a test for second order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series summary many time series are not second order stationary and it is not appropriate to analyse them by using methods designed for stationary series the paper introduces a new test for second order stationarity that detects kinds of departures from stationarity that are different from those based on fourier methods the new test is also computationally fast designed to work with gaussian and a wide range of non gaussian time series and can locate non stationarities in time and scale the test is demonstrated on earthquake explosion infant electrocardiogram and simulated time series showing varying degrees of stationarity the second main contribution develops approximate confidence intervals for time varying autocovariances for locally stationary series as the usual bands computed for stationary series are not appropriate our new bands enable practitioners to assess time varying autocovariances statistically and are exhibited on localized autocovariances of explosion and simulated time series

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

a test for aliasing using bispectral analysis abstract aliasing is a signal confounding problem that arises when a continuous time signal is sampled at a rate slower than twice the highest frequency component of a fourier series representation of the signal aliasing can be especially serious for social science time series applications since the sampling designs used to construct most social science data bases are fixed by considerations other than the nature of the underlying continuous time mechanisms after collecting sampled data it is of value to test the observations for the presence of aliasing it is shown that the nature of the support set of a sampled band limited stationary signal can be used to motivate an amended version of the hinich bispectrum test for gaussianity hinich 1982 as a test for aliasing

comments with reply on fast convolution with laplacian of gaussian masks by j s chen et al in a recent paper by j s chen et al ibid vol pami 9 p 584 90 july 1987 the authors presented a means of decomposing the laplacian of gaussian log kernel into the product of a gaussian and a smaller log mask they then proceeded to develop a fast algorithm for convolution which exploits the spatial frequency properties of these operators to allow the image to be decimated subsampled although this approach is both novel and interesting it is contended that the exposition suffers from some inconsistencies and minor errors the commenters clarify matters for those who wish to implement this technique the original authors acknowledge two of the three points raised and provide further clarification of the other one namely the claim that the masks gaussian and log are too small

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

adaptive relaxation labeling current implementation of probabilistic relaxation labeling prl is based on stationary compatibility coefficients scc s such labeling frequently diverges from an achieved minimum labeling error in this correspondence it is shown that by having nonstationary compatibility coefficients nscc s the prl stabilizes about the minimum error which is obtained during the early iterations also a noniterative labeling algorithm which uses nscc and has a performance similar to that of the modified prl is suggested

confidence and conflict in multivariate calibration summary multivariate calibration involves using an estimated relationship between a multivariate response y and an explanatory vector x to predict unknown x in future from further observed responses in controlled calibration with multivariate normal errors the profile likelihood function for the unknown x denoted 4 displays a term which measures the mutual inconsistency of the given response vector denoted z in predicting 4 this inconsistency diagnostic fundamentally differentiates the behaviour of likelihood based and bayes confidence regions from those of the unconditional sampling approach in addition the diagnostic serves to pinpoint an inadequate response vector z

restoration of severely blurred high range images using stochastic and deterministic relaxation algorithms in compound gauss markov random fields abstract over the last few years a growing number of researchers from varied disciplines have been utilizing markov random fields mrf models for developing optimal robust algorithms for various problems such as texture analysis image synthesis classification and segmentation surface reconstruction integration of several low level vision modules sensor fusion and image restoration however no much work has been reported on the use of simulated annealing sa and iterative conditional mode icm algorithms for maximum a posteriori estimation in image restoration problems when severe blurring is present in this paper we examine the use of compound gauss markov random fields cgmrf to restore severely blurred high range images for this deblurring problem the convergence of the sa and icm algorithms has not been established we propose two new iterative restoration algorithms which can be considered as extensions of the classical sa and icm approaches and whose convergence is established finally they are tested on real and synthetic images and the results compared with the restorations obtained by other iterative schemes

markov random field modeling for three dimensional reconstruction of the left ventricle in cardiac angiography this paper reports on a method for left ventricle three dimensional 3 d reconstruction from two orthogonal ventriculograms the proposed algorithm is voxel based and takes into account the conical projection geometry associated with the biplane image acquisition equipment the reconstruction process starts with an initial ellipsoidal approximation derived from the input ventriculograms this model is subsequently deformed in such a way as to match the input projections to this end the object is modeled as a 3 d markov gibbs random field and an energy function is defined so that it includes one term that models the projections compatibility and another one that includes the space time regularity constraints the performance of this reconstruction method is evaluated by considering the reconstruction of mathematically synthesized phantoms and two 3 d binary databases from two orthogonal synthesized projections the method is also tested using real biplane ventriculograms in this case the performance of the reconstruction is expressed in terms of the projection error which attains values between 9 50 and 11 78 for two biplane sequences including a total of 55 images

