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

periodic potentials and pt symmetry we enlarge the limited class of analytically solvable one dimensional periodic potentials with a finite number of band gaps by considering the complex pt symmetric generalized associated lame gal potential with four parameters and applying supersymmetry we obtain three duality relations which relate the band edge eigenstates of the twenty four gal potentials obtained by permutation of the four parameters

parametric inference for imperfectly observed gibbsian fields this paper presents a maximum likelihood estimation method for imperfectly observed gibbsian fields on a finite lattice this method is an adaptation of the algorithm given in younes 28 presentation of the new algorithm is followed by a theorem about the limit of the second derivative of the likelihood when the lattice increases which is related to convergence of the method some practical remarks about the implementation of the procedure are eventually given

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

a characterization of all elliptic algebro geometric solutions of the akns hierarchy here 9 x p x wl w3 denotes the elliptic weierstrass function with fundamental periods 2wl and 2w3 im w3 wl 0 in the special case where wl is real and w3 is purely imaginary the potential q x in 1 1 is real valued and ince s striking result 51 in modern spectral theoretic terminology yields that the spectrum of the unique self adjoint operator associated with the differential expression l2 d2 dx 2 q x in l2 r exhibits finitely many bands and gaps respectively that is

the heun equation and the calogero moser sutherland system iv the hermite krichever ansatz we develop a theory for the hermite krichever ansatz on the heun equation as a byproduct we find formulae which reduce hyperelliptic integrals to elliptic ones

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

elliptic algebro geometric solutions of the kdv and akns hierarchies an analytic approach we provide an overview of elliptic algebro geometric solutions of the kdv and akns hierarchies with special emphasis on floquet theoretic and spectral theoretic methods our treatment includes an effective characterization of all stationary elliptic kdv and akns solutions based on a theory developed by hermite and picard

estimation of generalized mixture in the case of correlated sensors this paper deals with unsupervised bayesian classification of multidimensional data we propose an extension of a previous method of generalized mixture estimation to the correlated sensors case the method proposed is valid in the independent data case as well as in the hidden markov chain or field model case with known applications in signal processing particularly speech or image processing the efficiency of the method proposed is shown via some simulations concerning hidden markov fields with application to unsupervised image segmentation

complex periodic potentials with a finite number of band gaps we obtain several new results for the complex generalized associated lame potential v x a a 1 msn2 y m b b 1 msn2 y k m m f f 1 msn2 y k m ik m m g g 1 msn2 y ik m m where y x k m 2 ik m 2 sn y m is the jacobi elliptic function with modulus parameter m and there are four real parameters a b f g first we derive two new duality relations which when coupled with a previously obtained duality relation permit us to relate the band edge eigenstates of the 24 potentials obtained by permutations of the parameters a b f g second we pose and answer the question how many independent potentials are there with a finite number a of band gaps when a b f g are integers and a b f g 0 for these potentials we clarify the nature of the band edge eigenfunctions we also obtain several analytic results when at least one of the four parameters is a half integer as a by product we also obtain new solutions of heun s differential equation

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

commutation methods applied to the mkdv equation an explicit construction of solutions of the modified korteweg de vries equation given a solution of the ordinary korteweg de vries equation is provided our theory is based on commutation methods i e n 1 supersymmetry underlying miura s transformation that links solutions of the two evolution equations

picard potentials and hill s equation on a torus hill s equation has drawn an enormous amount of consideration due to its ubiquity in applications as well as its structural richness of particular importance in the last 20 years is its connection with the kdv hierarchy and hence with integrable systems we show in this paper that regarding the independent variable as a complex variable yields a breakthrough for the problem of an efficient characterization of all elliptic finitegap potentials a major open problem in the field specifically we show that elliptic finitegap potentials of hill s equation are precisely those for which all solutions for all spectral parameters are meromorphic functions in the independent variable complementing a classical theorem of picard the intimate connection between picard s theorem and elliptic finite gap solutions of completely integrable systems is established in this paper for the first time in addition we construct the hyperelliptic riemann surface associated with a finitegap potential not necessarily elliptic i e determine its branch and singular points from a comparison of the geometric and algebraic multiplicities of eigenvalues of certain auxiliary operators associated with hill s equation these multiplicities are intimately correlated with the pole structure of the diagonal green s function of the operator h d2 dx2 q x in l2 r our construction is new in the present general complex valued periodic finite gap case before describing our approach in some detail we shall give a brief account of the history of the problem involved this theme dates back to a 1940 paper of ince 43 who studied what is presently called the lam6 ince potential

