an approach to time series analysis and arma spectral estimation this paper presents an approach to time series analysis and arma spectral estimation from only the output data corrupted by noise it is shown that the generalized not well known modified yule walker myw equations hold when the residual is some correlated noise to solve such equations a new version of the generalized least squares gls method is proposed yielding ar parameter estimates with higher accuracy this gls method can also be used to enhance the estimation accuracy of ar parameters for short and noisy data in case of the myw equation holding theoretically furthermore a simple procedure for improving ma parameter estimates is studied our approach as cadzow s singular value decomposition svd method has provided significantly higher performance spectral estimates for a low order arma model than those obtained via usual techniques which are based upon direct solution of the myw equations and which use a high order model without considering an additive noise

arma parameter estimation using a novel recursive estimation algorithm with selective updating the authors investigate an extension of a recursive estimation algorithm the so called optimal bounding ellipsoid or obe algorithm which features a discerning update strategy in particular an extension of the algorithm to arma autoregressive moving average parameter estimation is presented along with a convergence analysis the extension is similar to the extended least squares els algorithm however the convergence analysis is complicated due to the discerning update strategy which incorporates an information dependent updating factor the virtues of such an update strategy are more efficient use of the input data in terms of information processing and a modular adaptive filter structure which would facilitate the development of a parallel pipelined signal processing architecture it is shown that if the input noise is bounded and the moving average parameters satisfy a certain magnitude bound then the a posteriori prediction errors are uniformly bounded with an additional persistence of excitation condition the parameter estimates are shown to converge to a neighborhood of the true parameters and the a priori prediction errors are shown to be asymptotically bounded simulation results show that the parameter estimation error for the eobe algorithm is comparable to that for the els algorithm

an exact forward backward maximum likelihood autoregressive parameter estimation method a method for obtaining an exact maximum likelihood estimate mle of the autoregressive ar parameters is proposed the method is called the forward backward maximum likelihood algorithm based on a new form of the log likelihood function for a gaussian ar process an iterative maximization is used to obtain an mle of the inverse covariance matrix the ar parameters are then determined via the normal equations experimental results comparing the new method with other popular ar spectrum estimation methods indicate the new method achieves low bias and low variance ar parameter estimates comparable with the existing methods

on the exact maximum likelihood estimation of gaussian autoregressive processes it is shown that the true maximum likelihood estimates of a gaussian zero mean ar process can be calculated the steps toward their obtainment with standard subroutines are calculating extrema are given the likelihood of the data is maximized in contrast to current approximate methods however the computational cost is significantly higher also the order p of the process is presumed known

an asymptotically efficient arma estimator based on sample covariances an asymptotically efficient autoregressive moving average arma spectral estimator is presented based on the sample covariances of observed time series the estimate of the autoregressive ar part is shown to be identical to the optimal instrumental variable iv estimator in 7 although derived here using a different approach the moving average ma spectral parameter estimate is new

binary picture thinning by an iterative parallel two subcycle operation abstract a thinning algorithm for digital binary pictures is presented the algorithm repeats the removal of the deletable border points in parallel and the extraction of the final points it is implemented as an iterative parallel two subcycle operation consequently the number of iterations required is about equal to the maximum width of the input figures the algorithm erases the end points while the iteration number is smaller than a given threshold utilization of the final point condition makes the algorithm faster and the flexible deletion of end points produces a line pattern of good quality even for noisy figures

vector arma estimation a reliable subspace approach a parameter estimation method for finite dimensional multivariate linear stochastic systems which is guaranteed to produce valid models approximating the true underlying system in a computational time of a polynomial order in the system dimension is presented this is achieved by combining the main features of certain stochastic subspace identification techniques with sound matrix schur restabilizing procedures and multivariate covariance fitting both of which are formulated as linear matrix inequality problems all aspects of the identification method are discussed with an emphasis on the two issues mentioned above and examples of the overall performance are provided for two different systems

