks minimum entropy solutions for the reflection sequence and therefore the algorithm serves as a novel link between the classical wiener filter and methods for sparse or minimum entropy deconvolution the second subproblem is solved by introducing a new signal processing oriented linear discrete time model for frequency dependent attenuation in isotropic and homogeneous media the deconvolution algorithm is tested using simulated data and its performance for real normal incidence pulse echo data from a composite material is also demonstrated the results show that the algorithm in combination with the attenuation model yields estimates that reveal the internal structure of the composite and thus simplify the interpretation of the ultrasonic data

simultaneous parameter estimation and segmentation of gibbs random fields using simulated annealing an adaptive segmentation algorithm is developed which simultaneously estimates the parameters of the underlying gibbs random field grf and segments the noisy image corrupted by additive independent gaussian noise the algorithm which aims at obtaining the maximum a posteriori map segmentation is a simulated annealing algorithm that is interrupted at regular intervals for estimating the grf parameters maximum likelihood ml estimates of the parameters based on the current segmentation are used to obtain the next segmentation it is proven that the parameter estimates and the segmentations converge in distribution to the ml estimate of the parameters and the map segmentation with those parameter estimates respectively due to computational difficulties however only an approximate version of the algorithm is implemented the approximate algorithm is applied on several two and four region images with different noise levels and with first order and second order neighborhoods

estimation of multipath channels with long impulse response at low snr via an mcmc method this paper addresses the estimation of multipath channels with long impulse response at low signal to noise ratio snr the channel sparseness impulse response is modeled by means of a bernoulli gaussian process then the optimization of the resulting posterior distribution resorts to monte carlo markov chain mcmc simulation techniques special attention is devoted to noise correlation involved by matched filtering taking this correlation into account in the algorithm derivation leads to significantly improved performance for both amplitude and time delay estimation the method is also extended to cope with doppler frequency offsets in particular simultaneous paths with different doppler offsets can be estimated crameacuter rao lower bounds crlbs are derived and presented together with simulation results

maximum likelihood deconvolution an optimization theory perspective a large number of deconvolution procedures have appeared in the literature during the last three decades including a number of maximum likelihood deconvolution mld procedures the major advantages of the mld procedures are 1 no assumption is required about the phase of the wavelet most of the classical deconvolution techniques assume a minimum phase wavelet an assumption that may not be appropriate for many data sets 2 mld procedures can resolve closely spaced events i e they are high resolution techniques and 3 they can efficiently handle modeling and measurement errors as well as backscatter effects i e reflections from small features a comparative study of six different mld procedures for estimating the input of a linear time invariant system from measurements which have been corrupted by additive noise was made by using a common framework developed from fundamental optimization theory arguments to date only the kormylo and the chi t algorithms can be recommended

a novel approach to seismic signal processing and modeling this paper demonstrates some results obtained using state variable models and techniques on problems for which solutions either cannot be or are not easily obtained via more conventional input output techniques after a brief introduction to state variable notions the following seven problem areas are discussed modeling seismic source wavelets simultaneous deconvolution and correction for spherical divergence simultaneous wavelet estimation and deconvolution well log processing design of recursive wiener filters bremmer series decomposition of a seismogram including suppression of multiples and vertical seismic profiling and estimating reflection coefficients and traveltimes

estimation of generalized mixtures and its application in image segmentation we introduce the notion of a generalized mixture and propose some methods for estimating it along with applications to unsupervised statistical image segmentation a distribution mixture is said to be generalized when the exact nature of the components is not known but each belongs to a finite known set of families of distributions for instance we can consider a mixture of three distributions each being exponential or gaussian the problem of estimating such a mixture contains thus a new difficulty we have to label each of three components there are eight possibilities we show that the classical mixture estimation algorithms expectation maximization em stochastic em sem and iterative conditional estimation ice can be adapted to such situations once as we dispose of a method of recognition of each component separately that is when we know that a sample proceeds from one family of the set considered we have a decision rule for what family it belongs to considering the pearson system which is a set of eight families the decision rule above is defined by the use of skewness and kurtosis the different algorithms so obtained are then applied to the problem of unsupervised bayesian image segmentation we propose the adaptive versions of sem em and ice in the case of blind i e pixel by pixel segmentation global segmentation methods require modeling by hidden random markov fields and we propose adaptations of two traditional parameter estimation algorithms gibbsian em gem and ice allowing the estimation of generalized mixtures corresponding to pearson s system the efficiency of different methods is compared via numerical studies and the results of unsupervised segmentation of three real radar images by different methods are presented

