hilbert schmidt lower bounds for estimators on matrix lie groups for atr deformable template representations of observed imagery model the variability of target pose via the actions of the matrix lie groups on rigid templates in this paper we study the construction of minimum mean squared error estimators on the special orthogonal group so n for pose estimation due to the nonflat geometry of so n the standard bayesian formulation of optimal estimators and their characteristics requires modifications by utilizing hilbert schmidt metric defined on gl n a larger group containing so n a mean squared criterion is defined on so n the hilbert schmidt estimate hse is defined to be a minimum mean squared error estimator restricted to so n the expected error associated with the hse is shown to be a lower bound called the hilbert schmidt bound hsb on the error incurred by any other estimator analysis and algorithms are presented for evaluating the hse and the hsb in cases of both ground based and airborne targets

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

meta fibonacci codes efficient universal coding of natural numbers in this paper we address the problem of the universal coding of natural numbers a new numeration system is introduced which is based on variable r meta fibonacci sequences and it is a generalization of the zeckendorf numeration system this new numeration system is used to construct binary prefix free uniquely decodable universal codes called meta fibonacci codes the main advantage of these codes is that they are parametrized by a sequence of numbers the sequence o by controlling the growth of the values of this sequence we can control the length of the code word this means that we can provide a general framework for building efficient universal coders for natural numbers such framework is applied to the upper bounds of the code word length defined by leung yan cheong and cover 1978 levenshtein 1968 and ahlswede 1997 there is no other code meeting these bounds in each case we build meta fibonacci codes and demonstrate that the upper bound of their code word length is satisfied up to an additive constant thereby solving these open problems the framework may be applied to other upper bounds that satisfy kraft inequality

technical communique on the degree of polynomial parameter dependent lyapunov functions for robust stability of single parameter dependent lti systems a counter example to barmish s conjecture in this paper we consider the robust hurwitz stability analysis problems of a single parameter dependent matrix a q a email protected 1 over email protected 1 1 where a 0 a email protected r n x n with a 0 being hurwitz stable in particular we are interested in the degree n of the polynomial parameter dependent lyapunov matrix ppdlm of the form p q email protected i 0 email protected ip i that ensures the robust hurwitz stability of a q via p q 0 p q a q a t q p q 3 in general

a new sequential classifier using information criterion window abstract we propose a model based parametric unsupervised sequential classifier with an information criterion window icw based on the assumption that the number of clusters changes smoothly from a stage to the following stage to determine the number of clusters at each stage and to perform classification on the observed mixture data the proposed approach provides possible solutions for two problems of pattern recognition adaptive classification and sequential clustering validation simulation results demonstrate that the proposed algorithm provides good results for pure mixed data and successfully performs clustering for the mixed gaussian data in the large sample limit

regression modeling in back propagation and projection pursuit learning we study and compare two types of connectionist learning methods for model free regression problems 1 the backpropagation learning bpl and 2 the projection pursuit learning ppl emerged in recent years in the statistical estimation literature both the bpl and the ppl are based on projections of the data in directions determined from interconnection weights however unlike the use of fixed nonlinear activations usually sigmoidal for the hidden neurons in bpl the ppl systematically approximates the unknown nonlinear activations moreover the bpl estimates all the weights simultaneously at each iteration while the ppl estimates the weights cyclically neuron by neuron and layer by layer at each iteration although the bpl and the ppl have comparable training speed when based on a gauss newton optimization algorithm the ppl proves more parsimonious in that the ppl requires a fewer hidden neurons to approximate the true function to further improve the statistical performance of the ppl an orthogonal polynomial approximation is used in place of the supersmoother method originally proposed for nonlinear activation approximation in the ppl