nonasymptotic bounds for autoregressive time series modeling the subject of this paper is autoregressive ar modeling of a stationary gaussian discrete time process based on a finite sequence of observations the process is assumed to admit an ar representation with exponentially decaying coefficients we adopt the nonparametric minimax framework and study how well the process can be approximated by a finiteorder armodel a lower bound on the accuracy of arapproximations is derived and a nonasymptotic upper bound on the accuracy of the regularized least squares estimator is established it is shown that with a proper choice of the model order this estimator is minimax optimal in order these considerations lead also to a nonasymptotic upper bound on the mean squared error of the associated one step predictor a numerical study compares the common model selection procedures to the minimax optimal order choice 1 introduction the standard methods for estimating parameters of time series are based on the assumption that the observations come from an autoregressive ar moving average ma or mixed arma model of known orders this assumption can rarely be justified in practice and the less stringent assumption is that the time series data are observations from a linear stationary process a common approach to modeling linear stationary processes is based on an arapproximation in this framework a finite order armodel is fitted to the observations the order of the armodel should provide an optimal finite arapproximation to the process and it is usually chosen by selection procedures based on the data this nonparametric arapproach to modeling linear stationary processes has been investigated by shibata 1980 bhansali 1981 1986 an chen and hannan 1982 and hannan and kavalieris 1986 shibata 1980 considered the problem of predicting a gaussian infiniteorder arprocess by fitting a finite armodel the notion of optimality for the model selection procedure proposed by shibata 1980 is based on an asymptotic lower bound on the mean squared prediction error specifically the procedure is asymptotically efficient if it attains the lower bound asymptotically shibata 1980 also established that the final prediction error fpe akaike 1970 and the aic akaike 1974 criteria are asymptotically efficient in the above sense provided that the linear process does not degenerate to a finite order autoregression a similar result has been obtained

a modified hannan rissanen strategy for mixed autoregressive moving average order determination summary a modification to the model selection strategy for mixed autoregressive moving average order determination suggested by hannan rissanen 1982 is proposed the modification is designed to eliminate the bias discussed by hannan kavalieris 1984 and involves the use of an alternative model selection criterion asymptotic properties of the modified procedure are established and some simulation evidence on the finite sample performance is provided

almost sure convergence analysis of autoregressive spectral estimation in additive noise the almost sure convergence properties of autoregressive spectral estimates from noisy observations are derived sharp rates of almost sure convergence are established for the estimates of the autoregressive parameters innovation variance and spectral density function of the signal process the distributions of the signal and noise processes are arbitrary

brief papers linear identification of arma processes a new method for estimating the parameters of an arma process is presented the method consists of three linear least squares estimations in the first an autoregressive model is fitted to the observation sequence yielding an estimate of the values of the driving white noise sequence linear least squares is then used to fit an arma model to the observation and estimated white noise sequences this model is used to filter the observation and estimated white noise sequences finally an arma model is fitted to the filtered sequences it is shown that the resultant estimator is p consistent the asymptotic bias tends to zero as the degree p of the autoregressive model tends to infinity and is p efficient the asymptotic efficiency approaches the theoretical maximum as p tends to infinity

stable extensions of homeomorphisms on the pseudo arc we prove the following theorem if p is a proper subcontinuum of the pseudoarc p h is a homeomorphism from p onto itself and 0 is an open set in p that contains p then there is a homeomorphism h from p onto itself such that h p h and h x x for x 0 a pseudoarc can be characterized as a chainable hereditarily indecomposable continuum although the main result here extends a result of w lewis lw and answers in the affirmative a question he asked in that same paper stable homeomorphisms of the pseudoarc this paper was motivated by a conversation the author had with professor marcy barge who works in the area of topological dynamics professor barge is interested in knowing what sort of self homeomorphisms the pseudoarc admits and in particular what sort of homeomorphisms it admits with the property that some of the points of the space have periodic orbits that pseudoarcs admit many such homeomorphisms will follow from a much earlier result of g lehner lg and the result here it will also follow by combining the theorem proven here g lehner s theorem and a theorem in kj that any continuum with the property that all its proper nondegenerate subcontinua are pseudoarcs admits many such homeomorphisms examples of continua with this property include pseudocircles b pseudosolenoids f some examples due to t ingram i and h cook c as well as the pseudoarc itself we will prove the following theorem theorem if p is a proper nondegenerate subcontinuum of the pseudoarc p p c o an open set in p and h is a homeomorphism from p onto itself then h can be extended to a homeomorphism h of p onto itself such that h x x for x o a continuum is indecomposable if no proper subcontinuum of it has interior and it is hereditarily indecomposable if each subcontinuum is indecomposable a chain is a collection of sets c co cy cn such that ci f c3 0 if and only if i j 1 a continuum is chainable if it has open chain covers of arbitrarily small mesh as mentioned previously the pseudoarc p is a hereditarily indecomposable chainable continuum kb this continuum also has the fixed point property h received by the editors june 9 1987 this research was presented at the annual spring topology conference march 1 1987 university of alabama at birmingham this conference was supported by the nsf 1980 mathematics subject classification 1985 revision primary 54f20 54f50