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

using dynamic programming for solving variational problems in vision dynamic programming is discussed as an approach to solving variational problems in vision dynamic programming ensures global optimality of the solution is numerically stable and allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure as a specific example of the approach s efficacy applying dynamic programming to the energy minimizing active contours is described the optimization problem is set up as a discrete multistage decision process and is solved by a time delayed discrete dynamic programming algorithm a parallel procedure for decreasing computational costs is discussed

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

a stochastic method for bayesian estimation of hidden markov random field models with application to a color model we propose a new stochastic algorithm for computing useful bayesian estimators of hidden markov random field hmrf models that we call exploration selection estimation ese procedure the algorithm is based on an optimization algorithm of o francois called the exploration selection e s algorithm the novelty consists of using the a posteriori distribution of the hmrf as exploration distribution in the e s algorithm the ese procedure computes the estimation of the likelihood parameters and the optimal number of region classes according to global constraints as well as the segmentation of the image in our formulation the total number of region classes is fixed but classes are allowed or disallowed dynamically this framework replaces the mechanism of the split and merge of regions that can be used in the context of image segmentation the procedure is applied to the estimation of a hmrf color model for images whose likelihood is based on multivariate distributions with each component following a beta distribution meanwhile a method for computing the maximum likelihood estimators of beta distributions is presented experimental results performed on 100 natural images are reported we also include a proof of convergence of the e s algorithm in the case of nonsymmetric exploration graphs

markov modeling for bayesian restoration of two dimensional layered structures bayesian estimation of two dimensional stratified structures is described the major point addressed is the derivation of a statistical prior model that adequately describes such layered media this problem is of interest in applications in which the data are generally processed in one dimension only in order to take local interactions into account a markovian description is used the model is derived so as to fulfill a set of constraints that summarize physical and geometrical characteristics of the problem as well as practical requirements the resulting class of markov random fields presents a unilateral structure on a nonrectangular lattice and a hierarchical organization which involves a line process in addition it is shown to be an extension of one dimensional models already in use the properties of the model are investigated and its practicality is demonstrated by an application to seismic deconvolution simulation results show significant improvements with respect to the usual one dimensional methods

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

on the iwasawa lambda invariants of real abelian fields for a prime number p and a number field k let a denote the projective limit of the p parts of the ideal class groups of the intermediate fields of the cyclotomic zp extension over k it is conjectured that a is finite if k is totally real when p is an odd prime and k is a real abelian field we give a criterion for the conjecture which is a generalization of results of ichimura and sumida furthermore in a special case where p divides the degree of k we also obtain a rather simple criterion

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

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

on semi equivalence of generically finite polynomial mappings let f g x rightarrow y be continuous mappings we say that f is topologically equivalent to g if there exist homeomorphisms phi x rightarrow x and psi y rightarrow y such that psi circ f circ phi g moreover we say that f is topologically semi equivalent to g if there exist open dense subsets u v subset x and homeomorphisms phi u rightarrow v and psi y rightarrow y such that psi circ f circ phi u g u let x y be smooth irreducible affine complex varieties we show that every algebraic family f m times x ni m x mapsto f m x f m x in y of polynomial mappings contains only a finite number of topologically non equivalent proper mappings and only a finite number of topologically non semi equivalent generically finite mappings in particular there are only a finite number of classes of topologically non equivalent proper polynomial mappings f mathbb c n rightarrow mathbb c m of a bounded algebraic degree the same is true for a number of classes of topologically non semi equivalent generically finite polynomial mappings f mathbb c n rightarrow mathbb c m of a bounded algebraic degree