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

polynomially parameter dependent lyapunov functions for robust stability of polytopic systems an lmi approach in this note robust stability of state space models with respect to real parametric uncertainty is considered specifically a new class of parameter dependent quadratic lyapunov functions for establishing stability of a polytope of matrices is introduced i e the homogeneous polynomially parameter dependent quadratic lyapunov functions hpd qlfs the choice of this class which contains parameter dependent quadratic lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form is motivated by the property that a polytope of matrices is stable if and only there exists an hpd qlf the main result of the note is a sufficient condition for determining the sought hpd qlf which amounts to solving linear matrix inequalities lmis derived via the complete square matricial representation csmr of homogeneous matricial forms and the lyapunov matrix equation numerical examples are provided to demonstrate the effectiveness of the proposed approach

cooperative robust estimation using layers of support we present an approach to the problem of representing images that contain multiple objects or surfaces rather than using an edge based approach to represent the segmentation of a scene we propose a multilayer estimation framework which uses support maps to represent the segmentation of the image into homogeneous chunks this support based approach can represent objects that are split into disjoint regions or have surfaces that are transparently interleaved our framework is based on an extension of robust estimation methods that provide a theoretical basis for support based estimation we use a selection criteria derived from the minimum description length principle to decide how many support maps to use in describing an image our method has been applied to a number of different domains including the decomposition of range images into constituent objects the segmentation of image sequences into homogeneous higher order motion fields and the separation of tracked motion features into distinct rigid body motions

a network of autoregressive processing units for time series modeling a new approach for time series modeling has been developed this has a neural network structure with three layers the input switch and processing layers the processing layer contains processing units whose structure is defined by the user these units follow the structure of a general autoregressive model a hybrid training method that combines self organized and supervised training is used for parameter estimation the model selection of this network structure is studied by an information theory criterion that is based on the predictive minimum description length principle the aim is to determine the size and complexity of the model this network is found to perform as well as or even better than the multilayer perceptron network the radial basis function network the threshold autoregressive model and the autoregressive model in nonlinear time series modeling experiments other benefits of the network are its simple architecture and fast processing ability in the training and recalling phases

maximal unidirectional perturbation bounds for stability of polynomials and matrices abstract given a stable polynomial or matrix we consider a class of unidirectional perturbations in this note we provide a closed form for the maximal perturbation bounds under which stability is preserved the results are then used to derive a closed form for the maximal stability box around the coefficients of a nominally stable polynomial

an mdl framework for sparse coding and dictionary learning the power of sparse signal modeling with learned overcomplete dictionaries has been demonstrated in a variety of applications and fields from signal processing to statistical inference and machine learning however the statistical properties of these models such as underfitting or overfitting given sets of data are still not well characterized in the literature as a result the success of sparse modeling depends on hand tuning critical parameters for each data and application this work aims at addressing this by providing a practical and objective characterization of sparse models by means of the minimum description length mdl principle a well established information theoretic approach to model selection in statistical inference the resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which by virtue of the mdl principle are completely parameter free furthermore such framework allows to incorporate additional prior information to existing models such as markovian dependencies or to define completely new problem formulations including in the matrix analysis area in a natural way these virtues will be demonstrated with parameter free algorithms for the classic image denoising and classification problems and for low rank matrix recovery in video applications however the framework is not limited to this imaging data and can be applied to a wide range of signal and data types and tasks

detection and localization of multiple sources via the stochastic signals model a method for the detection of coherent and noncoherent signals based on the application of j rissanen s 1978 minimum description length principle for model selection to the stochastic signals model is presented the detection and localization are done simultaneously with the location estimator coinciding with the maximum likelihood estimator derived by j f bohme 1986 the proposed method outperforms the method of m wax and i ziskind 1989 especially in the threshold region simulation results demonstrating the improved performance are included

application of piece wise regression to detecting internal structure of signal abstract the problem of restoring the underlying structure of a signal with the help of piece wise regression is considered the case of interest is that the domain of definition of a response function consists of a number of regions of smoothness the number of regions and the location of change points are not fixed in advance and they should be found by analyzing the signal corrupted with noise for a given number of smooth regions the best piece wise regression may be found with the help of an approach based on dynamic programming the selection of the best model the best number of regions of smoothness is performed with the help of a probabilistic estimate some properties of the estimate and the whole procedure are studied and the results of experiments are presented

a new method for ar order determination of an arma process using a combination of the minimum description length mdl criterion and overdetermined instrumental variable method a computationally efficient method for ar order determination of an arma process is proposed it is shown that the well known singular value decomposition svd method for ar order determination is a special case of the proposed method numerical simulations are presented to show the effectiveness of this method