a general approach to lagrange multiplier model diagnostics abstract a diagnostic test can be formulated by taking the current model as the null hypothesis and a particular form of misspecification as the alternative the general approach of this paper is to calculate the score for some alternative and base a test on its distribution under the null this distribution is derived in two theorems corresponding to different models such a test is a langrange multiplier test and is asymptotically optimal these tests can be formulated as ways of looking at the residuals for particular types of non randomness the tests are simple to calculate even when the alternative may be very complicated examples are given of tests for omitted variables and block recursive structures

the hermite krichever ansatz for fuchsian equations with applications to the sixth painleve equation and to finite gap potentials several results including integral representation of solutions and hermite krichever ansatz on heun s equation are generalized to a certain class of fuchsian differential equations and they are applied to equations which are related with physics we investigate linear differential equations that produce painleve equation by monodromy preserving deformation and obtain solutions of the sixth painleve equation which include hitchin s solution the relationship with finite gap potential is also discussed we find new finite gap potentials namely we show that the potential which is written as the sum of the treibich verdier potential and additional apparent singularities of exponents 1 and 2 is finite gap which extends the result obtained previously by treibich we also investigate the eigenfunctions and their monodromy of the schrodinger operator on our potential

adaptive segmentation of speckled images using a hierarchical random field model a two level hierarchical random field model developed for speckled images and in particular for synthetic aperture radar sar imagery is described at the higher level is a gibbs random field governing the grouping of image pixels into regions while at the lower level are speckle processes for the different regions which are also modeled as random fields in accordance with the physical phenomena that cause speckle the speckle processes are modeled as circularly symmetric complex gaussian random fields as with real gaussian fields certain forms of autocovariance of complex gaussian field lead to markovianity properties with the assumption of a separable autocovariance for the complex gaussian random fields local joint statistics of the resulting speckle intensity fields magnitude squared of the complex field are determined the speckle model concurs with the known marginal statistics and also accounts for the autocorrelation observed in actual speckled images a map segmentation using simulated annealing and based on the hierarchical model is presented the algorithm is adaptive in that it recursively segments the image and estimates the model parameters necessary for the segmentation

quasi doubly periodic solutions to a generalized lame equation we consider the generalized lam equation with a k 21 b k 22 k 21 by introducing a generalization of jacobi s elliptic functions we transform this equation to a schr dinger equation with quasi doubly periodic potential we show that only for a finite set of integral values for the parameters quasi doubly periodic eigenfunctions expressible in terms of generalized jacobi functions exist for this purpose we also establish a relation to the generalized ince equation

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

data driven version of neyman s smooth test of fit abstract neyman s smooth test for testing uniformity is a recognized goodness of fit procedure as stated by lariccia the test can be viewed as a compromise between omnibus test procedures with generally low power in all directions and procedures whose power is focused in the direction of a specific alternative the basic idea behind this test is to embed the null density into say a k dimensional exponential family and then to construct an asymptotically optimal test for the parametric testing problem the resulting procedure is neyman s test with k components the most difficult problem related with using this test is the choice of k recommendations in statistical literature are sometimes confusing some authors advocate a small number of components whereas others show that in some situations a larger number of components is profitable all existing suggestions concerning how to select k exploit in fact some preliminary knowledge about a possible alternative in this article a new data driven met

a fuzzy locally adaptive bayesian segmentation approach for volume determination in pet accurate volume estimation in positron emission tomography pet is crucial for different oncology applications the objective of our study was to develop a new fuzzy locally adaptive bayesian flab segmentation for automatic lesion volume delineation flab was compared with a threshold approach as well as the previously proposed fuzzy hidden markov chains fhmc and the fuzzy c means fcm algorithms the performance of the algorithms was assessed on acquired datasets of the iec phantom covering a range of spherical lesion sizes 10 37 mm contrast ratios 4 1 and 8 1 noise levels 1 2 and 5 min acquisitions and voxel sizes 8 and 64 mm3 in addition the performance of the flab model was assessed on realistic nonuniform and nonspherical volumes simulated from patient lesions results show that flab performs better than the other methodologies particularly for smaller objects the volume error was 5 15 for the different sphere sizes down to 13 mm contrast and image qualities considered with a high reproducibility variation 4 by comparison the thresholding results were greatly dependent on image contrast and noise whereas fcm results were less dependent on noise but consistently failed to segment lesions 2 cm in addition flab performed consistently better for lesions 2 cm in comparison to the fhmc algorithm finally the flab model provided errors less than 10 for nonspherical lesions with inhomogeneous activity distributions future developments will concentrate on an extension of flab in order to allow the segmentation of separate activity distribution regions within the same functional volume as well as a robustness study with respect to different scanners and reconstruction algorithms