the iwasawa conjecture for totally real fields let f be a totally real number field let p be a prime number and for any integer n let fun denote the group of nth roots of unity let 41 be a p adic valued artin character for f and let f be the extension of f attached to 4 i e so that 4 is the character of a faithful representation of gal f f we will assume that f is also totally real for a number field k let k denote the cyclotomic zp extension of k following greenberg we say that 4 is of type s if f n fc f and of type w if 4 is one dimensional with f p c fcc deligne and ribet in dr following kubota and leopoldt for the case f q have proved the existence of a p adic l function associated to a one dimensional artin character 4 with f totally real this function lp s 4 is continuous for s e zp 1 and even at s 1 if 4 is not trivial and satisfies the following interpolation property

inhomogeneous prior models for image reconstruction abstract over recent years the use of homogeneous gibbs prior models in image processing has become widely accepted there has been however much discussion over precisely which models are most appropriate for most applications the simplest gaussian model tends to oversmooth reconstructions so it has been rejected in favor of various edge preserving alternatives we claim that the problem is not with the gaussian family but rather with the assumption of homogeneity in this article we propose an inhomogeneous gaussian random field as a general prior model for many image processing applications the simplicity of the gaussian model allows rapid calculation and the flexibility of the spatially varying prior parameter allows varying degrees of spatial smoothing this approach is in the spirit of adaptive kernel density methods where only the choice of the variable window width is important the analysis of real single photon emission computed tomography data is used to illustrate the methods and simu

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 class adaptive spatially variant mixture model for image segmentation we propose a new approach for image segmentation based on a hierarchical and spatially variant mixture model according to this model the pixel labels are random variables and a smoothness prior is imposed on them the main novelty of this work is a new family of smoothness priors for the label probabilities in spatially variant mixture models these gauss markov random field based priors allow all their parameters to be estimated in closed form via the maximum a posteriori map estimation using the expectation maximization methodology thus it is possible to introduce priors with multiple parameters that adapt to different aspects of the data numerical experiments are presented where the proposed map algorithms were tested in various image segmentation scenarios these experiments demonstrate that the proposed segmentation scheme compares favorably to both standard and previous spatially constrained mixture model based segmentation

a simulation based estimator for hidden markov random fields an estimator for estimating the parameters of a markov random field x from inaccurate observations is introduced the author considers first a markov gibbs random field x x sub i j on a lattice l i j i 1 2 n j 1 2 m the marginal distributions of x sub i j x sub i u j v u v 1 0 1 are first estimated from an image then random fields x are simulated with the probability of x sub i u j v b nearly equal to the estimate of p x sub i j x sub i u b a simulation method similar to the gibbs sampler is used the parameters of the markov random field model are estimated from the x s with the pseudolikelihood method

deconvolution of sparse spike trains by iterated window maximization a new algorithm for deconvolution of sparse spike trains is presented to maximize a joint map criterion an initial configuration is iteratively improved through a number of small changes computational savings are achieved by precomputing and storing two correlation functions and by employing a window strategy the resulting formulas are simple intuitive and efficient in addition they allow much more complicated transitions than state space solutions such as kormylo and mendel s 1982 single most likely replacement algorithm this makes it possible to reduce significantly the probability that the algorithm terminates in a local maximum synthetic data examples are presented that support these claims

an iterative gibbsian technique for reconstruction of m ary images abstract the reconstruction of m ary images corrupted by independent noise is treated the original image is modeled by a markov random field mrf whose parameters are unknown likewise the probabilistic structure of the noise is unknown this paper presents an iterative procedure which performs the parameter estimation and image reconstruction tasks at the same time the procedure that we call gibbsian em algorithm is a generalization to the mrf context of a general algorithm known as the em algorithm used to approximate maximum likelihood estimates for incomplete data problems a number of experiments are presented in the case of gaussian noise and binary noise showing that the gibbsian em algorithm is useful and effective for image reconstruction and segmentation