multiple target direction of arrival tracking a new algorithm is presented for estimating the directions of arrival of signals from an unknown number of moving signal sources the parameter space is a countable union of cartesian products of the torus each product space corresponding to a different number of signals reaching the sensor array a bayesian posterior probability measure is defined on this parameter space by combining the sensor array manifold models with the von mises prior on source motion the estimates are generated empirically using a random sampling algorithm based on jump diffusion processes and the results are presented from an implementation on a dap510 massively parallel computer

on information theoretic criteria for determining the number of signals in high resolution array processing an important problem in high resolution array processing is the determination of the number of signals arriving at the array information theoretic criteria provide a means to achieve this two commonly used criteria are the akaike information criterion aic and minimum descriptive length mdl criterion while the aic tends to overestimate even at a high signal to noise ratio snr the mdl criterion tends to underestimate at low or moderate snr by excluding irrelevant parameters a new log likelihood function has been chosen utilizing this new log likelihood function gives a set of more accurate estimates of the eigenvalues and in the establishment of modified information theoretic criteria which moderate the performance of the aic and the mdl criterion computer simulations confirm that the modified criteria have superior performance

twenty one ml estimators for model selection classical approaches to determine a suitable model structure from observed input output data are based on hypothesis tests and information based criteria recently the model structure has been considered as a stochastic variable and standard estimation techniques have been proposed the resulting estimators are closely related to the aforementioned methods however it turns out that there are a number of prior choices in the problem formulation which are crucial for the estimators behavior the contribution of this paper is to clarify the role of the prior choices to examine a number of possibilities and to show which estimators are consistent this is done in a linear regression framework for autoregressive models we also investigate a novel prior assumption on stability and give the estimator for the model order and the parameters themselves

a minimum description length model for recognizing objects with variable appearances the vapor model most object recognition systems can only model objects composed of rigid pieces whose appearance depends only on lighting and viewpoint many real world objects however have variable appearances because they are flexible and or have a variable number of parts these objects cannot be easily modeled using current techniques the author proposes the use of a knowledge representation method called the vapor variable appearance object representation model to represent objects with these kinds of variable appearances the vapor model is an idealization of the object all instances of the model in an image are variations from the ideal appearance the variations are evaluated by the description length of the data given the model i e the number of information theoretic bits needed to represent the model and the deviations of the data from the ideal appearance the shortest length model is chosen as the best description the author demonstrates how the vapor model performs in a simple domain of circles and polygons and in the complex domain of finding cloverleaf interchanges in aerial images of roads

robust and accurate arx and arma model order estimation of non gaussian processes the field of higher order statistics is emerging rapidly for analyzing non gaussian processes there are several motivations behind the use of higher order statistics the emphasis of this paper is based on the property that higher order cumulants are blind to any kind of gaussian process hence when the processed signal is non gaussian stationary and the additive noise is stationary gaussian the noise will vanish in the cumulant domain this paper presents an extension to the results of liang et al 1993 this extension is a straightforward generalization of liang s approach to third order cumulants tocs the new cumulant based algorithm provides a higher level of accuracy in the presence of noise than the original second order algorithm in addition the original results of liang have been extended to the case of colored gaussian noise examples are given to demonstrate the performance of this algorithm even when the observed signal is heavily corrupted by gaussian noise

an eigenvalue perturbation approach to stability analysis part ii when will zeros of time delay systems cross imaginary axis this paper presents an application of the eigenvalue series developed in part i j chen et al siam j control optim 48 2010 pp 5564 5582 to the study of linear time invariant delay systems focusing on the asymptotic behavior of critical characteristic zeros on the imaginary axis we consider systems given in state space form and as quasi polynomials and we develop an eigenvalue perturbation analysis approach which appears to be both conceptually appealing and computationally efficient our results reveal that the zero asymptotic behavior of time delay systems can in general be characterized by solving a simple eigenvalue problem and additionally when described by a quasi polynomial by computing the derivatives of the quasipolynomial

