rotation and gray scale transform invariant texture identification using wavelet decomposition and hidden markov model in this correspondence we have presented a rotation and gray scale transform invariant texture recognition scheme using the combination of quadrature mirror filter qmf bank and hidden markov model hmm in the first stage the qmf bank is used as the wavelet transform to decompose the texture image into subbands the gray scale transform invariant features derived from the statistics based on first order distribution of gray levels are then extracted from each subband image in the second stage the sequence of subbands is modeled as a hidden markov model hmm and one hmm is designed for each class of textures the hmm is used to exploit the dependence among these subbands and is able to capture the trend of changes caused by rotation during recognition the unknown texture is matched against all the models the best matched model identifies the texture class up to 93 33 classification accuracy is reported

classification of noisy signals using fuzzy artmap neural networks this paper describes an approach to classification of noisy signals using a technique based on the fuzzy artmap neural network famnn the proposed method is a modification of the testing phase of the fuzzy artmap that exhibits superior generalization performance compared to the generalization performance of the standard fuzzy artmap in the presence of noise an application to textured gray scale image segmentation is presented the superiority of the proposed modification over the standard fuzzy artmap is established by a number of experiments using various texture sets feature vectors and noise types the texture sets include various aerial photos and also samples obtained from the brodatz album furthermore the classification performance of the standard and the modified fuzzy artmap is compared for different network sizes classification results that illustrate the performance of the modified algorithm and the famnn are presented

cylindrical cellular automata a one dimensional cellular automaton with periodic boundary conditions may be viewed as a lattice of sites on a cylinder evolving according to a local interaction rule a technique is described for finding analytically the set of attractors for such an automaton given any one dimensional automaton rule a matrixa is defined such that the number of fixed points on an arbitrary cylinder size is given by the trace ofa n where the powern depends linearly on the cylinder size more generally the number of strings of arbitrary length that appear in limit cycles of any fixed period is found as the solution of a linear recurrence relation derived from the characteristic equation of an associated matrix the technique thus makes it possible for any rule to compute the number of limit cycles of any period on any cylinder size to illustrate the technique closed form expressions are provided for the complete attractor structure of all two neighbor rules the analysis of attractors also identifies shifts as a basic mechanism underlying periodic behavior every limit cycle can be equivalently defined as a set of strings on which the action of the rule is a shift of sizes h i e each string cyclically shifts bys sites inh iterations of the rule the study of shifts provides detailed information on the structure and number of limit cycles for one dimensional automata

geodesic active regions and level set methods for supervised texture segmentation this paper presents a novel variational framework to deal with frame partition problems in computer vision this framework exploits boundary and region based segmentation modules under a curve based optimization objective function the task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework the textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters and analyzing their responses as multi component conditional probability density functions the texture segmentation is obtained by unifying region and boundary based information as an improved geodesic active contour model the defined objective function is minimized using a gradient descent method where a level set approach is used to implement the obtained pde according to this pde the curve propagation towards the final solution is guided by boundary and region based segmentation forces and is constrained by a regularity force the level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled the performance of our method is demonstrated on a variety of synthetic and real textured frames

statistical principles in image modeling images of natural scenes contain a rich variety of visual patterns to learn and recognize these patterns from natural images it is necessary to construct statistical models for these patterns in this review article we describe three statistical principles for modeling image patterns the sparse coding principle the minimax entropy principle and the meaningful alignment principle we explain these three principles and their relationships in the context of modeling images as compositions of gabor wavelets these three principles correspond to three regimes of composition patterns of gabor wavelets and these three regimes are connected by changes in scale or resolution

structure texture image decomposition modeling algorithms and parameter selection this paper explores various aspects of the image decomposition problem using modern variational techniques we aim at splitting an original image f into two components u and where u holds the geometrical information and holds the textural information the focus of this paper is to study different energy terms and functional spaces that suit various types of textures our modeling uses the total variation energy for extracting the structural part and one of four of the following norms for the textural part l2 g l1 and a new tunable norm suggested here for the first time based on gabor functions apart from the broad perspective and our suggestions when each model should be used the paper contains three specific novelties first we show that the correlation graph between u and may serve as an efficient tool to select the splitting parameter second we propose a new fast algorithm to solve the tv l1 minimization problem and third we introduce the theory and design tools for the tv gabor model