whitney theorem for complex polynomial mappings for given natural numbers d 1 d 2 we describe the topology of a generic polynomial mapping f f g x rightarrow mathbb c 2 with deg f le d 1 and deg g le d 2 here x is a complex plane or a complex sphere

noniterative manipulation of discrete energy based models for image analysis abstract with emphasis on the graph structure of energy based models devoted to image analysis we investigate efficient procedures for sampling and inferring we show that triangulated graphs whom trees are simple instances of always support causal models for which noniterative procedures can be devised to minimize the energy to extract probabilistic descriptions to sample from corresponding prior and posterior distributions or to infer from local marginals the relevance and efficiency of these procedures are illustrated for classification problems

ml parameter estimation for markov random fields with applications to bayesian tomography markov random fields mrfs have been widely used to model images in bayesian frameworks for image reconstruction and restoration typically these mrf models have parameters that allow the prior model to be adjusted for best performance however optimal estimation of these parameters sometimes referred to as hyperparameters is difficult in practice for two reasons i direct parameter estimation for mrfs is known to be mathematically and numerically challenging ii parameters can not be directly estimated because the true image cross section is unavailable we propose a computationally efficient scheme to address both these difficulties for a general class of mrf models and we derive specific methods of parameter estimation for the mrf model known as generalized gaussian mrf ggmrf we derive methods of direct estimation of scale and shape parameters for a general continuously valued mrf for the ggmrf case we show that the ml estimate of the scale parameter spl sigma has a simple closed form solution and we present an efficient scheme for computing the ml estimate of the shape parameter p by an off line numerical computation of the dependence of the partition function on p we present a fast algorithm for computing ml parameter estimates when the true image is unavailable to do this we use the expectation maximization em algorithm we develop a fast simulation method to replace the e step and a method to improve the parameter estimates when the simulations are terminated prior to convergence experimental results indicate that our fast algorithms substantially reduce the computation and result in good scale estimates for real tomographic data sets

a markov random field regulated pitman yor process prior for spatially constrained data clustering in this work we propose a markov random field regulated pitman yor process mrf pyp prior for nonparametric clustering of data with spatial interdependencies the mrf pyp is constructed by imposing a pitman yor process over the distribution of the latent variables that allocate data points to clusters model states the discount hyperparameter of which is regulated by an additionally postulated simplified pointwise markov random field gibbsian distribution with a countably infinite number of states further based on the stick breaking construction of the pitman yor process we derive an efficient truncated variational bayesian algorithm for model inference we examine the efficacy of our approach by considering an unsupervised image segmentation application using a real world dataset we show that our approach completely outperforms related methods from the field of bayesian nonparametrics including the recently proposed infinite hidden markov random field model and the dirichlet process prior

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

unsupervised deconvolution of sparse spike trains using stochastic approximation this paper presents an unsupervised method for restoration of sparse spike trains these signals are modeled as random bernoulli gaussian processes and their unsupervised restoration requires i estimation of the hyperparameters that control the stochastic models of the input and noise signals and ii deconvolution of the pulse process classically the problem is solved iteratively using a maximum generalized likelihood approach despite questionable statistical properties the contribution of the article is threefold first we present a new core algorithm for supervised deconvolution of spike trains which exhibits enhanced numerical efficiency and reduced memory requirements second we propose an original implementation of a hyperparameter estimation procedure that is based upon a stochastic version of the expectation maximization em algorithm this procedure utilizes the same core algorithm as the supervised deconvolution method third monte carlo simulations show that the proposed unsupervised restoration method exhibits satisfactory theoretical and practical behavior and that in addition good global numerical efficiency is achieved

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

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

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

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

the infinite hidden markov random field model hidden markov random field hmrf models are widely used for image segmentation as they appear naturally in problems where a spatially constrained clustering scheme is asked for a major limitation of hmrf models concerns the automatic selection of the proper number of their states i e the number of region clusters derived by the image segmentation procedure existing methods including likelihood or entropy based criteria and reversible markov chain monte carlo methods usually tend to yield noisy model size estimates while imposing heavy computational requirements recently dirichlet process dp infinite mixture models have emerged in the cornerstone of nonparametric bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori infinite mixture models based on the original dp or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results under this motivation to resolve the aforementioned issues of hmrf models in this paper we introduce a nonparametric bayesian formulation for the hmrf model the infinite hmrf model formulated on the basis of a joint dirichlet process mixture dpm and markov random field mrf construction we derive an efficient variational bayesian inference algorithm for the proposed model and we experimentally demonstrate its advantages over competing methodologies