the weak galerkin finite element method for the transport reaction equation abstract we present and analyze a weak galerkin finite element method for solving the transport reaction equation in d space dimensions this method is highly flexible by allowing the use of discontinuous finite element on general meshes consisting of arbitrary polygon polyhedra we derive the l 2 error estimate of o h k 1 2 order for the discrete solution when the kth order polynomials are used for k 0 moreover for a special class of meshes we also obtain the optimal error estimate of o h k 1 order in the l 2 norm a derivative recovery formula is presented to approximate the convection directional derivative and the corresponding superconvergence estimate is given numerical examples on compatible and non compatible meshes are provided to show the effectiveness of this weak galerkin method

classification based adaptive filtering for multiframe blind image restoration in this paper the blind restoration of a scene is investigated when multiple degraded blurred and noisy acquisitions are available an adaptive filtering technique is proposed where the distorted images are filtered classified and then fused based upon the classification decisions finite normal density mixture fnm models are used to model the filtered outputs at each iteration for simplicity fixed number of gaussian components classes is initially considered for each degraded frame and the selection of the optimal number of classes is performed according to the global relative entropy criterion however there exist cases where dynamically varying fnm models should be considered where the optimal number of classes is selected according to the akaike information criterion the iterative application of classification and fusion followed by optimal adaptive filtering converges to a global enhanced representation of the original scene in only a few iterations the proposed restoration method does not require knowledge of the point spread function support size or exact alignment of the acquired frames simulation results on synthetic and real data using both fixed and dynamically varying fnm models demonstrate its efficiency under both noisy and noise free conditions

detection of the number of coherent signals by the mdl principle an approach is presented to the problem of detecting the number of sources impinging on a passive sensor array that is based on j rissanen s 1983 minimum description length mdl principle the approach is applicable to any type of sources including the case of sources which are fully correlated referred to as the coherent signals case two slightly different detection criteria are derived both requiring the estimation of the locations of the sources the first is tailored to the detection problem per se whereas the second is tailored to the combined detection estimation problem consistency of the two criteria is proved and their performance is demonstrated by computer simulations

on estimating the order of an arma process abstract an order estimation scheme is proposed for scalar autoregressive moving average processes it is based on the determination of the rank of estimated matrices numerous heuristic tests have already been derived around the relations existing between the rank of covariance matrices and arma orders using results from matrix perturbation theory we indicate how to build and justify statistical tests which permit decisions about e g how many eigenvalues should be declared equal to zero the usefulness of these asymptotic developments is verified by simulations the results are in agreement with the predictions for quite small sample sizes and the performances are satisfactory

bayesian detection and estimation of cisoids in colored noise the problem of estimating the number of cisoids in colored noise is addressed it is assumed that the noise can be modeled by an autoregression whose order has also to be estimated a new criterion is proposed for estimating the number of cisoids and the autoregressive model order as well as a new algorithm for estimating the cisoidal frequencies in the derivation a bayesian methodology and subspace decomposition are employed the proposed criterion significantly outperforms the popular mdl and aic as applied in a paper by nagesha and kay in addition an algorithm that reduces the computational complexity of the solution is developed computer simulations that demonstrate the performance of the criterion are included

model selection using wavelet decomposition and applications in this paper we discuss how to use wavelet decompositions to select a regression model the methodology relies on a minimum description length criterion which is used to determine the number of nonzero coefficients in the vector of wavelet coefficients consistency properties of the selection rule are established and simulation studies reveal information on the distribution of the minimum description length selector we then apply the selection rule to specific problems including testing for pure white noise the power of this test is investigated via simulation studies and the selection criterion is also applied to testing for no effect in nonparametric regression

model change detection with the mdl principle we are concerned with the issue of detecting model changes in probability distributions we specifically consider the strategies based on the minimum description length mdl principle we theoretically analyze their basic performance from the two aspects data compression and hypothesis testing from the view of data compression we derive a new bound on the minimax regret for model changes here the mini max regret is defined as the minimum of the worst case code length relative to the least normalized maximum likelihood code length over all model changes from the view of hypothesis testing we reduce the model change detection into a simple hypothesis testing problem we thereby derive upper bounds on error probabilities for the mdl based model change test the error probabilities are valid for finite sample size and are related to the information theoretic complexity as well as the discrepancy measure of the hypotheses to be tested