color image segmentation using adaptive mean shift and statistical model based methods in this paper we propose an unsupervised segmentation algorithm for color images based on gaussian mixture models gmms the number of mixture components is determined automatically by adaptive mean shift in which local clusters are estimated by repeatedly searching for higher density points in feature vector space for the estimation of parameters of gmms the mean field annealing expectation maximization em is employed the mean field annealing em provides a global optimal solution to overcome the local maxima problem in a mixture model by combining the adaptive mean shift and the mean field annealing em natural color images are segmented automatically without over segmentation or isolated regions the experiments show that the proposed algorithm can produce satisfactory segmentation without any a priori information

on hill s equation with a singular complex valued potential 1 introduction the differential equation y00 qy ey is called hill s equation if q is a realvalued periodic locally integrable function of a real variable it is very well known that the spectrum of the operator associated with this equation consists of a countably in nite number of compact intervals of the real line these intervals are called spectral bands and are generally separated by open intervals called gaps in some instances however all but a nite number of gaps are empty resulting in a spectrum consisting of a nite number of compact bands and one closed interval extending to negative in nity in this case one calls q a nite band or nite gap potential the relationship of nite band potentials with the hierarchy of korteweg de vries equations has been the reason for a heightened interest in them during the past twenty years for recent accounts see for instance the monographs by dickey 8 and belokolos et al 3 the rst non trivial example of a nite band potential was given by ince in 1940 18 consider the lame potentials q x yg g 1 x c jq q0 where g 2n and jq q0 denotes weierstrass s elliptic function with fundamental half periods q and q0 if q is real q0 is pure imaginary and c q0 then q is realvalued periodic and continuous ince s result when translated to the present language shows that q then is a nite band potential with g non empty gaps between the bands this however raises immediately the question of what happens when c 6 q0 or when the half periods are more general in these cases one encounters potentials which are complex valued but continuous as well as potentials which have singularities of the form yg g 1 x and are realor complex valued before giving an overview of the content of the paper i want to give a brief account of the history of the subject let q be a real locally integrable periodic function with period p l the differential expression d dx q and h the self adjoint operator in l r associated with l then consider the following four statements a there are precisely 2g 1 real numbers e2g e0 such that the spectrum of h is given by

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

quasiperiodic and periodic solutions for vector nonlinear schrodinger equations we consider quasiperiodic and periodic cnoidal wave solutions of a set of n component vector nonlinear schrodinger equations vnlses in a biased photorefractive crystal with a drift mechanism of nonlinear response and kerr type nonlinearity n component nonlinear schrodinger equations can be used to model self trapped mutually incoherent wave packets these equations also model pulse pulse interactions in wavelength division multiplexed channels of optical fiber transmission systems quasiperiodic wave solutions for the vnlses in terms of n dimensional kleinian functions are presented periodic solutions in terms of hermite polynomials and generalized hermite polynomials for n component nonlinear schrodinger equations are found

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

lax representation for two particle dynamics splitting on two tori the lax representation in terms of matrices is constructed for separable multiply periodic systems splitting on two tori hyperelliptic kleinian functions and their reduction to elliptic functions are used

pairwise markov chains we propose a model called a pairwise markov chain pmc which generalizes the classical hidden markov chain hmc model the generalization which allows one to model more complex situations in particular implies that in pmc the hidden process is not necessarily a markov process however pmc allows one to use the classical bayesian restoration methods like maximum a posteriori map or maximal posterior mode mpm so akin to hmc pmc allows one to restore hidden stochastic processes with numerous applications to signal and image processing such as speech recognition image segmentation and symbol detection or classification among others furthermore we propose an original method of parameter estimation which generalizes the classical iterative conditional estimation ice valid for a classical hidden markov chain model and whose extension to possibly non gaussian and correlated noise is briefly treated some preliminary experiments validate the interest of the new model

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

a lifetime asymptotic growth curve for human height a new seven parameter asymptotic growth curve has been applied to longitudinal data on the height of 13 boys and 14 girls from 1 month to 19 years of age the residual sums of squares with this new curve were 7 5 times lower on the average than with the currently used five parameter curve no 1 of preece and baines 1978 annals of human biology 5 1 24 and 2 4 times lower than with the recent six parameter curve of shohoji and sasaki 1987 growth 51 432 450 the new curve is expressed with respect to total age passes through the origin and fits infants as satisfactorily as older children