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

discrete markov image modeling and inference on the quadtree noncasual markov or energy based models are widely used in early vision applications for the representation of images in high dimensional inverse problems due to their noncausal nature these models generally lead to iterative inference algorithms that are computationally demanding in this paper we consider a special class of nonlinear markov models which allow one to circumvent this drawback these models are defined as discrete markov random fields mrf attached to the nodes of a quadtree the quadtree induces causality properties which enable the design of exact noniterative inference algorithms similar to those used in the context of markov chain models we first introduce an extension of the viterbi algorithm which enables exact maximum a posteriori map estimation on the quadtree two other algorithms related to the mpm criterion and to bouman and shapiro s 1994 sequential map smap estimator are derived on the same hierarchical structure the estimation of the model hyper parameters is also addressed two expectation maximization em type algorithms allowing unsupervised inference with these models are defined the practical relevance of the different models and inference algorithms is investigated in the context of image classification problem on both synthetic and natural images

estimating components of univariate gaussian mixtures using prony s method a new technique for estimating the component parameters of a mixture of univariate gaussian distributions using the method of moments is presented the method of moments basically involves equating the sample moments to the corresponding mixture moments expressed in terms of component parameters and solving these equations for the unknown parameters these moment equations however are nonlinear in the unknown parameters and heretofore an analytic solution of these equations has been obtained only for two component mixtures 2 numerical solutions also tend to be unreliable for more than two components due to the large number of nonlinear equations and parameters to be solved for in this correspondence under the condition that the component distributions have equal variances or equal means the nonlinear moment equations are transformed into a set of linear equations using prony s method the solution of these equations for the unknown parameters is analytically feasible and numerically reliable for mixtures with several components numerous examples using the proposed technique for two three and four component mixtures are presented

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

maximum likelihood discriminant analysis on the plane using a markovian model of spatial context abstract a method is presented for utilising spatial information in performing discriminant analysis on multivariate data at each point on a regular lattice as for example with landsat the spatial information is modelled as a particularly simple markov random field the discriminant analysis is based on the maximum likelihood method the results are compared with alternatives by monte carlo simulation and seem to be encouraging

estimation of fuzzy gaussian mixture and unsupervised statistical image segmentation this paper addresses the estimation of fuzzy gaussian distribution mixture with applications to unsupervised statistical fuzzy image segmentation in a general way the fuzzy approach enriches the current statistical models by adding a fuzzy class which has several interpretations in signal processing one such interpretation in image segmentation is the simultaneous appearance of several thematic classes on the same site we introduce a new procedure for estimating of fuzzy mixtures which is an adaptation of the iterative conditional estimation ice algorithm to the fuzzy framework we first describe the blind estimation i e without taking into account any spatial information valid in any context of independent noisy observations then we introduce in a manner analogous to classical hard segmentation the spatial information by two different approaches contextual segmentation and adaptive blind segmentation in the first case the spatial information is taken into account at the segmentation step level and in the second case it is taken into account at the parameter estimation step level the results obtained with the iterative conditional estimation algorithm are compared to those obtained with expectation maximization em and the stochastic em algorithms on both parameter estimation and unsupervised segmentation levels via simulations the methods proposed appear as complementary to the fuzzy c means algorithms

