asymptotic properties of high order yule walker estimates of the ar parameters of an arma time series the high order yule walker equations are used to estimate the autoregressive parameters of an autoregressive moving average time series the asymptotic statistical properties of these estimates are derived it is shown that they are asymptotically unbiased and normal the covariance matrix of the limit distribution is derived the special case of estimating the autoregressive parameters of a noise corrupted autoregressive series is also examined

obtaining planarity by contracting few edges the planar contraction problem is to test whether a given graph can be made planar by using at most k edge contractions this problem is known to be np complete we show that it is fixed parameter tractable when parameterized by k

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

computer vision for robust 3d aircraft recognition with fast library search abstract a fast but accurate classification method is presented which takes the fundamental problems of aircraft recognition in 3d space into consideration elliptic fourier descriptors are used for aircraft classification and pose determination from a two dimensional image recorded at an arbitrary viewing angle the computation model of the nearest neighbor classification rule or simply nnr is analysed to come up with proper necessary conditions used by our method for reducing the set of near neighbors of a test projection for a fast partial library search on the other hand our method is robust to noise by incorporating a perturbation analysis of feature variation into the classifier design both graphics generated data and real data of five aircraft have been used to demonstrate the applicability of the new method the results indicate that the method is almost as accurate as the nnr method but is much faster the method is also shown to outperform other existing classification methods including the decision tree classification method

obtaining split graphs by edge contraction we study the parameterized complexity of the following split contraction problem given a graph g and an integer k as parameter determine whether g can be modified into a split graph by contracting at most k edges we show that split contraction can be solved in fpt time 2 o k 2 n 5 but admits no polynomial kernel unless np conp poly

stochastic models for closed boundary analysis representation and reconstruction the analysis of closed boundaries of arbitrary shapes on a plane is discussed specifically the problems of representation and reconstruction are considered a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers is set up univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary the stochastic model representing the closed boundary is invariant to transformations like sealing translation choice of starting point and rotation over angles that are multiples of 2 pi n where n is the number of observations methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate number of coefficients is included constraints on the estimates are derived so that the estimates are invariant to the transformations of the boundaries the stochastic model enables the reconstruction of a dosed boundary using fft algorithms results of simulations are included and the application to contour coding is discussed

signal plus noise models in shape classification abstract in this study we show how a signal plus noise formulation can be used to improve the performance of auto regressive shape classifiers in environments with time varying noise characteristics variations of this type may be due to changes in atmospheric conditions or the relative effect of discretization errors this approach is compared to existing methodologies using a number of noisy templates in a cluttered environment typical applications are to aircraft identification and automatic signature validation

fish species recognition by shape analysis of images abstract size and species grading of fish e g on board a fishing boat might in future be done entirely automatically using image analysis this has been investigated by creating a data bank of shapes from photographs of seven different types of fish on a computer three methods of discriminating between the different species of fish are compared and these are invariant moments optimisation of the mismatch and shape descriptors each approach was evaluated using discriminant analysis the methods sorted the fish with a reliability of 73 63 and 90 respectively further work is required to make a commercial grading system feasible

increasing the minimum degree of a graph by contractions abstract the degree contractibility problem is to test whether a given graph g can be modified to a graph of minimum degree at least d by using at most k contractions we prove the following three results first degree contractibility is np complete even when d 14 second it is fixed parameter tractable when parameterized by k and d third it is w 1 hard when parameterized by k we also study its variant where the input graph is weighted i e has some edge weighting and the contractions preserve these weights the weighted degree contractibility problem is to test if a weighted graph g can be contracted to a weighted graph of minimum weighted degree at least d by using at most k weighted contractions we show that this problem is np complete and that it is fixed parameter tractable when parameterized by k in addition we pinpoint a relationship with the problem of finding a minimal edge cut of maximum size in a graph and study the parameterized complexity of this problem and its variants

shape reconstruction on a varying mesh a central class of image understanding problems is concerned with reconstructing a shape from an incomplete data set such as fitting a surface to partially given contours a new theory for solving such problems is presented unlike the current heuristic methods the method used starts from fundamental principles that should be followed by any reconstruction method regardless of its mathematical or physical implementation a mathematical procedure which conforms to these principles is presented one major advantage of the method is the ability to handle shapes containing both smooth and sharp parts without using thresholds a sharp variation such as a corner requires a high resolution mesh for adequate representation while slowly varying sections can be represented with sparser mesh points unlike current methods this procedure fits the surface on a varying mesh the mesh is constructed automatically to be more dense at parts of the image that have more rapid variation analytical examples are given in simple cases followed by numerical experiments