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

unsupervised statistical segmentation of nonstationary images using triplet markov fields recent developments in statistical theory and associated computational techniques have opened new avenues for image modeling as well as for image segmentation techniques thus a host of models have been proposed and the ones which have probably received considerable attention are the hidden markov fields hmf models this is due to their simplicity of handling and their potential for providing improved image quality although these models provide satisfying results in the stationary case they can fail in the nonstationary one in this paper we tackle the problem of modeling a nonstationary hidden random field and its effect on the unsupervised statistical image segmentation we propose an original approach based on the recent triplet markov field tmf model which enables one to deal with nonstationary class fields moreover the noise can be correlated and possibly non gaussian an original parameter estimation method which uses the pearson system to find the natures of the noise margins which can vary with the class is also proposed and used to perform unsupervised segmentation of such images experiments indicate that the new model and related processing algorithm can improve the results obtained with the classical ones

maximum likelihood parameter estimation for unsupervised stochastic model based image segmentation an unsupervised stochastic model based approach to image segmentation is described and some of its properties investigated in this approach the problem of model parameter estimation is formulated as a problem of parameter estimation from incomplete data and the expectation maximization em algorithm is used to determine a maximum likelihood ml estimate previously the use of the em algorithm in this application has encountered difficulties since an analytical expression for the conditional expectations required in the em procedure is generally unavailable except for the simplest models in this paper two solutions are proposed to solve this problem a monte carlo scheme and a scheme related to besag s 1986 iterated conditional mode icm method both schemes make use of markov random field modeling assumptions examples are provided to illustrate the implementation of the em algorithm for several general classes of image models experimental results on both synthetic and real images are provided

signal and image segmentation using pairwise markov chains the aim of this paper is to apply the recent pairwise markov chain model which generalizes the hidden markov chain one to the unsupervised restoration of hidden data the main novelty is an original parameter estimation method that is valid in a general setting where the form of the possibly correlated noise is not known several experimental results are presented in both gaussian and generalized mixture contexts they show the advantages of the pairwise markov chain model with respect to the classical hidden markov chain one for supervised and unsupervised restorations

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

exact solutions for a class of integrable henon heiles type systems we study the exact solutions of a class of integrable henon heiles type systems according to the analysis of bountis et al phys rev a 25 1257 1982 these solutions are expressed in terms of two dimensional kleinian functions special periodic solutions are expressed in terms of the well known weierstrass function we extend some of our results to a generalized henon heiles type system with n 1 degrees of freedom

sar amplitude probability density function estimation based on a generalized gaussian model in the context of remotely sensed data analysis an important problem is the development of accurate models for the statistics of the pixel intensities focusing on synthetic aperture radar sar data this modeling process turns out to be a crucial task for instance for classification or for denoising purposes in this paper an innovative parametric estimation methodology for sar amplitude data is proposed that adopts a generalized gaussian gg model for the complex sar backscattered signal a closed form expression for the corresponding amplitude probability density function pdf is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model specifically the recently proposed method of log cumulants molc is applied which stems from the adoption of the mellin transform instead of the usual fourier transform in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant for the developed gg based amplitude model the resulting molc estimates turn out to be numerically feasible and are also analytically proved to be consistent the proposed parametric approach was validated by using several real ers 1 xsar e sar and nasa jpl airborne sar images and the experimental results prove that the method models the amplitude pdf better than several previously proposed parametric models for backscattering phenomena

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

the mean field theory in em procedures for blind markov random field image restoration a markov random field mrf model based em expectation maximization procedure for simultaneously estimating the degradation model and restoring the image is described the mrf is a coupled one which provides continuity inside regions of smooth gray tones and discontinuity at region boundaries constraints for the restoration problem which is in general ill posed the computational difficulty associated with the em procedure for mrfs is resolved by using the mean field theory from statistical mechanics an orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates experimental results on synthetic and real world images show that this approach provides good blur estimates and restored images the restored images are comparable to those obtained by a wiener filter in mean square error but are most visually pleasing

on a theorem of hochstadt in fact hochstadt gives an explicit formula for the discriminant which will be reproduced below since hochstadt s work there has been a considerable interest in finite band potentials i e potentials q such that the spectrum of the operator associated with d2 dx 2 q consists of finitely many regular analytic arcs due to their close relationship with the korteweg de vries hierarchy and hence with integrable systems however the interest is not restricted to real valued potentials for instance

the inverse periodic problem for hill s equation with a finite gap potential let h q d d q x be the hill s operator with a periodic potential q of period one consider the following inverse problem find all potentials q x with the same periodic spectrum as a given potential p x two explicit solutions are known for finite gap potentials its and matveev 6 give an explicit formula in terms of theta functions their solution was generalized by mckean and trubowitz lo to infinite gap potentials finkel et al 5 give a second formula which expresses q in terms of the base potential p the dirichlet eigenfunctions of p and the floquet solutions of p the formula involves no algebraic geometry in this paper we represent finite gap potentials q as rational functions of the base potential p and the derivatives ofp the representation makes use of the finkel isaacson trubowitz fit formula

an explicit characterization of calogero moser systems combining theorems of halphen floquet and picard and a frobenius type analysis we characterize rational meromorphic simply periodic and elliptic kdv potentials in particular we explicitly describe the proper extension of the airault mckean moser locus associated with these three classes of algebro geometric solutions of the kdv hierarchy with special emphasis on the case of multiple collisions between the poles of solutions this solves a problem left open since the mid 1970s