stability analysis of polynomially dependent systems by eigenvalue perturbation in this technical note we present a stability analysis approach for polynomially dependent one parameter systems the approach which appears to be conceptually appealing and computationally efficient and is referred to as an eigenvalue perturbation approach seeks to characterize the analytical and asymptotic properties of eigenvalues of matrix valued functions or operators the essential problem dwells on the asymptotic behavior of the critical eigenvalues on the imaginary axis that is on how the imaginary eigenvalues may vary with respect to the varying parameter this behavior determines whether the imaginary eigenvalues cross from one half plane into another and hence plays a critical role in determining the stability of such systems our results reveal that the eigenvalue asymptotic behavior can be characterized by solving a simple generalized eigenvalue problem leading to numerically efficient stability conditions

a bayes procedure for the identification of univariate time series models on presente un critere d identification qui est asymptotiquement equivalent a une regle de decision bayesienne

a probabilistic criterion to detect rigid point matches between two images and estimate the fundamental matrix the perspective projections of n physical points on two views stereovision are constrained as soon as n 8 however to prove in practice the existence of a rigid motion between two images more than 8 point matches are desirable in order to compensate for the limited accuracy of the matches in this paper we propose a computational definition of rigidity and a probabilistic criterion to rate the meaningfulness of a rigid set as a function of both the number of pairs of points n and the accuracy of the matches this criterion yields an objective way to compare say precise matches of a few points and approximate matches of a lot of points it gives a yes no answer to the question could this rigid points correspondence have occurred by chance since it guarantees that the expected number of meaningful rigid sets found by chance in a random distribution of points is as small as desired it also yields absolute accuracy requirements for rigidity detection in the case of non matched points and optimal values of n depending on the expected accuracy of the matches and on the proportion of outliers we use it to build an optimized random sampling algorithm that is able to detect a rigid motion and estimate the fundamental matrix when the set of point matches contains up to 90 of outliers which outperforms the best currently known methods like m estimators lmeds classical ransac and tensor voting

α investing a procedure for sequential control of expected false discoveries summary investing is an adaptive sequential methodology that encompasses a large family of procedures for testing multiple hypotheses all control mfdr which is the ratio of the expected number of false rejections to the expected number of rejections mfdr is a weaker criterion than the false discovery rate which is the expected value of the ratio we compensate for this weakness by showing that investing controls mfdr at every rejected hypothesis investing resembles spending that is used in sequential trials but it has a key difference when a test rejects a null hypothesis investing earns additional probability towards subsequent tests investing hence allows us to incorporate domain knowledge into the testing procedure and to improve the power of the tests in this way investing enables the statistician to design a testing procedure for a specific problem while guaranteeing control of mfdr

technical communique exact robust stability analysis of uncertain systems with a scalar parameter via lmis this paper provides an exact linear matrix inequality lmi condition for robust asymptotic stability of uncertain systems depending polynomially on a scalar parameter in both continuous time and discrete time cases specifically this condition exploits sum of squares sos techniques and is based on the construction of polynomials of known degree that detect the presence of eigenvalues on the boundary of the stability region it is shown that this condition requires a much smaller computational burden than existing exact lmi conditions which might be prohibitive even for small scale systems

an objective approach to prior mass functions for discrete parameter spaces we present a novel approach to constructing objective prior distributions for discrete parameter spaces these types of parameter spaces are particularly problematic as it appears that common objective procedures to design prior distributions are problem specific we propose an objective criterion based on loss functions instead of trying to define objective probabilities directly we systematically apply this criterion to a series of discrete scenarios previously considered in the literature and compare the priors the proposed approach applies to any discrete parameter space making it appealing as it does not involve different concepts according to the model supplementary materials for this article are available online