a quick method for estimation of parameters of individual pulses in a multipath signal abstract consider a multipath signal whose individual signals are deterministic known increasing or decreasing pulses the problem is to estimate the amplitudes and delay times of individual signals several methods have been devoted to the solution of these unknown parameters the maximum likelihood ml estimation and the estimate maximize em algorithm are commonly used but they are computationally intensive and still insufficient to obtain accurate estimations the method can provide a quick and accurate estimate of the amplitudes and arrival delay times even in the closely spaced multipaths and heavy noise

optimal gabor filters for texture segmentation texture segmentation involves subdividing an image into differently textured regions many texture segmentation schemes are based on a filter bank model where the filters called gabor filters are derived from gabor elementary functions the goal is to transform texture differences into detectable filter output discontinuities at texture boundaries by locating these discontinuities one can segment the image into differently textured regions distinct discontinuities occur however only if the gabor filter parameters are suitably chosen some previous analysis has shown how to design filters for discriminating simple textures designing filters for more general natural textures though has largely been done ad hoc we have devised a more rigorously based method for designing gabor filters it assumes that an image contains two different textures and that prototype samples of the textures are given a priori we argue that gabor filter outputs can be modeled as rician random variables often approximated well as gaussian rv s and develop a decision theoretic algorithm for selecting optimal filter parameters to improve segmentations for difficult texture pairs we also propose a multiple filter segmentation scheme motivated by the rician model experimental results indicate that our method is superior to previous methods in providing useful gabor filters for a wide range of texture pairs

partial differential equation based approach for empirical mode decomposition application on image analysis the major problem with the empirical mode decomposition emd algorithm is its lack of a theoretical framework so it is difficult to characterize and evaluate this approach in this paper we propose in the 2 d case the use of an alternative implementation to the algorithmic definition of the so called sifting process used in the original huang s emd method this approach especially based on partial differential equations pdes was presented by niang in previous works in 2005 and 2007 and relies on a nonlinear diffusion based filtering process to solve the mean envelope estimation problem in the 1 d case the efficiency of the pde based method compared to the original emd algorithmic version was also illustrated in a recent paper recently several 2 d extensions of the emd method have been proposed despite some effort 2 d versions for emd appear poorly performing and are very time consuming so in this paper an extension to the 2 d space of the pde based approach is extensively described this approach has been applied in cases of both signal and image decomposition the obtained results confirm the usefulness of the new pde based sifting process for the decomposition of various kinds of data some results have been provided in the case of image decomposition the effectiveness of the approach encourages its use in a number of signal and image applications such as denoising detrending or texture analysis

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

an incomplete data approach to the analysis of covariance structures in this paper linear structural equation models with latent variables are considered it is shown how many common models arise from incomplete observation of a relatively simple system subclasses of models with conditional independence interpretations are also discussed using an incomplete data point of view the relationships between the incomplete and complete data likelihoods assuming normality are highlighted for computing maximum likelihood estimates the em algorithm and alternatives are surveyed for the alternative algorithms simplified expressions for computing function values and derivatives are given likelihood ratio tests based on complete and incomplete data are related and an example on using their relationship to improve the fit of a model is given

automatic surface inspection using wavelet reconstruction abstract in this paper we present a multiresolution approach for the inspection of local defects embedded in homogeneous textured surfaces the proposed method does not rely on the extraction of local textural features in a pixel by pixel basis it is based on an efficient image restoration scheme using the wavelet transforms by properly selecting the smooth subimage or the combination of detail subimages in different decomposition levels for backward wavelet transform the reconstructed image will remove regular repetitive texture patterns and enhance only local anomalies then a simple thresholding can be used to discriminate between defective regions and homogeneous regions in the reconstructed image this converts the difficult defect detection in complicated textured images into a simple binary thresholding in nontextured images effects of different wavelet bases the number of multiresolution levels the decomposed subimages used for reconstruction and the change in image rotation on defect detection are thoroughly evaluated and discussed based on the experiment on a variety of real textures including machined surfaces natural wood textile fabrics sandpaper and leather