percolation and contact processes with low dimensional inhomogeneity we consider inhomogeneous nearest neighbor bernoulli bond percolation on z d where the bonds in a fixed s dimensional hyperplane 1 s d 1 have density p 1 and all other bonds have fixed density p c z d the homogeneous percolation critical value for s 2 it is natural to conjecture that there is a new critical value p c s z d for p 1 strictly between p c z d and p c z s we prove this for large d and 2 s d 3 for s 1 it is natural to conjecture that p c 1 z d 1 as shown for d 2 by zhang we prove this for large d related results for the contact process are also presented

c 4 exploring multiple solutions in graphical models by cluster sampling this paper presents a novel markov chain monte carlo mcmc inference algorithm called c4 clustering with cooperative and competitive constraints for computing multiple solutions from posterior probabilities defined on graphical models including markov random fields mrf conditional random fields crf and hierarchical models the graphs may have both positive and negative edges for cooperative and competitive constraints c4 is a probabilistic clustering algorithm in the spirit of swendsen wang 34 by turning the positive edges on off probabilistically c4 partitions the graph into a number of connected components ccps and each ccp is a coupled subsolution with nodes connected by positive edges then by turning the negative edges on off probabilistically c4 obtains composite ccps called cccps with competing ccps connected by negative edges at each step c4 flips the labels of all nodes in a cccp so that nodes in each ccp keep the same label while different ccps are assigned different labels to observe both positive and negative constraints thus the algorithm can jump between multiple competing solutions or modes of the posterior probability in a single or a few steps it computes multiple distinct solutions to preserve the intrinsic ambiguities and avoids premature commitments to a single solution that may not be valid given later context c4 achieves a mixing rate faster than existing mcmc methods such as various gibbs samplers 15 26 and swendsen wang cuts 2 34 it is also more dynamic than common optimization methods such as icm 3 lbp 21 37 and graph cuts 4 20 we demonstrate the c4 algorithm in line drawing interpretation scene labeling and object recognition

motion estimation methods for overlapped block motion compensation an extension of conventional block motion compensation bmc overlapped block motion compensation obmc has been shown to reduce residual errors and blocking effects in motion compensated video however the overlap creates a noncausal spatial dependence between blocks and complicates motion estimation me for obmc iterative methods have traditionally been employed for overlapped block motion estimation obme for compression the rate for the motion vector field mvf may also be constrained this work considers several rate constrained obme algorithms both iterative and noniterative experiments demonstrate that a simple raster scan algorithm is effective as a suboptimal noniterative solution with comparable or better rate distortion performance and computational complexity than iterative obme algorithms depending on the application either this method or a simple block matching algorithm plus iteration are the most attractive of the tested obme schemes

grouped coordinate ascent algorithms for penalized likelihood transmission image reconstruction presents a new class of algorithms for penalized likelihood reconstruction of attenuation maps from low count transmission scans we derive the algorithms by applying to the transmission log likelihood a version of the convexity technique developed by de pierro for emission tomography the new class includes the single coordinate ascent sca algorithm and lange s convex algorithm for transmission tomography as special cases the new grouped coordinate ascent gca algorithms in the class overcome several limitations associated with previous algorithms 1 fewer exponentiations are required than in the transmission maximum likelihood expectation maximization ml em algorithm or in the sca algorithm 2 the algorithms intrinsically accommodate nonnegativity constraints unlike many gradient based methods 3 the algorithms are easily parallelizable unlike the sca algorithm and perhaps line search algorithms we show that the gca algorithms converge faster than the sca algorithm even on conventional workstations an example from a low count positron emission tomography pet transmission scan illustrates the method

physical consideration of an image in image restoration using bayes formula abstract we consider image restoration by bayes formula and investigate the relationship between an image and a prior probability from the following two viewpoints hyperparameter estimation and the accuracy of a restored image the q ising model is adopted as a prior probability in bayes formula not the q ising energy but the potts energy plays an important role in the hyperparameter estimation from the viewpoint of the hyperparameter estimation the relationship between a natural image and a prior probability is characterized through the potts energy and magnetization of an image the potts energy and magnetization of an image are defined by a set of pixels state of an image the closer to the average potts energy and magnetization over a prior probability the potts energy and magnetization of a natural image is the closer to the true value of a hyperparameter the estimated value of a hyperparameter from a degraded image is for the accuracy of a restored image the image which has a smaller q ising energy is better restored by bayes formula composed of the q ising prior the consideration for the relationship between an image and a prior probability is expected to be valid for a more complicated prior probability

relaxation algorithms for map estimation of gray level images with multiplicative noise the authors present a comparison between stochastic and deterministic relaxation algorithms for maximum a posteriori estimation of gray level images modeled by noncausal gauss markov random fields gmrf and corrupted by film grain noise the degradation involves nonlinear transformation and multiplicative noise parameters for the gmrf model were estimated from the original image using maximum likelihood techniques to overcome modeling errors a constraint minimization approach is suggested for estimating the parameters to ensure the positivity of the power spectral density function real image experiments with various noise variances and magnitudes of the nonlinear transformation are presented