brief identification of dynamic errors in variables models approaches based on two dimensional arma modeling of the data in this paper we propose a parametric and a non parametric identification algorithm for dynamic errors in variables model we show that the two dimensional process composed of the input output data admits a finite order arma representation the non parametric method uses the arma structure to compute a consistent estimate of the joint spectrum of the input and the output a frisch scheme is then employed to extract an estimate of the joint spectrum of the noise free input output data which in turn is used to estimate the transfer function of the system the parametric method exploits the arma structure to give estimates of the system parameters the performances of the algorithms are illustrated using the results obtained from a numerical simulation study

on generalized distance transformation of digitized pictures in this paper we present a generalization of the distance transformation of a digitized picture in two different aspects first we define the generalized distance transformation of a binary picture gdtb a subclass of gdtb called a local minimum filter family of gdtb lmf gdtb characterized by a series of local minimum filters with varying neighborhoods is discussed in detail a skeleton is defined for lmf gdtb and it is proved that any binary picture can be reconstructed exactly from its skeleton with the distance value on it second the gray weighted distance transformation gwdt is extended to a generalized gwdt ggwdt by introducing an arbitrary initial picture after the fundamental equation of ggwdt and its solution are derived it is proved that an arbitrary gray picture is generated by iterative application of ggwdt from a uniquely determined elementary picture and a sequence of initial value pictures

morphological filters part i their set theoretic analysis and relations to linear shift invariant filters this paper examines the set theoretic interpretation of morphological filters in the framework of mathematical morphology and introduces the representation of classical linear filters in terms of morphological correlations which involve supremum infimum operations and additions binary signals are classified as sets and multilevel signals as functions two set theoretic representations of signals are reviewed filters are classified as set processing sp or function processing fp conditions are provided for certain fp filters that pass binary signals to commute with signal thresholding because then they can be analyzed and implemented as sp filters the basic morphological operations of set erosion dilation opening and closing are related to minkowski set operations and are used to construct fp morphological filters emphasis is then given to analytically and geometrically quantifying the similarities and differences between morphological filtering of signals by sets and functions the latter case allows the definition of morphological convolutions and correlations toward this goal various properties of fp morphological filters are also examined linear shift invariant filters due to their translation invariance are uniquely characterized by their kernel which is a special collection of input signals increasing linear filters are represented as the supremum of erosions by their kernel functions if the filters are also discrete and have a finite extent impulse response they can be represented as the supremum of erosions only by their minimal with respect to a signal ordering kernel functions stable linear filters can be represented as the sum of at most two weighted suprema of erosions these results demonstrate the power of mathematical morphology as a unifying approach to both linear and nonlinear signal shaping strategies

a brouwer translation theorem for free homeomorphisms we prove a generalization of the brouwer translation theorem which applies to a class of homeomorphisms free homeomorphisms which admit fixed points but retain a dynamical property of fixed point free orientation preserving homeomorphsims that is if h m2 m2 is a free homeomorphism where m2 is a surface then whenever d is a disc and h d n d 0 we have that hn d n d 0 for all n 0 theorem let h be a free homeomorphism of s2 the two sphere with finite fixed point set f then each p e s2 f lies in the image of an embedding xp r2 o s2 f p such that i hxp xpf where er z z 1 is the canonical tranalation of the plane and ii the image of each vertical line under xp is closed in s2 f the class of free homeomorphisms has been introduced and studied by m brown in connection with the dynamics of surface homeomorphisms introduction l e j brouwer from 1909 to 1919 formulated and presented the brouwer plane translation theorem 2 6 9 10 in modern terminology it can be stated thusly theorem let h be a fixed point free orientation preserving self homeomorphism of r2 the plane then each p e r2 lies in the image of an embedding xp r2 0 r2 p such that i hxp xpor where or z z 1 is the canonical translation of the plane and ii the image of each vertical line under xp is closed in r2 in his first proof of this theorem 3 6 he assumed that a simple curve bounded only two domains later 7 he discovered the lakes of wada continuum and realized the error in his proof the second proof 9 utilized the brouwer translation arc lemma which was proved using the no retraction theorem 8 and the concept of index of a fixed point however this proof contained serious gaps since 1920 a succession of authors 1 13 16 17 18 have presented proofs of this theorem each either correcting errors in the previous proof or embarking upon a simplification for the proof for a more thorough discussion of this problem the reader should consult 11 which presents the history of brouwer s work and 16 for the history of the plane translation theorem received by the editors august 18 1986 1980 mathematics subject classification 1985 revision primary 54h20 secondary 58f99