double precision errors in the logistic map statistical study and dynamical interpretation the nature of the round off errors that occur in the usual double precision computation of the logistic map is studied in detail different iterative regimes from the whole panoply of behaviors exhibited in the bifurcation diagram are examined histograms of errors in trajectories given and for the case of fully developed chaos an explicit formula is found it is shown that the statistics of the largest double precision error as a function of the map parameter is characterized by jumps whose location is determined by certain boundary crossings in the bifurcation diagram both jumps and locations seem to present geometric convergence characterized by the two first feigenbaum constants eventually a comparison with benford s law for the distribution of the leading digit of compilation of numbers is discussed

global properties of cellular automata cellular automata are discrete mathematical systems that generate diverse often complicated behavior using simple deterministic rules analysis of the local structure of these rules makes possible a description of the global properties of the associated automata a class of cellular automata that generate infinitely many aperiodic temporal sequences is defined as is the set of rules for which inverses exist necessary and sufficient conditions are derived characterizing the classes of nearest neighbor rules for which arbitrary finite initial conditions i evolve to a homogeneous state ii generate at least one constant temporal sequence

basin of attraction of cycles of discretizations of dynamical systems with srb invariant measures computer simulations of dynamical systems arediscretizations where the finite space of machine arithmetic replaces continuum state spaces so any trajectory of a discretized dynamical system is eventually periodic consequently the dynamics of such computations are essentially determined by the cycles of the discretized map this paper examines the statistical properties of the event that two trajectories generate the same cycle under the assumption that the original system has a sinai ruelle bowen invariant measure the statistics of the computed mapping are shown to be very close to those generated by a class of random graphs theoretical properties of this model successfully predict the outcome of computational experiments with the implemented dynamical systems

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

collapsing effects in numerical simulation of a class of chaotic dynamical systems and random mappings with a single attracting centre computer simulations of dynamical systems contain discretizations where finite machine arithmetic replaces continuum state spaces in some circumstances complicated theoretical behaviour has a tendency to collapse to trivial and degenerate behaviour as a result of discretizations characteristics of such collapsing effects often seem to depend on the corresponding discretization only in a random way we describe a procedure to construct a stochastic process with similar statistical characteristics results of computer modelling are discussed

texture segmentation using 2 d gabor elementary functions many texture segmentation schemes use an elaborate bank of filters to decompose a textured image into a joint space spatial frequency representation although these schemes show promise and although some analytical work has been done the relationship between texture differences and the filter configurations required to distinguish them remain largely unknown this paper examines the issue of designing individual filters using a 2 d texture model we show analytically that applying a properly configured bandpass filter to a textured image produces distinct output discontinuities at texture boundaries the analysis is based on gabor elementary functions but it is the bandpass nature of the filter that is essential depending on the type of texture difference these discontinuities form one of four characteristic signatures a step ridge valley or a step change in average local output variation accompanying experimental evidence indicates that these signatures are useful for segmenting an image the analysis indicates those texture characteristics that are responsible for each signature type detailed criteria are provided for designing filters that can produce quality output signatures we also illustrate occasions when asymmetric filters are beneficial an issue not previously addressed

a bayesian analysis for change point problems a sequence of observations undergoes sudden changes at unknown times we model the process by supposing that there is an underlying sequence of parameters partitioned into contiguous blocks of equal parameter values the beginning of each block is said to be a change point observations are then assumed to be independent in different blocks given the sequence of parameters in a bayesian analysis it is necessary to give probability distributions to both the change points and the parameters we use product partition models barry and hartigan 1992 which assume that the probability of any partition is proportional to a product of prior cohesions one for each block in the partition and that given the blocks the parameters in different blocks have independent prior distributions given the observations a new product partition model holds with posterior cohesions for the blocks and new independent block posterior distributions for parameters the product model thus provides a convenient machinery for allo

localized measurement of emergent image frequencies by gabor wavelets the authors derive implement and demonstrate a computational approach for the measurement of emergent image frequencies measuring emergent signal frequencies requires spectral measurements accurate in both frequency and time or space conflicting requirements that are shown to be balanced by a generalized uncertainty relationship such spectral measurements can be obtained from the responses of multiple wavelet like channel filters that sample the signal spectrum and that yield a locus of possible solutions for each locally emergent frequency it is shown analytically that this locus of solutions is maximally localized in both space and frequency if the channel filters used are gabor wavelets a constrained solution is obtained by imposing a stabilizing term that develops naturally from the assumptions on the signal the measurement of frequencies is then cast as an ill posed extremum problem regularized by the stabilizing term leading to an iterative constraint propagation algorithm the technique is demonstrated by application to a variety of 2 d textured images