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

inference for clustered data using the independence loglikelihood we use the properties of independence estimating equations to adjust the independence loglikelihood function in the presence of clustering the proposed adjustment relies on the robust sandwich estimator of the parameter covariance matrix which is easily calculated the methodology competes favourably with established techniques based on independence estimating equations we provide some insight as to why this is so the adjustment is applied to examples relating to the modelling of wind speed in europe and annual maximum temperatures in the u k

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

wavelet processes and adaptive estimation of the evolutionary wavelet spectrum this article defines and studies a new class of non stationary random processes constructed from discrete non decimated wavelets which generalizes the cramer fourier representation of stationary time series we define an evolutionary wavelet spectrum ews which quantifies how process power varies locally over time and scale we show how the ews may be rigorously estimated by a smoothed wavelet periodogram and how both these quantities may be inverted to provide an estimable time localized autocovariance we illustrate our theory with a pedagogical example based on discrete non decimated haar wavelets and also a real medical time series example

comments on application of the conditional population mixture model to image segmentation in the above correspondence1 a maximum likelihood method is proposed for estimating class memberships and underlying statistical parameters within the context of distribution mixtures in the present comment it is pointed out that biases are incurred in parameter estimation that the class memberships and parameters are conceptually different and therefore that the so called standard mixture likelihood is to be preferred also in the correspondence 1 akaike s information criterion aic is used to choose the number of classes in the mixture here a brief theoretical caveat is issued

contact process in a wedge we prove that the supercritical one dimensional contact process survives in certain wedge like space time regions and that when it survives it couples with the unrestricted contact process started from its upper invariant measure as an application we show that a type of weak coexistence is possible in the nearest neighbor grass bushes trees successional model introduced in durrett and swindle stoch proc appl 37 19 31 1991

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

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

a test for the absence of aliasing or local white noise in locally stationary wavelet time series aliasing is often overlooked in time series analysis but can seriously distort the spectrum autocovariance and their estimates we show that dyadic subsampling of a locally stationary wavelet process which can cause aliasing results in a process that is the sum of asymptotic white noise and another locally stationary wavelet process with a modified spectrum we develop a test for the absence of aliasing in a locally stationary wavelet series at a fixed location and illustrate it on simulated data and a wind energy time series a useful by product is a new test for local white noise the tests are robust to model misspecification in that it is unnecessary for the analysis and synthesis wavelets to be identical hence in principle the tests work irrespective of which wavelet is used to analyze the time series though in practice there is a tradeoff between increasing statistical power and time localization of the test

bayesian calibration of a large scale geothermal reservoir model by a new adaptive delayed acceptance metropolis hastings algorithm 1 the aim of this research is to estimate the parameters of a large scale numerical model of a geothermal reservoir using markov chain monte carlo mcmc sampling within the framework of bayesian inference all feasible parameters that are consistent with the measured data are summarized by the posterior distribution and hence parameter estimation and uncertainty quantification are both given by calculating expected values of statistics of interest over the posterior distribution it appears to be computationally infeasible to use the standard metropolis hastings algorithm mh to sample the high dimensional computationally expensive posterior distribution to improve the sampling efficiency a new adaptive delayed acceptance mh algorithm adamh is implemented to adaptively build a stochastic model of the error introduced by the use of a reduced order model this use of adaptivity differs from existing adaptive mcmc algorithms that tune proposal distributions of the metropolis hastings algorithm mh though adamh also implements that technique for the 3 d geothermal reservoir model we present here adamh shows a great improvement in the computational efficiency of the mcmc sampling and promising results for parameter estimation and uncertainty quantification are obtained this algorithm could offer significant improvement in computational efficiency when implementing sample based inference in other large scale inverse problems

turbo segmentation of textured images we consider the problem of semi supervised segmentation of textured images existing model based approaches model the intensity field of textured images as a gauss markov random field to take into account the local spatial dependencies between the pixels classical bayesian segmentation consists of also modeling the label field as a markov random field to ensure that neighboring pixels correspond to the same texture class with high probability well known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion but these techniques are usually computationally intensive because they require a large number of iterations to converge in this paper we propose a new bayesian framework by modeling two dimensional textured images as the concatenation of two one dimensional hidden markov autoregressive models for the lines and the columns respectively a segmentation algorithm which is similar to turbo decoding in the context of error correcting codes is obtained based on a factor graph approach the proposed method estimates the unknown parameters using the expectation maximization algorithm