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

a smooth test of goodness of fit for growth curves and monotonic nonlinear regression models nous proposons pour des courbes de croissance un test d adequation base sur une adaptation du paradigme des tests lisses pilotes par les donnees le test est facile a mettre en oeuvre et permet de determinersi un modele ajuste adequatement un ensemble d experiences de croissance une etude de simulation montre que pour de petits echantillons le test donne le bon niveau de plus elle montre que sa puissance est generalement superieure a celle des tests existants l article se termine en revenant sur le probleme recurrent de valider un modele pour la croissance de la stature humaine

functional regression analysis of fluorescence curves summary fluorescence curves are useful for monitoring changes in photosynthesis activity various summary measures have been used to quantify differences among fluorescence curves corresponding to different treatments but these approaches may forfeit valuable information as each individual fluorescence curve is a functional observation it is natural to consider a functional regression model the proposed model consists of a nonparametric component capturing the general form of the curves and a semiparametric component describing the differences among treatments and allowing comparisons of treatments several graphical model checking approaches are introduced both approximate asymptotic confidence intervals as well as simulation based confidence intervals are available analysis of data from a crop experiment using the proposed model shows that the salient features in the fluorescence curves are captured adequately the proposed functional regression model is useful for analysis of high throughput fluorescence curve data from regular monitoring or screening of plant growth

kpca for semantic object extraction in images in this paper we kernelize conventional clustering algorithms from a novel point of view based on the fully mathematical proof we first demonstrate that kernel kmeans kkmeans is equivalent to kernel principal component analysis kpca prior to the conventional kmeans algorithm by using kpca as a preprocessing step we also generalize gaussian mixture model gmm to its kernel version the kernel gmm kgmm consequently conventional clustering algorithms can be easily kernelized in the linear feature space instead of a nonlinear one to evaluate the newly established kkmeans and kgmm algorithms we utilized them to the problem of semantic object extraction segmentation of color images based on a series of experiments carried out on a set of color images we indicate that both kkmeans and kgmm can offer more elaborate output than the conventional kmeans and gmm respectively

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

integral representation of solutions to fuchsian system and heun s equation we obtain integral representations of solutions to special cases of the fuchsian system of differential equations and heun s differential equation in particular we calculate the monodromy of solutions to the fuchsian equation that corresponds to picard s solution of the sixth painleve equation and to heun s equation

a differential equation for a four point correlation function in liouville field theory and elliptic four point conformal blocks liouville field theory on a sphere is considered we explicitly derive a differential equation for four point correlation functions with one degenerate field we also introduce and study a class of four point conformal blocks which can be calculated exactly and represented by finite dimensional integrals of elliptic theta functions for an arbitrary intermediate dimension we also study the bootstrap equations for these conformal blocks and derive integral representations for corresponding four point correlation functions a relation between the one point correlation function of a primary field on a torus and a special four point correlation function on a sphere is proposed

the 192 solutions of the heun equation a machine generated list of 192 local solutions of the heun equation is given they are analogous to kummer s 24 solutions of the gauss hypergeometric equation since the two equations are canonical fuchsian differential equations on the riemann sphere with four and three singular points respectively tabulation is facilitated by the identification of the automorphism group of the equation with n singular points as the coxeter group d n each of the 192 expressions is labeled by an element of d 4 of the 192 24 are equivalent expressions for the local heun function hl and it is shown that the resulting order 24 group of transformations of hl is isomorphic to the symmetric group s 4 the isomorphism encodes each transformation as a permutation of an abstract four element set not identical to the set of singular points

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

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

treibich verdier potentials and the stationary m kdv hierarchy here x x col co3 denotes the elliptic weierstrass function with fundamental periods f p 2a l 2co3 im co3 wl 5 0 see 1 ch 18 in the special case where col is real and co3 is purely imaginary the potential q is real valued and ince s striking result 31 in modern spectral theoretic terminology yields the fact that the self adjoint operator l associated with the differential expression d 2 q in l2 ir has a finite gap spectrum of the type