linear cellular automata and recurring sequences in finite fields a one dimensional linear cellular automaton with periodic boundary conditions consists of a lattice of sites on a cylinder evolving according to a linear local interaction rule limit cycles for such a system are studied as sets of strings on which the rule acts as a shift of sizes h i e each string in the limit cycle cyclically shifts bys sites inh iterations of the rule for any given rule the size of the shift varies with the cylinder sizen the analysis of shifts establishes an equivalence between the strings of values appearing in limit cycles for these automata and linear recurring sequences in finite fields specifically it is shown that a string appears in a limit cycle for a linear automaton rule on a cylinder sizen iff its values satisfy a linear recurrence relation defined by the shift value for thatn the rich body of results on recurring sequences and finite fields can then be used to obtain detailed information on periodic behavior for these systems topics considered here include the inverse problem of identifying the set of linear automata rules for which a given string appears in a limit cycle and the structure under operations such as addition and complementation of sets of limit cycle strings

mixed moments of random mappings and chaotic dynamical systems some statistical characteristics of completely random mappings and of random mappings with an absorbing or an attracting centre are calculated results are applied to validation of some phenomenological models of computer simulations of dynamical systems

segmentation of textured images based on fractals and image filtering this paper describes a new approach to the segmentation of textured gray scale images based on image pre ltering and fractal features traditionally lter bank decomposition methods consider the energy in each band as the textural feature a parameter that is highly dependent on image intensity in this paper we use fractal based features which depend more on textural characteristics and not intensity information to reduce the total number of features used in the segmentation the signi cance of each feature is examined using a test similar to the f test and less signi cant features are not used in the clustering process the commonly used k means algorithm is extended to an iterative k means by using a variable window size that preserves boundary details the number of clusters is estimated using an improved hierarchical approach that ignores information extracted around region boundaries 2001 pattern recognition society published by elsevier science ltd all rights reserved

effects of phase space discretization on the long time behavior of dynamical systems abstract we investigate the effects that roundoff errors have on discrete time dynamical systems computer generated orbits terminate in loops whose lengths scale with the machine precision in a universal way we present arguments to explain this fact

parameter estimation of superimposed signals using the em algorithm a computationally efficient algorithm for parameter estimation of superimposed signals based on the two step iterative em estimate and maximize with an e step and an m step algorithm is developed the idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately the algorithm iterates back and forth using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates the application of the algorithm to the multipath time delay and multiple source location estimation problems is considered

collapsing of chaos in one dimensional maps in their numerical investigation of the family of one dimensional maps f x d 1 2jxj where 2 diamond et al p diamond et al physica d 86 1999 559 571 have observed the surprising numerical phenomenon that a large fraction of initial conditions chosen at random eventually wind up at 1 a repelling fixed point this is a numerical artifact because the continuous maps are chaotic and almost every true trajectory can be shown to be dense in 1 1 the goal of this paper is to extend and resolve this obvious contradiction we model the numerical simulation with a randomly selected map while they used 27 bit precision in computing f we prove for our model that this numerical artifact persists for an arbitrary high numerical prevision the fraction of initial points eventually winding up at 1 remains bounded away from 0 for every numerical precision 2000 elsevier science b v all rights reserved

multipath time delay estimation using change point technique consider a multipath signal whose individual signals are deterministic known pulses our problem is to estimate the amplitudes and delay times of individual signals several methods have been devoted to solution of these unknown parameters the maximum likelihood estimation and the estimate maximize algorithm are commonly used but they are computationally intensive we consider the multipath signal as a changing linear model and use a change point technique to obtain a quick and accurate estimate of the amplitudes and arrival delay times we detect the pulse in a multipath signal which first arrives and then finish one by one in a sequence until no pulse appears therefore by using the change point procedure the number of individual pulses need not be known the results of a monte carlo simulation study with trapezoidal and sinusoidal pulses are presented to demonstrate a quick and accurate estimate of arrival times and amplitudes