chaos periodicity and snakelike continua the results of this paper relate the dynamics of a continuous map f of the interval and the topology of the inverse limit space with bonding map f these inverse limit spaces have been studied by many authors and are examples of what bing has called snakelike continua roughly speaking we show that when the dynamics of f are complicated the inverse limit space contains indecomposable subcontinua we also establish a partial converse

optimal instrumental variable estimates of the ar parameters of an arma process the modified yule walker myw equations for estimating the ar parameters of an arma process are presented as a special case of an instrumental variable iv method the consistency and accuracy of the ar parameter estimates are studied it is shown that estimation accuracy increases monotonically with the number of myw equations for an optimal choice of the weighting matrix used in the least squares solution of these equations the asymptotic error covariance of the optimal iv method equals that of the prediction error method the results of this paper verify experimental results reported in the literature regarding the performance of the myw method and provide the necessary accuracy analysis furthermore they suggest several simple asymptotically efficient multistep algorithms for estimating the ar parameters which are presented in a companion paper

an optimal instrumental variable method for arma spectral estimation a multistep iterative and fast recursive algorithm for autoregressive moving average arma spectral estimation is presented the ar parameters of an arma process are estimated using the extended instrumental variable eiv method the optimal choice of instruments prefilter and weighting matrix is investigated a bootstrapping procedure that has computational convenience is proposed for the algorithm the statistical analysis and experiments show that the optimal iv estimate is unbiased consistent efficient asymptotically normal and equivalent to the maximum likelihood ml estimate and the prediction error pe estimate and the proposed algorithm has the advantages of sharper resolution less frequency bias and better efficiency of convergence

adaptive stochastic filters with no strict positive real condition a new adaptive stochastic filter structure is introduced which avoids the strict passivity test used as a sufficient condition for convergence required by existing adaptive schemes the proposed algorithm consists of three stages in the first stage an autoregressive model is fitted and the residue obtained is used as an estimate of the noise in the second stage an autoregressive recursive moving average model is fitted using the residual of the first stage a modified residual is then filtered using a parameter and the model obtained from the second stage to generate an improved estimate of the noise in the third stage this improved estimate of the noise is used to obtain a better autoregressive moving average model it is shown that the proposed algorithm will also reduce the bias in the estimated parameters the simulation results given show that the proposed filter compares favorably to the algorithm introduced by mayne and clark and also landau this filter is then applied to the adaptive line enhancement sinusoidal detection and adaptive spectral estimation problems to illustrate its usefulness

determining a portfolio of linear time series models on applique les concepts de degre d evidence suggeres par jeffreys 1961 au probleme de la determination de l ordre dans des modeles de series temporelles lineaires

estimation of the interpolation error variance and an index of linear determinism summary the autoregressive and window estimators of the inverse variance ri 0 say are adopted for estimating the interpolation error variance ri o and an index of linear determinism a of a stationary process x the index a is defined as 1 r o ri 0 where r o denotes the variance of x a measures the proportion of total variance explained by the interpolator when interpolating x say from xs s t some uses of a and ri o are discussed the asymptotic distributions of the estimators are derived the order of consistency of the autoregressive and window estimators of a is different when a 0 than when 0 a 1 the finite sample behaviour of the estimators is examined by means of a simulation study

a covariance extension approach to identification of time series in this paper we consider a three step procedure for identification of time series based on covariance extension and model reduction and we present a complete analysis of its statistical convergence properties a partial covariance sequence is estimated from statistical data then a high order maximum entropy model is determined which is finally approximated by a lower order model by stochastically balanced model reduction such procedures have been studied before in various combinations but an overall convergence analysis comprising all three steps has been lacking supposing the data is generated from a true finite dimensional system which is minimum phase it is shown that the transfer function of the estimated system tends in h to the true transfer function as the data length tends to infinity if the covariance extension and the model reduction is done properly the proposed identification procedure and some variations of it are evaluated by simulations

estimation of the parameters of a random amplitude sinusoid by correlation fitting we consider the best asymptotic accuracy that can be achieved when estimating the parameters of a random amplitude sinusoid from its sample covariances an estimator based on matching in a weighted least squares sense the sample correlation sequence to the theoretical sequence is presented the asymptotic properties of the estimator are analyzed a lower bound on the estimation of the parameters from sample covariances is derived this bound is shown to be attainable by appropriately choosing the weighting matrix however the unweighted nonlinear least squares estimate performance is shown to come close to the lower bound the influence of the number of samples the number of correlation samples and the lowpass envelope characteristics are studied finally a comparison with yule walker yw methods is given