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

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

phase diagram of inhomogeneous percolation with a defect plane let mathbb l be the d dimensional hypercubic lattice and let mathbb l 0 be an s dimensional sublattice with 2 le s p c d and a surface supercritical regime for p sigma p we show that sigma p is a strictly decreasing function for p in 0 p c d with a jump discontinuity at p c d we extend the aizenman barsky differential inequalities for homogeneous percolation to the inhomogeneous model and use them to prove that the susceptibility is finite inside the subcritical phase we prove that the cluster size distribution decays exponentially in the subcritical phase and sub exponentially in the supercritical phases for a model of lattice animals with a defect plane the free energy is related to functions of the inhomogeneous percolation model and we show how the percolation transition implies a non analyticity in the free energy of the animal model finally we present simulation estimates of the critical curve sigma p

bayes smoothing algorithms for segmentation of binary images modeled by markov random fields a new image segmentation algorithm is presented based on recursive bayes smoothing of images modeled by markov random fields and corrupted by independent additive noise the bayes smoothing algorithm yields the a posteriori distribution of the scene value at each pixel given the total noisy image in a recursive way the a posteriori distribution together with a criterion of optimality then determine a bayes estimate of the scene the algorithm presented is an extension of a 1 d bayes smoothing algorithm to 2 d and it gives the optimum bayes estimate for the scene value at each pixel computational concerns in 2 d however necessitate certain simplifying assumptions on the model and approximations on the implementation of the algorithm in particular the scene noiseless image is modeled as a markov mesh random field a special class of markov random fields and the bayes smoothing algorithm is applied on overlapping strips horizontal vertical of the image consisting of several rows columns it is assumed that the signal scene values vector sequence along the strip is a vector markov chain since signal correlation in one of the dimensions is not fully used along the edges of the strip estimates are generated only along the middle sections of the strips the overlapping strips are chosen such that the union of the middle sections of the strips gives the whole image the bayes smoothing algorithm presented here is valid for scene random fields consisting of multilevel discrete or continuous random variables

robust voxel similarity metrics for the registration of dissimilar single and multimodal images in this paper we develop data driven registration algorithms relying on pixel similarity metrics that enable an accurate subpixel rigid registration of dissimilar single or multimodal 2d 3d images gross dissimilarities are handled by considering similarity measures related to robust m estimators in particular a novel robust similarity metric is proposed for comparing multimodal images the proposed robust similarity metrics are compared to the most popular standard similarity metrics on synthetic as well as on real world image pairs showing gross dissimilarities three case studies are considered the registration of single modal and multimodal 3d medical images the matching of multispectral remotely sensed images and the registration of intensity and range images the proposed robust similarity measures compare favourably with the standard non robust techniques

a dynamic generating graphical model for point sets matching this paper presents a new dynamic generating graphical model for point sets matching the existing algorithms on graphical models proved to be quite robust to noise but are susceptible to the effect of outliers we discuss the separator s influences on point sets matching in inference on graphical models theoretically and find that the separator which consists of outliers will break the message passing which will directly lead to the breaking down of the existing methods due to the conclusion above in order to minimize the outliers in separator we propose a new algorithm in generating a graphical model and the corresponding junction tree for point sets matching the experimental results show that the proposed algorithm is significantly more stable and possesses higher accuracy on point sets matching which can overcome the limitation of sensitivity on outliers in the existing graphical models

the debiased whittle likelihood the whittle likelihood is a widely used and computationally efficient pseudolikelihood however it is known to produce biased parameter estimates with finite sample sizes for large classes of models we propose a method for debiasing whittle estimates for second order stationary stochastic processes the debiased whittle likelihood can be computed in the same o n log n operations as the standard whittle approach we demonstrate the superior performance of our method in simulation studies and in application to a large scale oceanographic dataset where in both cases the debiased approach reduces bias by up to two orders of magnitude achieving estimates that are close to those of the exact maximum likelihood at a fraction of the computational cost we prove that the method yields estimates that are consistent at an optimal convergence rate of n 1 2 for gaussian processes and for certain classes of non gaussian or nonlinear processes this is established under weaker assumptions than in the standard theory and in particular the power spectral density is not required to be continuous in frequency we describe how the method can be readily combined with standard methods of bias reduction such as tapering and differencing to further reduce bias in parameter estimates

the second lowest extremal invariant measure of the contact process ii we continue the investigation of the behavior of the contact process on infinite connected graphs of bounded degree some questions left open by salzano and schonmann 1997 concerning the notions of complete convergence partial convergence and the criterion r s are answered the continuity properties of the survival probability and the recurrence probability are studied these order parameters are found to have a richer behavior than expected with the possibility of the survival probability being discontinuous at or above the threshold for survival a condition which guarantees the continuity of the survival probability above the survival point is introduced and exploited the recurrence probability is shown to always be left continuous above the recurrence point and a necessary and sufficient condition for its right continuity is introduced and exploited it is shown that for homogeneous graphs the survival probability can only be discontinuous at the survival point and the recurrence probability can only be discontinuous at the recurrence point for graphs which are obtained by joining a finite number of severed homogeneous trees by means of a finite number of vertices and edges the survival point the recurrence point and the discontinuity points of the survival and recurrence probabilities are located