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

universal modeling and coding the problems arising in the modeling and coding of strings for compression purposes are discussed the notion of an information source that simplifies and sharpens the traditional one is axiomatized and adaptive and nonadaptive models are defined with a measure of complexity assigned to the models a fundamental theorem is proved which states that models that use any kind of alphabet extension are inferior to the best models using no alphabet extensions at all a general class of so called first in first out fifo arithmetic codes is described which require no alphabet extension devices and which therefore can be used in conjunction with the best models because the coding parameters are the probabilities that define the model their design is easy and the application of the code is straightforward even with adaptively changing source models

an eigenvalue perturbation approach to stability analysis part i eigenvalue series of matrix operators this two part paper is concerned with stability analysis of linear systems subject to parameter variations of which linear time invariant delay systems are of particular interest we seek to characterize the asymptotic behavior of the characteristic zeros of such systems this behavior determines for example whether the imaginary zeros cross from one half plane into another and hence plays a critical role in determining the stability of a system in part i of the paper we develop necessary mathematical tools for this study which focuses on the eigenvalue series of holomorphic matrix operators while of independent interest the eigenvalue perturbation analysis has a particular bearing on stability analysis and indeed has the promise to provide efficient computational solutions to a class of problems relevant to control systems analysis and design of which time delay systems are a notable example

a convex approach to robust stability for linear systems with uncertain scalar parameters in this paper robust stability for linear systems with several uncertain complex and or real scalar parameters is studied a countable family of conditions sufficient for robust stability is given in terms of solvability of some simple linear matrix inequalities lmis these conditions are of increasing precision and it is shown conversely that robust stability implies solvability of these lmis from a certain rank and beyond this result constitutes an extension of the characterization by solvability of lyapunov inequality of the asymptotic stability for usual linear systems it is based on the search of parameter dependent quadratic lyapunov functions polynomial of increasing degree in the parameters

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

functional graphical models graphical models have attracted increasing attention in recent years especially in settings involving high dimensional data in particular gaussian graphical models are used to model the conditio

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

some notes on rissanen s stochastic complexity a new version of stochastic complexity for a parametric statistical model is derived based on a class of two part codes we show that choosing the quantization in the first step according to the fisher information is optimal and we compare our approach to a recent result of rissanen 1983 an application to robust regression model selection is presented

lyapunov based exact stability analysis and synthesis for linear single parameter dependent systems we propose a class of polynomially parameter dependent quadratic ppdq lyapunov functions for assessing the stability of single parameter dependent linear time invariant s pdlti systems in a non conservative manner it is shown that the stability of s pdlti systems is equivalent to the existence of a ppdq lyapunov function a bound on the degree of the polynomial dependence of the lyapunov function in the system parameter is given explicitly the resulting stability conditions are expressed in terms of a set of matrix inequalities whose feasibility over a compact and connected set can be cast as a convex finite dimensional optimisation problem extensions of the approach to state feedback controller synthesis are also provided

statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing the performances of the akaike 1974 information criterion and the minimum descriptive length criterion methods are examined the events which lead to erroneous decisions are considered and on the basis of these events the probabilities of error for the two criteria are derived the probabilities of the first two events are derived based on the asymptotic distribution of the sample eigenvalues of an estimated hermitian matrix it is further shown that the probabilities of missing and false alarm for these two criteria can be evaluated to a close approximation although the derivation of the probabilities of error is based on an asymptotic analysis the results are confirmed to be in very close agreement with computer simulation results

arma order estimation via matrix perturbation theory using matrix perturbation theory we obtain the statistical distribution of the smallest eigenvalue of the hankel matrix built upon the estimated covariances under the hypothesis that the corresponding exact hankel matrix possesses one single zero eigenvalue this allows us to develop and justify a new order determination scheme whose performance appears similar to those based on likelihood maximization but with a much lower computational complexity

modeling of two dimensional random fields by parametric cepstrum a method is presented for parametric modeling of stationary random fields the class of parametric models considered allows the most general elliptic field and by linear constraints can include such special cases as isotropic quarter plane and separable fields the technique based on the cepstrum has the great advantage of requiring only the use of fast fourier transforms in the fitting process thus unlike the fitting of two dimensional autoregressions no iteration is necessary other advantages are that any wiener filters constructed from the fitted spectrum are guaranteed to be stable and that the spectrum is guaranteed to be positive statistical tests for determining various special types of field from data are developed the choice of model order is discussed as well