new method of order estimation for arma armax processes let the observation y k be generated by the multivariate arma process a z y k c z w k with unknown coefficients theta a theta c and orders p r where w k is a sequence of independent and identically distributed i i d random vectors with zero mean and unknown covariance matrix r w 0 a new method for estimating the orders p r is introduced in contrast to most of the existing results the new method is not based on optimizing a certain criterion and the order estimates given in the paper are rather easy to update computationally in comparison with the criterion optimization based methods when new data arrive the method is then extended to determining the orders of armax processes under reasonable conditions the estimates are proved to converge to the true orders with probability one as time tends to infinity

a transitive homeomorphism on the pseudoarc which is semiconjugate to the tent map a powerful theorem and construction of wayne lewis are used to build two homeomorphisms on the pseudoarc each of which is semiconjugate to the tent map on the unit interval the first homeomorphism is transitive thus answering a question of marcy barge as to whether such homeomorphisms exist the second homeomorphism admits wandering points also it is proven that any homeomorphism on the pseudoarc that is semiconjugate to the tent map and is irreducible with respect to the semiconjugacy must either be transitive or admit wandering points a continuum is a compact connected metric space a continuum x is indecomposable if every proper subcontinuum of x is nowhere dense in x and x is hereditarily indecomposable if each subcontinuum of x is indecomposable a continuum x is chainable if for each e 0 there is a chain c c0 cn of open sets of diameter less than e that covers x c is a chain means that ci n ej 0 iff ii ii 2 or in the hilbert cube are pseudoarcs here we will show that this continuum admits a transitive homeomorphism thus answering a question of marcy barge in addition this homeomorphism has the property that it is semiconjugate to the tent map on the unit interval for more information on pseudoarcs and indecomposable continua see bil bi4 l1 l2 k km kr and ot exotic continua have been making their appearance in dynamical systems ever since the early part of this century with the work of c caratheodory c received by the editors may 20 1988 and in revised form july 25 1989 presented at the 1988 spring topology conference university of florida gainesville florida 32611 1980 mathematics subject classification 1985 revision primary 54f20 secondary 54h20

arma spectral estimation of narrow band processes via model reduction the problem of estimating autoregressive moving average arma models for narrowband processes is considered the following approach is proposed estimate a high order autoregressive ar approximation of the process by model reduction based on a truncated internally balanced realization or optimal hankel norm model reduction reduce the order of this high order ar estimate to find a lower order arma model this algorithm gives arma spectral estimates with excellent resolution properties without using iterative numerical minimization methods as for the maximum likelihood method how to take the narrowband assumption into account in the model reduction step is discussed in detail

subspace estimation and prediction methods for hidden markov models hidden markov models hmms are probabilistic functions of finite markov chains or put in other words state space models with finite state space in this paper we examine subspace estimation methods for hmms whose output lies a finite set as well in particular we study the geometric structure arising from the nonminimality of the linear state space representation of hmms and consistency of a subspace algorithm arising from a certain factorization of the singular value decomposition of the estimated linear prediction matrix for this algorithm we show that the estimates of the transition and emission probability matrices are consistent up to a similarity transformation and that the m step linear predictor computed from the estimated system matrices is consistent i e converges to the true optimal linear m step predictor

a method for autoregressive moving average estimation summary the problem considered is that of estimating an autoregressive moving average system including estimating the degrees of the autoregressive and moving average lag operators the basic method is that introduced by hannan rissanen 1982 however that method may sometimes overestimate the degrees and modifications are here introduced to correct this the problem is itself due to the use of a long autoregression of order clog t when t is large in the first stage of the process the effect of this is investigated and in particular its effect on the speed of convergence of the estimates

optimal arma parameter estimation based on the sample covariances for data with missing observations the problem of spectral estimation through the autoregressive moving average arma modeling of stationary processes with missing observations is considered a class of estimators based on the sample covariances is presented and an asymptotically optimal estimator in this class is proposed the proposed algorithm is based on a nonlinear least squares fit of the sample covariances computed from the data to the true covariances of the assumed arma model the statistical properties of the algorithm are explored and used to show that it is asymptotically optimal in the sense of achieving the smallest possible asymptotic variance the performance of the algorithm is illustrated by some numerical examples

arma model order estimation based on the eigenvalues of the covariance matrix an approach to model order determination based on the minimum description length mdl criterion is proposed and shown to depend on the minimum eigenvalues of a covariance matrix derived from the observed data a selection procedure for estimating the model order by means of the mdl method is proposed examples are given to illustrate the significantly improved accuracy of the technique