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

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 critical behavior of the contact process in deterministic inhomogeneous environments we consider the contact process with inhomogeneous deterministic death rates we prove the following 1 such models may have discontinuous transitions in the sense of surviving at the critical point 2 if the death rates are identically 1 except on a set which is small enough in a proper sense and where the death rates take a fixed value smaller than 1 then the critical point is identical to that of the homogeneous system extensions of the results to other d 1 dimensional systems with d dimensional deterministic inhomogeneities are also discussed

a segmentation based regularization term for image deconvolution this paper proposes a new and original inhomogeneous restoration deconvolution model under the bayesian framework for observed images degraded by space invariant blur and additive gaussian noise in this model regularization is achieved during the iterative restoration process with a segmentation based a priori term this adaptive edge preserving regularization term applies a local smoothness constraint to pre estimated constant valued regions of the target image these constant valued regions the segmentation map of the target image are obtained from a preliminary wiener deconvolution estimate in order to estimate reliable segmentation maps we have also adopted a bayesian markovian framework in which the regularized segmentations are estimated in the maximum a posteriori map sense with the joint use of local potts prior and appropriate gaussian conditional luminance distributions in order to make these segmentations unsupervised these likelihood distributions are estimated in the maximum likelihood sense to compute the map estimate associated to the restoration we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration the experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state of the art methods in benchmark tests

compound gauss markov random fields for image estimation algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound gauss markov random fields are discussed the authors consider both the maximum a posteriori probability map estimate and the minimum mean squared error mmse estimate for image estimation and image restoration compound image models consist of several submodels having different characteristics along with an underlying structure model which govern transitions between these image submodels two different compound random field models are employed the doubly stochastic gaussian dsg random field and a compound gauss markov cgm random field the authors present map estimators for dsg and cgm random fields using simulated annealing a fast converging algorithm called deterministic relaxation which however converges to only a locally optimal map estimate is also presented as an alternative for reducing computational loading on sequential machines for comparison purposes the authors include results on the fixed lag smoothing mmse estimator for the dsg field and its suboptimal m algorithm approximation

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

dpa a deterministic approach to the map problem deterministic pseudo annealing dpa is a new deterministic optimization method for finding the maximum a posteriori map labeling in a markov random field in which the probability of a tentative labeling is extended to a merit function on continuous labelings this function is made convex by changing its definition domain this unambiguous maximization problem is solved and the solution is followed down to the original domain yielding a good if suboptimal solution to the original labeling assignment problem the performance of dpa is analyzed on randomly weighted graphs

sar image regularization with fast approximate discrete minimization synthetic aperture radar sar images like other coherent imaging modalities suffer from speckle noise the presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms numerous approaches have been proposed to filter speckle noise markov random field mrf modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image in this context total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges speckle noise follows heavy tailed distributions and the mrf formulation leads to a minimization problem involving nonconvex log likelihood terms such a minimization can be performed efficiently by computing minimum cuts on weighted graphs due to memory constraints exact minimization although theoretically possible is not achievable on large images required by remote sensing applications the computational burden of the state of the art algorithm for approximate minimization namely the alpha expansion is too heavy specially when considering joint regularization of several images we show that a satisfying solution can be reached in few iterations by performing a graph cut based combinatorial exploration of large trial moves this algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area sar images

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

parameter estimation and tissue segmentation from multispectral mr images a statistical method is developed to classify tissue types and to segment the corresponding tissue regions from relaxation time t sub 1 t sub 2 and proton density p sub d weighted magnetic resonance images the method assumes that the distribution of image intensities associated with each tissue type can be expressed as a multivariate likelihood function of three weighted signal intensity values t sub 1 t sub 2 p sub d at each location within that tissue regions the method further assumes that the underlying tissue regions are piecewise contiguous and can be characterized by a markov random field prior in classifying the tissue types the method models the likelihood of realizing the images as a finite multivariate mixture function the class parameters associated with the tissue types i e the weighted intensity means variances and correlation coefficients of the multivariate function as well as the number of voxels within regions of the tissue types of are estimated by maximum likelihood the estimation fits the class parameters to the image data via the expectation maximization algorithm the number of classes associated with the tissue types is determined by the information criterion of minimum description length the method segments the tissue regions given the estimated class parameters by maximum a posteriori probability the prior is constructed by the tissue region membership of the first and second order neighborhood the method is tested by a few sets of t sub 1 t sub 2 and p sub d weighted images of the brain acquired with a 1 5 tesla whole body scanner the number of classes and the associated class parameters are automatically estimated the regions of different brain tissues are satisfactorily segmented