maximum entropy as a special case of the minimum description length criterion corresp the maximum entropy me and maximum likelihood ml criteria are the bases for two approaches to statistical inference problems a new criterion called the minimum description length mdl has been recently introduced this criterion generalizes the ml method so it can be applied to more general situations e g when the number of parameters is unknown it is shown that me is also a special case of the mdl criterion maximizing the entropy subject to some constraints on the underlying probability function is identical to minimizing the code length required to represent all possible i i d realizations of the random variable such that the sample frequencies or histogram satisfy those given constraints

a new method for model order selection and modal parameter estimation in time domain abstract this paper mainly deals with the identification of structural modal parameters from output accelerometers only using a vector autoregressive moving average varma p q model method the problem of determining the order p of the ar part or equivalently the number of modes in a frequency band is also examined using a combination of the multivariate minimum description length mdl criterion and an overdetermined instrumental variable sequence the ar coefficients are then obtained from this instrumental variable sequence the companion matrix is formed and the modal parameters of the vibrating system deduced numerical and experimental results are treated to show the effectiveness of this new procedure

objective priors for discrete parameter spaces this article considers the development of objective prior distributions for discrete parameter spaces formal approaches to such development such as the reference prior approach often result in a constant prior for a discrete parameter which is questionable for problems that exhibit certain types of structure to take advantage of structure this article proposes embedding the original problem in a continuous problem that preserves the structure and then using standard reference prior theory to determine the appropriate objective prior four different possibilities for this embedding are explored and applied to a population size model the hypergeometric distribution the multivariate hypergeometric distribution the binomial beta distribution and the binomial distribution the recommended objective priors for the first third and fourth problems are new

bounds on the entropy series upper bounds on the entropy of a countable integer valued random variable are furnished in terms of the expectation of the logarithm function in particular an upper bound is derived that is sharper than that of p elias ibid vol it 21 no 2 p 194 203 1975 for all values of e sub p log bounds that are better only for large values of e sub p than the previous known upper bounds are also provided

hierarchical color correction for camera cell phone images in this paper we propose a hierarchical color correction algorithm for enhancing the color of digital images obtained from low quality digital image capture devices such as cell phone cameras the proposed method is based on a multilayer hierarchical stochastic framework whose parameters are learned in an offline training procedure using the well known expectation maximization em algorithm this hierarchical framework functions by first making soft assignments of images into defect classes and then processing the images in each defect class with an optimized algorithm the hierarchical color correction is performed in three stages in the first stage global color attributes of the low quality input image are used in a gaussian mixture model gmm framework to perform a soft classification of the image into m predefined global image classes in the second stage the input image is processed with a nonlinear color correction algorithm that is designed for each of the m global classes this color correction algorithm which we refer to as resolution synthesis color correction rscc applies a spatially varying color correction determined by the local color attributes of the input image in the third stage the outputs of the rscc predictors are combined using the global classification weights to yield the color corrected output image we compare the performance of the proposed method to other commercial color correction algorithms on cell phone camera images obtained from different sources both subjective and objective measures of quality indicate that the new color correction algorithm improves quality over the existing methods

data mapping by probabilistic modular networks and information theoretic criteria the quantitative mapping of a database that represents a finite set of classified and or unclassified data points may be decomposed into three distinctive learning tasks 1 detection of the structure of each class model with locally mixture clusters 2 estimation of the data distributions for each induced cluster inside each class and 3 classification of the data into classes that realizes the data memberships the mapping function accomplished by the probabilistic modular networks may then be constructed as the optimal estimator with respect to information theory and each of the three tasks can be interpreted as an independent objective in real world applications we adapt a model fitting scheme that determines both the number and kernel of local clusters using information theoretic criteria the class distribution functions are then obtained by learning generalized gaussian mixtures where a soft classification of the data is performed by an efficient incremental algorithm further classification of the data is treated as a hard bayesian detection problem in particular the decision boundaries between the classes are fine tuned by a reinforce or antireinforce supervised learning scheme examples of the application of this framework to medical image quantification automated face recognition and featured database analysis are presented as well