multichannel blind deconvolution of seismic signals a new algorithm for simultaneous wavelet estimation and deconvolution of seismic reflection signals is given to remove the inherent ambiguity in this blind deconvolution problem we introduce relevant a priori information our major assumption is sparseness of the reflectivity which corresponds to a layered earth model this allows nonminimum phase wavelets to be recovered reliably and closely spaced reflectors to be resolved to combine a priori knowledge and data we use a bayesian framework and derive a maximum a posteriori estimate computing this estimate is a difficult optimization problem solved by a suboptimal iterative procedure the procedure alternates steps of wavelet estimation and reflectivity estimation the first step only requires a simple least squares fit while the second step is solved by the iterated window maximization algorithm proposed by kaaresen this enables better efficiency and optimality than established alternatives the resulting optimization method can easily handle multichannel models with only a moderate increase of the computational load lateral continuity of the reflectors is achieved by modeling local dependencies between neighboring traces major improvements in both wavelet and reflectivity estimates are obtained by taking the wavelet to be invariant across several traces the practicality of the algorithm is demonstrated on synthetic and real seismic data an application to multivariate well log segmentation is also given

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

a fuzzy clustering approach toward hidden markov random field models for enhanced spatially constrained image segmentation hidden markov random field hmrf models have been widely used for image segmentation as they appear naturally in problems where a spatially constrained clustering scheme taking into account the mutual influences of neighboring sites is asked for fuzzy c means fcm clustering has also been successfully applied in several image segmentation applications in this paper we combine the benefits of these two approaches by proposing a novel treatment of hmrf models formulated on the basis of a fuzzy clustering principle we approach the hmrf model treatment problem as an fcm type clustering problem effected by introducing the explicit assumptions of the hmrf model into the fuzzy clustering procedure our approach utilizes a fuzzy objective function regularized by kullback leibler divergence information and is facilitated by application of a mean field like approximation of the mrf prior we experimentally demonstrate the superiority of the proposed approach over competing methodologies considering a series of synthetic and real world image segmentation applications

on quadratic polynomial mappings from the plane into the n dimensional space abstract we show that up to linear equivalence there are only finitely many polynomial quadratic mappings f c 2 c n and f r 2 r n we list all possibilities

optimal simultaneous detection and estimation of filtered discrete semi markov chains an optimal algorithm for the detection of noisy filtered discrete semi markov chains is presented estimation of the underlying model parameters is also considered for a given path of the discrete semi markov chain the optimum estimates of the model parameters obtained by the maximum likelihood method are expressed as functions of the path these functions are then used to derive a single maximum a posteriori criterion for the optimal detection of the unknown single path the final optimization is carried out numerically by a combination of gradient divide and conquer and search techniques this set of techniques is referred to as the integer most likely search detector experimental results using synthetic data demonstrate the potential of the algorithm

em procedures using mean field like approximations for markov model based image segmentation this paper deals with markov random field model based image segmentation this involves parameter estimation in hidden markov models for which one of the most widely used procedures is the em algorithm in practice difficult ies arise due to the dependence structure in the models and approximations are required to make the algorithm tractable we propose a class of algorithms in which the idea is to deal with systems of independent variables this corresponds to approximations of the pixels interactions similar to the mean field approximation it follows algorithms that have the advantage of taking the markovian structure into account while preserving the good features of em in addition this class that includes new and already known procedures is presented in a unified framework showing that apparently distant algorithms come from similar approximation principles we illustrate the algorithms performance on synthetic and real images these experiments point out the ability of our procedures to take the spatial information into account our algorithms often show significant improvement when comparing with the em algorithm applied with no account of the spatial structure and with the icm algorithm based on maximization of the pseudo likelihood and commonly used in image segmentation

on the estimation of noisy binary markov random fields possolo technical report no 77 department of statistics gn 22 university of washington seattle 1986 and derin and elliott ieee trans pattern analysis mach intell pami 9 39 55 1987 proposed for the estimation of binary and more general m ary markov random fields the logit method based on histogramming an image the authors applied the method to noise free markov random fields for estimation of noisy images one might recursively implement the logit method within an iterative restoration algorithm such as the iterated conditional modes icm method of besag j r statist soc b48 259 302 1986 by alternating parameter estimation and restoration it is noted that failure to smooth zero histogram counts for the purposes of estimation can cause icm to cycle indefinitely