segmentation registration and measurement of shape variation via image object shape a model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives metrics are described that compute an object representation s prior probability of local geometry by reflecting variabilities in the net s node and link parameter values and that compute a likelihood function measuring the degree of match of an image to that object representation a paradigm for image analysis of deforming such a model to optimize a posteriori probability is described and this paradigm is shown to be usable as a uniform approach for object definition object based registration between images of the same or different imaging modalities and measurement of shape variation of an abnormal anatomical object compared with a normal anatomical object examples of applications of these methods in radiotherapy surgery and psychiatry are given

interval estimation in discrimination the multivariate normal equal covariance case summary a general approach to discrimination problems is described which emphasizes the viewpoint of individual cases and expresses the uncertainty with which individual decisions are made it is applied to the particular case of two multivariate normal distributions with a common covariance matrix an affine transformation to which the key quantities are invariant simplifies discussion of the distribution of the estimated log odds ratio and suggests a practically useful plot which generalizes the usual display of discriminant scores and has several attractive features an illustration is given two approximate interval estimation techniques for the true log odds ratio are described and evaluated in a range of practical situations by a simulation study some further applications of our general approach are briefly indicated

on the covariance of two noncentral f random variables and the variance of the estimated liner discriminant function summary the covariance of two noncentral f random variables with a common covariance matrix is obtained from which the variance of their difference follows easily an application of this latter result in discriminant analysis is then given

a markov random field model based approach to image interpretation an image is segmented into a collection of disjoint regions that form the nodes of an adjacency graph and image interpretation is achieved through assigning object labels or interpretations to the segmented regions or nodes using domain knowledge extracted feature measurements and spatial relationships between the various regions the interpretation labels are modeled as a markov random field mrf on the corresponding adjacency graph and the image interpretation problem is then formulated as a maximum a posteriori map estimation rule given domain knowledge and region based measurements simulated annealing is used to find this best realization or optimal map interpretation this approach also provides a systematic method for organizing and representing domain knowledge through appropriate design of the clique functions describing the gibbs distribution representing the pdf of the underlying mrf a general methodology is provided for the design of the clique functions results of image interpretation experiments on synthetic and real world images are described

mean field annealing using compound gauss markov random fields for edge detection and image estimation the authors consider the problem of edge detection and image estimation in nonstationary images corrupted by additive gaussian noise the noise free image is represented using the compound gauss markov random field developed by f c jeng and j w woods 1990 and the problem of image estimation and edge detection is posed as a maximum a posteriori estimation problem since the a posteriori probability function is nonconvex computationally intensive stochastic relaxation algorithms are normally required a deterministic relaxation method based on mean field annealing with a compound gauss markov random cgmrf field model is proposed the authors present a set of iterative equations for the mean values of the intensity and both horizontal and vertical line processes with or without taking into account some interaction between them the relationship between this technique and two other methods is considered edge detection and image estimation results on several noisy images are included

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

nonparametric bayesian image segmentation image segmentation algorithms partition the set of pixels of an image into a specific number of different spatially homogeneous groups we propose a nonparametric bayesian model for histogram clustering which automatically determines the number of segments when spatial smoothness constraints on the class assignments are enforced by a markov random field a dirichlet process prior controls the level of resolution which corresponds to the number of clusters in data with a unique cluster structure the resulting posterior is efficiently sampled by a variant of a conjugate case sampling algorithm for dirichlet process mixture models experimental results are provided for real world gray value images synthetic aperture radar images and magnetic resonance imaging data

image segmentation by iterated region merging with localized graph cuts this paper presents an iterated region merging based graph cuts algorithm which is a novel extension of the standard graph cuts algorithm graph cuts addresses segmentation in an optimization framework and finds a globally optimal solution to a wide class of energy functions however the extraction of objects in a complex background often requires a lot of user interaction the proposed algorithm starts from the user labeled sub graph and works iteratively to label the surrounding un segmented regions in each iteration only the local neighboring regions to the labeled regions are involved in the optimization so that much interference from the far unknown regions can be significantly reduced meanwhile the data models of the object and background are updated iteratively based on high confident labeled regions the sub graph requires less user guidance for segmentation and thus better results can be obtained under the same amount of user interaction experiments on benchmark datasets validated that our method yields much better segmentation results than the standard graph cuts and the grabcut methods in either qualitative or quantitative evaluation