information tradeoffs in using the sample autocorrelation function in arma parameter estimation this paper considers bounds on the statistical efficiency of estimators of the poles and zeros of an arma process based on estimates of the process autocorrelation function acf special attention is paid to autoregressive ar and ar plus white noise processes it is seen that reducing the arma process data to a given set of consecutive lags of the popular lagged product acf estimates prior to parameter estimation increases cramer rao bounds on the generalized error covariance a parametric study of the bound deterioration for some illustrative signal and noise situations reveals some empirical strategies for choosing acf estimate lags to preserve statistical information analysis is based on the relative information index rii 2 and derivations of the large sample fisher s information matrix for the raw data and for the lagged product acf estimate of an arma process are included

model reductions of high order estimated models the asymptotic ml approach abstract the reduction of order of high order models obtained from an identification experiment is discussed from a statistical point of view the asymptotic maximum likelihood ml approach is defined to reduce the order of an estimated model this approach considers the maximum likelihood criterion given the asymptotic statistics both in the number of data and the order of the estimated model and corresponds to frequency weighted l 2 norm model reduction by using the insight from the asymptotic ml approach an identification algorithm is proposed based on a high order arx estimate and model reduction via a frequency weighted balanced realization the advantage of this algorithm is that iterative minimization methods are not required to find the estimate

a criterion for selecting information preserving data reductions for use in the design of multiple parameter estimators corresp a scalar measure of the fractional amount of the total information for parameter estimation that is retained when a record of raw data is reduced to a given statistic is introduced this measure the relative information index rii is a function of fisher s information matrices for the statistic and for the raw data and it resembles an efficiency measure in that it acquires values between zero and one a criterion based on the rii is formulated for statistic selection and some applications are discussed

parametric identification using weighted null space fitting in identification of dynamical systems the prediction error method with a quadratic cost function provides asymptotically efficient estimates under gaussian noise but in general it requires solving a nonconvex optimization problem which may imply convergence to nonglobal minima an alternative class of methods uses a nonparametric model as intermediate step to obtain the model of interest weighted null space fitting wnsf belongs to this class starting with the estimate of a nonparametric arx model with least squares then the reduction to a parametric model is a multistep procedure where each step consists of the solution of a quadratic optimization problem which can be obtained with weighted least squares the method is suitable for both open and closed loop data and can be applied to many common parametric model structures including output error armax and box jenkins the price to pay is the increase of dimensionality in the nonparametric model which needs to tend to infinity as function of the sample size for certain asymptotic statistical properties to hold in this paper we conduct a rigorous analysis of these properties namely consistency and asymptotic efficiency also we perform a simulation study illustrating the performance of wnsf and identify scenarios where it can be particularly advantageous compared with state of the art methods

an efficient linear method for arma spectral estimation a three step method for obtaining asymptotically maximum likelihood arma spectral estimates using only linear transformations of the data is presented the computational efficiency of the algorithm is comparable to that of yule walker algorithms but the three step method gives asymptotically statistically efficient estimates the implementation of the algorithm is discussed in detail and numerical examples are presented to illustrate its performance

a width independent fast thinning algorithm the skeleton of a digital figure can often be regarded as a convenient alternative to the figure itself it is useful both to diminish drastically the amount of data to be handled and to simplify the computational procedures required for description and classification purposes thinning a digital figure down to its skeleton is a time consuming process when conventional sequential computers are employed the procedure we propose allows one to speed up the thinning transformation and to get a well shaped skeleton after cleaning of the input picture has been performed the pixels of the figure are labeled according to their distance from the background and a set whose pixels are symmetrically placed with respect to distinct contour parts of the figure is found this set is then given a linear structure by applying topology preserving removal operations finally a pruning step regarding branches not relevant in the framework of the problem domain completes the process the resulting skeleton is a labeled set of pixels which is shown to possess all the required properties particularly those concerning connectedness topology and shape moreover the original figure can almost completely be recovered by means of a reverse distance transformation only a fixed and small number of sequential passes through the picture is necessary to achieve the goal the computational effort is rather modest and the use of the proposed algorithm turns out to be more advantageous the greater the width of the figure to be thinned

performance evaluation of the modified yule walker estimator the modified yule walker myw equations are often used to estimate the autoregressive parameters of time series the asymptotic estimation error variance of these parameters can be computed using a formula developed for the instrumental variable method the performance of the myw estimator is studied by evaluating this formula for different signal to noise ratios and process bandwidths as a function of the number of equations used by the estimator the cramer rao lower bound for the estimation error variance is computed for comparison the optimally weighted myw estimator is briefly discussed