on the parameterized complexity of multiple interval graph problems multiple interval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it many applications of interval graphs also generalize to multiple interval graphs often allowing for more robustness in the modeling of the specific application with this motivation in mind a recent systematic study of optimization problems in multiple interval graphs was initiated in this sequel we study multiple interval graph problems from the perspective of parameterized complexity the problems under consideration are k independent set k dominating set and k clique which are all known to be w 1 hard for general graphs and np complete for multiple interval graphs we prove that k clique is in fpt while k independent set and k dominating set are both w 1 hard we also prove that k independent dominating set a hybrid of the two above problems is also w 1 hard our hardness results hold even when each vertex is associated with at most two intervals and all intervals have unit length furthermore as an interesting byproduct of our hardness results we develop a useful technique for showing w 1 hardness via a reduction from the k multicolored clique problem a variant of k clique we believe this technique has interest in its own right as it should help in simplifying w 1 hardness results which are notoriously hard to construct and technically tedious

a linear time algorithm for finding tree decompositions of small treewidth in this paper we give for constant k a linear time algorithm that given a graph g v e determines whether the treewidth of g is at most k and if so finds a tree decomposition of g with treewidth at most k a consequence is that every minor closed class of graphs that does not contain all planar graphs has a linear time recognition algorithm another consequence is that a similar result holds when we look instead for path decompositions with pathwidth at most some constant k

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

vector measure maurey rosenthal type factorizations and l sums of l1 spaces consider a vector measure of bounded variation m with values in a banach space and an operator t x l 1 m where l 1 m is the space of integrable functions with respect to m we characterize when t can be factorized through the space l 2 m by means of a multiplication operator given by a function of l 2 m where m is the variation of m extending in this way the maurey rosenthal theorem we use this result to obtain information about the structure of the space l 1 m when m is a sequential vector measure in this case the space l 1 m is an sum of l 1 spaces

shape description by time series time series modeling techniques are adapted to represent or describe two dimensional closed contours both linear and nonlinear models are fitted it is found that to detect small changes in shape nonlinear modeling is necessary even though linear models may be sufficient to differentiate between shapes which differ widely a nonlinear model called the noncausal quadratic volterra model is developed for the purpose implementation is illustrated with shapes of aircraft

a bivariate autoregressive technique for analysis and classification of planar shapes a bivariate autoregressive model is introduced for the analysis and classification of closed planar shapes the boundary coordinate sequence of a digitized binary image is sampled to produce a polygonal approximation to an object s shape this circular sample sequence is then represented by a vector autoregressive difference equation which models the individual cartesian coordinate sequences as well as coordinate interdependencies several classification features which are functions or transformations of the estimated coefficient matrices and the associated residual error covariance matrices are developed these features are shown to be invariant to object transformations such as translation rotation and scaling laboratory experiments involving object sets representative of industrial shapes are presented superior classification results are demonstrated

auto regressive shape classifiers in time varying noise abstract good results have been reported in a number of recent studies where auto regressive shape classifiers have been used to allocate objects to a pre determined number of classes it is shown that this approach may give unsatisfactory results when applied to imaging systems whose noise characteristics vary substantially over time such variation may be due to changes in atmospheric conditions or the relative effect of discretization errors observations are based on the reconstruction of a number of noisy synthetic templates

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

autoregressive spectral estimation in additive noise the estimation of the spectral density of a discrete time stationary gaussian autoregressive process ar p from a finite set of noise observations is considered a modified spectral estimator based on the high order yule walker equations is considered joint asymptotic normality of this spectral estimator is established a precise asymptotic expression for the covariance matrix of the limiting distribution is obtained the special case of ar 1 plus noise is considered in some detail

spaces of integrable functions with respect to a vector measure and factorizations through lp and hilbert spaces we use the integration structure of the spaces of scalar integrable functions with respect to a vector measure to provide factorization theorems for operators between banach function spaces through hilbert spaces a broad class of banach function spaces can be represented as spaces of scalar integrable functions with respect to a vector measure but this representation the vector measure is not unique since our factorization depends on the vector measure that is used for the representation we also give a characterization of those vector measures whose corresponding spaces of integrable functions coincide

complex autoregressive model for shape recognition a complex autoregressive model for invariant feature extraction to recognize arbitrary shapes on a plane is presented a fast algorithm to calculate complex autoregressive coefficients and complex parcor coefficients of the model is also shown the coefficients are invariant to rotation around the origin and to choice of the starting point in tracing a boundary it is possible to make them invariant to scale and translation experimental results that the complicated shapes like nonconvex boundaries can be recognized in high accuracy even in the low order model it is seen that the complex parcor coefficients tend to provide more accurate classification than the complex ar coefficients