multichannel deconvolution of seismic signals using statistical mcmc methods in this paper we propose two multichannel blind deconvolution algorithms for the restoration of two dimensional 2d seismic data both algorithms are based on a 2d reflectivity prior model and use iterative multichannel deconvolution procedures which deconvolve the seismic data while taking into account the spatial dependency between neighboring traces the first algorithm employs in each step a modified maximum posterior mode mpm algorithm which estimates a reflectivity column from the corresponding observed trace using the estimate of the preceding reflectivity column the second algorithm takes into account estimates of both the preceding and subsequent columns in the estimation process both algorithms are applied to synthetic and real data and demonstrate better results compared to those obtained by a single channel deconvolution method expectedly the second algorithm which utilizes more information in the estimation process of each reflectivity column is shown to produce better results than the first algorithm

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

testing sets for properness of polynomial mappings in this paper we characterize testing sets for properness of polynomial mappings f mathbb c n rightarrow mathbb c m we also study the set of points at which such mappings are not proper as the first application we give a proof of the complementary conjecture of mckay and wang conjecture 12 in 16 the second application is an answer to the problem of kraft russell about a characterization of mathbb c n the third application is given in 13 a solution of the problem of van den essen and shpilrain about endomorphism of the ring mathbb c x 1 x n the fourth application is a theorem about extensions of affine varieties

on quadratic polynomial mappings of the plane abstract we show that up to linear equivalence there is only finitely many polynomial quadratic mappings f c 2 c 2 and f r 2 r 2 we list all possibilities

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

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

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

a computationally fast approach to maximum likelihood deconvolution in this paper we derive and implement a maximum likelihood deconvolution mld algorithm based on the same channel and statistical models used by kormylo and mendel 1983a that leads to many fewer computations than their mld algorithm both algorithms can simultaneously estimate a nonminimum phase wavelet and statistical parameters detect locations of significant reflectors and deconvolve the data our mld algorithm is implemented by a two phase block component method bcm the phase 1 block functions like a coarse adjustment of unknown quantities and provides a set of good initial conditions for the phase 2 block which functions like a fine adjustment of unknown quantities we demonstrate good performance of our algorithm for both synthetic and real data

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

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

evaluation and applications of the iterated window maximization method for sparse deconvolution estimating a sparse signal from a linearly degraded and noisy data record is often desirable in seismic and ultrasonic applications bernoulli gaussian modeling and maximum a posteriori estimation has proven successful but entails computationally difficult optimization problems that must be solved by suboptimal methods the iterated window maximization iwm algorithm was proposed for such optimization by kaaresen see ibid vol 45 p 1173 83 1997 the purpose of this paper is twofold first the iwm is evaluated against several established alternatives for bernoulli gaussian deconvolution the restoration quality is quantified by various loss functions and the average performance is studied through simulation in all cases examined the iwm combined better restoration and significantly faster execution than the other algorithms this motivates extension of iwm to other models which is the second objective of this paper promising real data results are obtained from such diverse applications as robust modeling of ultrasonic nondestructive evaluation data deblurring of two dimensional 2 d astronomical star fields and segmentation of seismic well logs it is also argued that iwm can be used for other deconvolution problems as long as the function to be reconstructed is in some sense sparse

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

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

on the iwasawa invariant of the cyclotomic ℤ extension of ℚ we study the iwasawa invariant of the cyclotomic 2 extension of q p for an odd prime number p which satisfies p 1 mod 16 relating it to units having certain properties we give an upper bound of and show 0 in certain cases we also give new numerical examples of 0

unsupervised image segmentation using an unlabeled region process abstract the segmentation of a gray scale image of regions of uniform or slowly varying intensity is discussed a gibbsian representation is given for a partition of a lattice with no labels the homogeneity of each segment is measured by the sample variance of observations in a region merging algorithm the posterior probability of the segmentation is gradually increased it is shown how to simulate partitions with the gibbs sampler and how to combine information in simulated segmentations when the segments cannot be grouped into genuine classes the segmentation methods are preferable to classification by iterated conditional modes icm or by the maximizer of posterior marginals mpm