three dimensional structural texture modeling and segmentation the structural approach one of the various modeling techniques in texture analysis perceives texture as a region composed of detectable primitive elements tokens in this paper we extend this concept to three dimensional 3d image and develop a segmentation scheme based on clustering of 3d texture tokens 3d structural texture is composed of texture tokens which are modeled as tiny objects embedded inside image sequence texture tokens located spatially close to one another and having similar shape are grouped into homogenous texture volume some of the texture tokens may be in contact with one another to form clump like structures our approach first disconnects these clumps by a 3d clump decomposition process a 3d irregular pyramid construction process is then carried out on these isolated 3d tokens the process inputs a delaunay graph with each vertex representing the shape feature vector of a texture token and each edge representing the neighborhood relationship of two texture tokens through stepwise grouping of similar shape tokens a segmentation of the texture volume is obtained

technical communique linear estimation of arma processes the method of estimating arma parameters first discussed by mayne and firoozan is investigated it is shown that if at the first stage the order of the fitted autoregression is allowed to depend on the number of time points in a reasonable manner then it will still be true that the final estimate of the parameter vector will converge almost surely to the true value this is to be compared to the result in the original paper where the order is fixed and it is shown that as the sample size increases the estimate converges to a value which if the order of the autoregression is high enough will be arbitrarily near to the true value some comments are made on other extensions on the law of the iterated logarithm on the central limit theorem and on the choice of the order of the fitted autoregression the innovation sequence need not be gaussian and for the convergence result only a natural condition relating to prediction needs be imposed

bounds on the accuracy of gaussian arma parameter estimation methods based on sample covariances the asymptotic accuracy of gaussian arma parameter estimation methods based on a fixed number of sample covariances is considered several key results are briefly reviewed including i a general asymptotic expression for the error covariance of the arma parameter estimates ii the fact that this error covariance is always greater than a certain lower bound iii the fact that this lower bound is strictly greater than the cramer rao bound iv an explicit arma estimation technique that asymptotically achieves the bound the key result of this note is a proof that this lower bound approaches the cramer rao bound as the number of sample covariances tends to infinity

nonparametric estimation of transfer functions rates of convergence and adaptation the paper deals with estimating the transfer functions of stable linear time invariant systems under stochastic assumptions we adopt a nonparametric minimax approach for measuring the estimation accuracy the quality of an estimator is measured by its worst case error over a family of transfer functions the families with polynomially and exponentially decaying impulse response sequences are considered we establish nonasymptotic upper bounds on the accuracy of the least squares estimator for finite impulse response approximation it is shown that the attainable estimation accuracy is determined essentially by the rate at which the true impulse response tends to zero lower bounds on the estimation accuracy are presented an adaptive estimator which does not exploit any a priori information about the true system is developed

new fusion operations for digitized binary images and their applications this paper proposes a new class of fusion operations which are useful for binary image processing to begin with an algorithm for the classical fusion operations is presented they are sequentially composed of two basic operations that is expansion and contraction the strategy of the proposed algorithm is as follows the first operation is performed with the distance transformation and the second operation utilizes the distance information obtained in the first operation next a topological contraction and a topological expansion are defined the topological contraction preserves the euler number of an input image except that some simply connected components of 1 pixels are erased the topological expansion preserves the euler number of an input image except that some simply connected holes are filled then several new fusion operations are obtained by combining the classical contraction and the topological expansion or the classical expansion and the topological contraction sequentially the algorithms for them use the same strategy as the proposed algorithm for the classical fusion operations finally experimental results show that the new fusion operations and their combinations are effectively used in the binary image processing such as shape smoothing merging and separating connected components and structure analysis

some sequential algorithms for a generalized distance transformation based on minkowski operations a generalized distance transformation gdt of binary images and the related medial axis transformation mat are discussed these transformations are defined in a discrete space of arbitrary dimension and arbitrary grids the gdt is based on successive morphological operations using alternatively n arbitrary structuring elements n is called the period of the gdt the gdt differs from the classical distance transformations based on a point to point distance however the well known chessboard city block and hexagonal distance transformations are special cases of the one period gdt whereas the octagonal distance transformation is a special case of the two period gdt in this paper both one and two period gdts are discussed different sequential algorithms are proposed for computing such gdts these algorithms need a maximum of two scannings of the image the computation of the mat is also discussed