fully bayesian reconstructions from single photon emission computed tomography data abstract with suitably chosen priors bayesian models are useful in image reconstruction i consider reconstructions from single photon emission computerized tomography data using a gibbs pairwise difference prior a fully bayesian approach is presented where the prior parameters are considered drawn from hyperpriors the approach is problematical because the normalization constant in the prior is an intractable function of its parameters here the constant is estimated off line by reverse logistic regression markov chain monte carlo methods are used on simulated and real data to gain estimates of the posterior mean and pixelwise credibility bounds the resulting reconstructions are compared to those obtained by filtered back projection maximum likelihood em and the one step late solution to the fixed parameter posterior mode

spatially regularized estimation for the analysis of dynamic contrast enhanced magnetic resonance imaging data competing compartment models of different complexities have been used for the quantitative analysis of dynamic contrast enhanced magnetic resonance imaging data we present a spatial elastic net approach that allows to estimate the number of compartments for each voxel such that the model complexity is not fixed a priori a multi compartment approach is considered which is translated into a restricted least square model selection problem this is done by using a set of basis functions for a given set of candidate rate constants the form of the basis functions is derived from a kinetic model and thus describes the contribution of a specific compartment using a spatial elastic net estimator we chose a sparse set of basis functions per voxel and hence rate constants of compartments the spatial penalty takes into account the voxel structure of an image and performs better than a penalty treating voxels independently the proposed estimation method is evaluated for simulated images and applied to an in vivo dataset copyright 2013 john wiley sons ltd

inhomogeneous contact processes on trees we consider an inhomogeneous contact process on a tree mathbb t k of degreek where the infection rate at any site is the death rate at any site in s subset mathbb t k is with 0 4 if s mathbb t sigma a subtree embedded in mathbb t k with 1 k then three exists c strictly between lambda c mathbb t k lambda c mathbb t sigma and 1 such that theta delta lambda c mathbb t k 0 when c and c theta delta lambda c mathbb t k 0 0 when c ifs o the origin of theta delta lambda c mathbb t k 0 then theta delta lambda c mathbb t k 0 for any e 0 1

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

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

improving consistency and reducing ambiguity in stochastic labeling an optimization approach we approach the problem of labeling a set of objects from a quantitative standpoint we define a world model in terms of transition probabilities and propose a definition of a class of global criteria that combine both ambiguity and consistency a projected gradient algorithm is developed to minimize the criterion we show that the minimization procedure can be implemented in a highly parallel manner results are shown on several examples and comparisons are made with relaxation labeling techniques

testing mutual independence between two discrete valued spatial processes a correction to pearson chi squared a common feature of data collected in environmental and earth sciences is that they typically exhibit spatial autocorrelation violating the assumption of independent observations can have dramatic effects on inferences derived from standard statistical methods in this article we examine the consequences of spatial autocorrelation on pearson s chi squared test of mutual independence between two categorical responses with a general number of classes correspondingly we suggest a simple modification to the standard test statistic that allows for spatial autocorrelation our modified statistic is based on a first order correction factor and thus provides only an approximate test however we show by monte carlo simulation that this approximation results in satisfactory inferences in several situations of practical interest the usefulness of the method is displayed through an application to categorical data arising in the study of the relationship between the distribution pattern of plant species and woodland age in a forest in northern belgium

a tree structured markov random field model for bayesian image segmentation we present a new image segmentation algorithm based on a tree structured binary mrf model the image is recursively segmented in smaller and smaller regions until a stopping condition local to each region is met each elementary binary segmentation is obtained as the solution of a map estimation problem with the region prior modeled as an mrf since only binary fields are used and thanks to the tree structure the algorithm is quite fast and allows one to address the cluster validation problem in a seamless way in addition all field parameters are estimated locally allowing for some spatial adaptivity to improve segmentation accuracy a split and merge procedure is also developed and a spatially adaptive mrf model is used numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on flat mrf models and its performance in terms of segmentation accuracy and map smoothness is comparable or even superior

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

on the principal domain of the discrete bispectrum of a stationary signal the paper presents a simplifying yet general approach to determining the symmetry structure of a bispectrum the principal domain pd of the bispectrum and its region of positive support are derived in a way that illuminates the controversy surrounding the triangle in the pd which is called the outer triangle ot by hinich and wolinsky 1988 where the bispectrum is zero for a stationary random sampled process that is not aliased the basic statistical issues of testing for nonzero bispectral structure are reviewed

a new algorithm for subgraph optimal isomorphism abstract in this paper a new algorithm for subgraph isomorphism is proposed the main idea of the new algorithm is to decompose the graphs to be matched into smaller subgraphs the matching process is then done at the level of the decomposed subgraphs based on the concept of error correcting transformations the cost of matching two graphs is defined as the minimum of a weighted bipartite graph constructed from the decomposed subgraphs the average computational complexity of the proposed algorithm is found to be o n 4 the results of the application of the new algorithm show that the new technique is quite efficient and in many respects superior to similar existing techniques in the literature besides it overcomes most of the problems encountered in using tree search algorithms the new algorithm is also suitable for parallel processing implementation

locally adaptive estimation of evolutionary wavelet spectra we introduce a wavelet based model of local stationarity this model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time a notion of time varying wavelet spectrum is uniquely de ned as a wavelet type transform of the autocovariance function with respect to so called autocorrelation wavelets this leads to a natural representation of the autocovariance which is localized on scales we propose a pointwise adaptive estimator of the time varying spectrum the behavior of the estimator studied in homogeneous and inhomogeneous regions of the wavelet spectrum

statistical approach to segmentation of single channel cerebral mr images a statistical model is presented that represents the distributions of major tissue classes in single channel magnetic resonance mr cerebral images using the model cerebral images are segmented into gray matter white matter and cerebrospinal fluid csf the model accounts for random noise magnetic field inhomogeneities and biological variations of the tissues intensity measurements are modeled by a finite gaussian mixture smoothness and piecewise contiguous nature of the tissue regions are modeled by a three dimensional 3 d markov random field mrf a segmentation algorithm based on the statistical model approximately finds the maximum a posteriori map estimation of the segmentation and estimates the model parameters from the image data the proposed scheme for segmentation is based on the iterative conditional modes icm algorithm in which measurement model parameters are estimated using local information at each site and the prior model parameters are estimated using the segmentation after each cycle of iterations application of the algorithm to a sample of clinical mr brain scans comparisons of the algorithm with other statistical methods and a validation study with a phantom are presented the algorithm constitutes a significant step toward a complete data driven unsupervised approach to segmentation of mr images in the presence of the random noise and intensity inhomogeneities

haar fisz estimation of evolutionary wavelet spectra summary we propose a new haar fisz technique for estimating the time varying piecewise constant local variance of a locally stationary gaussian time series we apply our technique to the estimation of the spectral structure in the locally stationary wavelet model our method combines haar wavelets and the variance stabilizing fisz transform the resulting estimator is mean square consistent rapidly computable and easy to implement and performs well in practice we also introduce the haar fisz transform a device for stabilizing the variance of scaled x2 data and bringing their distribution close to gaussianity

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

minimization of monotonically levelable higher order mrf energies via graph cuts a feature of minimizing images of submodular binary markov random field mrf energies is introduced using this novel feature the collection of minimizing images of levels of higher order monotonically levelable multilabel mrf energies is shown to constitute a monotone collection this implies that these minimizing binary images can be combined to give minimizing images of the multilabel mrf energies thanks to the graph cuts framework the mentioned class of binary mrf energies is known to be minimized by maximum flow computations on appropriately constructed graphs with the aid of these developments an exact and efficient algorithm to minimize monotonically levelable multilabel mrf energies of any order which is composed of a series of maximum flow computations is proposed and an application of the proposed algorithm to image denoising is given

graphical and recursive models for contingency tables summary we discuss two classes of models for contingency tables graphical and recursive models both of which arise from restrictions that are expressible as conditional independencies of variable pairs the first of these is a subclass of hierarchical log linear models each of its models can be represented by an undirected graph in the second class each model corresponds to a particular kind of a directed graph instead and can be characterized by a nontrivial factorization of the joint distribution in terms of response variables we derive decomposable or multiplicative models as the intersecting class this result has useful consequences for exploratory types of analysis as well as for the model interpretation we can give an aid for detecting well fitting decomposable models in a transformation of the observed contingency table and each decomposable model may be interpreted with the help of an undirected or directed graph

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

mixture modeling with pairwise instance level class constraints the goal of semisupervised clustering mixture modeling is to learn the underlying groups comprising a given data set when there is also some form of instance level supervision available usually in the form of labels or pairwise sample constraints most prior work with constraints assumes the number of classes is known with each learned cluster assumed to be a class and hence subject to the given class constraints when the number of classes is unknown or when the one cluster per class assumption is not valid the use of constraints may actually be deleterious to learning the ground truth data groups we address this by 1 allowing allocation of multiple mixture components to individual classes and 2 estimating both the number of components and the number of classes we also address new class discovery with components void of constraints treated as putative unknown classes for both real world and synthetic data our method is shown to accurately estimate the number of classes and to give favorable comparison with the recent approach of shental bar hillel hertz and weinshall 2003