paper a new algorithm for recursive estimation of parameters in controlled arma processes a recursive algorithm for estimating the constant but unknown parameters of a controlled arma process is presented the algorithm is a recursive version of an off line algorithm using three stages of standard least squares in the first stage the parameters of a controlled ar model of degree p are estimated the residuals used in this stage are employed in the second stage to estimate the parameters of a controlled arma process the first two stages constitute a recursive version of durbin s algorithm the model obtained in the second stage is used to filter the input output and residuals and these filtered variables are used in the final stage to obtain improved estimates of the controlled arma process it is shown that the estimate is globally p consistent i e that the estimate converges a s as the number of data tends to infinity to a vector which in turn converges to the true parameter vector as the degree p of the ar model tends to infinity

recursive estimation of mixed autoregressive moving average order summary the order p q of an autoregressive moving average sequence y t may be estimated by minimizing a criterion log 2 p q log t t with respect to p and q where 2 is the maximum likelihood estimate of the variance of the innovations t it is suggested that instead a2 be estimated from a series of regressions of y t on y t 1 y t 2 y t p 5 t 1 t q where the t are obtained by fitting a long autoregression to the data it is shown how the sequence of regressions may for p q be economically recursively calculated by embedding them in a sequence of bivariate autoregressions asymptotic properties of the procedure are established under very general conditions

strongly consistent online forecasting of centered gaussian processes an estimator e spl circ d sub n n of the conditional expectation e x sub n 1 x sub n x n d sub n 1 in a centered stationary and ergodic gaussian process x sub i sub i with absolutely summable wold coefficients is constructed on the basis of having observed x sub 1 x sub n for a suitable choice of the length dn spl rarr spl infin n spl rarr spl infin of the past covered by the conditional expectation it is established that e spl circ d sub n n e x sub n 1 x sub n x n d sub n 1 spl rarr 0 with probability 1 in addition sufficient conditions for e x sub n 1 x sub n x sub n 1 e x sub n 1 x sub n x n d sub n 1 spl rarr 0 to hold with probability 1 are given that is conditions under which e spl circ d sub n n can be used as a strongly consistent forecaster for e x sub n 1 x sub n x sub n 1

on the conjecture of wood and projective homogeneity abstract in 2005 kawamura and rambla independently constructed a metric counterexample to wood s conjecture from 1982 we exhibit a new nonmetric counterexample of a space l such that c 0 l c is almost transitive and show that it is distinct from a nonmetric space whose existence follows from the work of greim and rajagopalan in 1997 up to our knowledge this is only the third known counterexample to wood s conjecture we also show that contrary to what was expected if a one point compactification of a space x is r h bing s pseudo circle then c 0 x c is not almost transitive for a generic choice of points finally we point out close relation of these results on wood s conjecture to a work of irwin and solecki on projective fraisse limits and projective homogeneity of the pseudo arc and addressing their conjecture we show that the pseudo circle is not approximately projectively homogeneous

approximate maximum likelihood frequency estimation the high resolution frequency estimators most commonly used such as music esprit and yule walker determine estimates of the sinusoidal frequencies from the sample covariances of noise corrupted data in this paper a frequency estimation method termed approximate maximum likelihood aml is derived from the approximate likelihood function of sample covariances the statistical performance of aml is studied both analytically and numerically and compared with the cramer rao bound as well as the statistical performance corresponding to the aforementioned methods of frequency estimation aml is shown to provide the minimum asymptotic error variance in the class of all estimators based on a given set of covariances the implementation of the aml frequency estimator is discussed in detail the paper also introduces an aml based procedure for estimating the number of sinusoidal signals in the measured data which is shown to possess high detection performance

a method for adaptive estimation of arma processes abstract when the noise process in adaptive identification of linear stochastic systems is correlated and can be represented by a moving average model extended least squares algorithms are commonly used and converge under a strictly positive real spr condition on the noise model in this paper we present an adaptive algorithm for the estimation of autoregressive moving average arma processes and show that it is convergent without any spr condition and has a convergence rate of o loglog t t 1 2

a fast estimation method for arma processes an improvement of a batch algorithm for parameter estimation of an arma process is presented a fast and iterative algorithm is presented and provides estimates with the same asymptotic distribution as the maximum likelihood estimates this algorithm is a modified version of the method suggested by mayne and firoozan 1982 linear identification of arma processes automatica 18 461 466 and requires one less regression than the previous method if only one pass is executed

a new order estimation technique for time series modeling a new approach to estimating the order of the autoregressive moving average model is proposed which is based on the approximate stochastic realization introduced in davis and fotopoulos 1991 the present approach is attractive because overparameterization a very common problem in order determination is avoided successfully simulation results are included to illustrate the effectiveness of the proposed order estimation approach