efficient gabor filter design for texture segmentation gabor filters have been successfully applied to a broad range of image processing tasks the present paper considers the design of a single filter to segment a two texture image a new efficient algorithm for gabor filter design is presented along with methods for estimating filter output statistics the algorithm draws upon previous results that showed that the output of a gabor filtered texture is modeled well by a rician distribution a measure of the total output power is used to select the center frequency of the filter and is used to estimate the rician statistics of the gabor filtered image the method is further generalized to include the statistics of postfiltered outputs that are generated by a gaussian filtering operation following the gabor filter the new method typically requires an order of magnitude less computation to design a filter than a previously proposed method experimental results demonstrate the efficacy of the method

gabor filter based edge detection abstract it is common practice to utilize evidence from biological and psychological vision experiments to develop computational models for low level feature extraction the receptive profiles of simple cells in mammalian visual systems have been found to closely resemble gabor filters daugman proved that gabor filters achieve joint minimal joint uncertainty these results led researchers to develop computational models based on gabor filters for several low level vision applications such as edge detection texture classification optical flow estimation and data compression in this paper the performance of a gabor odd filter based edge detector is investigated using the measures proposed by canny based on this performance analysis a design criterion for one dimensional 1d gabor filter based edge detector is derived it is shown that this design criterion also holds good for a two dimensional 2d gabor filter based edge detector experimental results are presented to demonstrate the performance of the gabor filter based edge detector

interactive image segmentation via adaptive weighted distances an interactive algorithm for soft segmentation of natural images is presented in this paper the user first roughly scribbles different regions of interest and from them the whole image is automatically segmented this soft segmentation is obtained via fast linear complexity computation of weighted distances to the user provided scribbles the adaptive weights are obtained from a series of gabor filters and are automatically computed according to the ability of each single filter to discriminate between the selected regions of interest we present the underlying framework and examples showing the capability of the algorithm to segment diverse images

orthogonalizing em a design based least squares algorithm we introduce an efficient iterative algorithm intended for various least squares problems based on a design of experiments perspective the algorithm called orthogonalizing em oem works for ordinary least squares ols and can be easily extended to penalized least squares the main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework we establish several attractive theoretical properties concerning oem for the ols with a singular regression matrix an oem sequence converges to the moore penrose generalized inverse based least squares estimator for ordinary and penalized least squares with various penalties it converges to a point having grouping coherence for fully aliased regression matrices convergence and the convergence rate of the algorithm are examined finally we demonstrate that oem is highly efficient for large scale least squares and penalized least squares proble

boundary crossing probabilities and statistical applications abstract this paper surveys recent results involving boundary crossing probabilities and related statistical applications the first part is concerned with problems of sequential analysis especially repeated significance tests and their application to sequential clinical trials involving survival data the second part develops the probability theory motivated by the problems of part 1 a method for computing first passage distributions of brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries the third part is concerned with fixed sample statistical problems especially change point problems which involve boundary crossing probabilities examples are given of problems for which methods of part 2 appear adequate and of problems which require new methods

noisy integer maps abstract the combined effects of discretization and noise in iterated maps are studied with simulations and a transfer matrix technique the resulting changes in a typical map s invariant distribution are illustrated

nonparametric estimation of the distribution of time to onset for specific diseases in survival sacrifice experiments this paper concerns the analysis of an animal survival sacrifice experiment designed to investigate the incidence of a particular disease of interest the disease is assumed to be irreversible and detectable only at death for example by a necropsy each observation can be of one of three types i death caused by the disease ii death from a competing cause such as sacrifice with the disease present or iii death with the disease absent a two dimensional em algorithm is proposed for the nonparametric maximum likelihood estimation of the distributions of the time to onset and of the time to death from the disease these can be compared with nonparametric estimators recently proposed by kodell shaw and johnson 1982 biometrics 38 43 58 and by dinse and lagakos 1982 biometrics 38 921 932 a slight modification of the algorithm permits the construction of likelihood based interval estimates of quantiles of the distributions some extensions and generalizations are indicated

em algorithms for ml factor analysis the details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models the algorithm is essentially the same for both cases and involves only simple least squares regression operations the largest matrix inversion required is for aq q symmetric matrix whereq is the matrix of factors the example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation

wavelet based level set evolution for classification of textured images we present a supervised classification model based on a variational approach this model is specifically devoted to textured images we want to get a partition of an image composed of texture regions separated by regular interfaces each kind of texture defines a class we use a wavelet packet transform to analyze the textures characterized by their energy distribution in each sub band in order to have an image segmentation according to the classes we model the regions and their interfaces by level set functions we define a functional on these level sets whose minimizers define the optimal classification according to texture a system of coupled pdes is deduced from the functional by solving this system each region evolves according to its wavelet coefficients and interacts with the neighbor regions in order to obtain a partition with regular contours experiments are shown on synthetic and real images

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

visually improved image compression by combining a conventional wavelet codec with texture modeling human observers are very sensitive to a loss of image texture in photo realistic images for example a portrait image without the fine skin texture appears unnatural once the image is decomposed by a wavelet transformation this texture is represented by many wavelet coefficients of low and medium amplitude the conventional encoding of all these coefficients is very bitrate expensive instead such an unstructured or stochastic texture can be modeled by a noise process and be characterized with very few parameters thus a hybrid scheme can be designed that encodes the structural image information by a conventional wavelet codec and the stochastic texture in a model based manner such a scheme called witch wavelet based image texture coding hybrid is proposed it implements such an hybrid coding approach while nevertheless preserving the features of progressive and lossless coding its low computational complexity and the parameter coding costs of only 0 01 bpp make it a valuable extension of conventional codecs a comparison with the jpeg2000 image compression standard showed that the witch scheme achieves the same subjective quality while increasing the compression ratio by more than a factor of two

an em algorithm for fitting two level structural equation models maximum likelihood is an important approach to analysis of two level structural equation models different algorithms for this purpose have been available in the literature in this paper we present a new formulation of two level structural equation models and develop an em algorithm for fitting this formulation this new formulation covers a variety of two level structural equation models as a result the proposed em algorithm is widely applicable in practice a practical example illustrates the performance of the em algorithm and the maximum likelihood statistic

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

texture measures for carpet wear assessment two standard approaches for texture analysis make use of numerical features of the second order gray level statistics and on first order statistics of gray level differences respectively feature sets of these types all designed analogously were used to analyze four sets of carpet samples exposed to different degrees of wear it was found that some of the features extracted from the spatial gray level dependence matrix neighboring gray level dependence matrix gray level difference method and the gray level run length method allowed discrimination of degrees of wear in wool carpet the methods developed could be of use in quality control

integrated active contours for texture segmentation we address the issue of textured image segmentation in the context of the gabor feature space of images gabor filters tuned to a set of orientations scales and frequencies are applied to the images to create the gabor feature space a two dimensional riemannian manifold of local features is extracted via the beltrami framework the metric of this surface provides a good indicator of texture changes and is used therefore in a beltrami based diffusion mechanism and in a geodesic active contours algorithm for texture segmentation the performance of the proposed algorithm is compared with that of the edgeless active contours algorithm applied for texture segmentation moreover an integrated approach extending the geodesic and edgeless active contours approaches to texture segmentation is presented we show that combining boundary and region information yields more robust and accurate texture segmentation results

rigid motion invariant classification of 3 d textures this paper studies the problem of 3 d rigid motion invariant texture discrimination for discrete 3 d textures that are spatially homogeneous by modeling them as stationary gaussian random fields the latter property and our formulation of a 3 d rigid motion of a texture reduce the problem to the study of 3 d rotations of discrete textures we formally develop the concept of 3 d texture rotations in the 3 d digital domain we use this novel concept to define a distance between 3 d textures that remains invariant under all 3 d rigid motions of the texture this concept of distance can be used for a monoscale or a mill tiscale 3 d rigid motion invariant testing of the statistical similarity of the 3 d textures to compute the distance between any two rotations r1 and r2 of two given 3 d textures we use the kullback leibler divergence between 3 d gaussian markov random fields fitted to the rotated texture data then the 3 d rigid motion invariant texture distance is the integral average with respect to the haar measure of the group so 3 of all of these divergences when rotations r1 and r2 vary throughout so 3 we also present an algorithm enabling the computation of the proposed 3 d rigid motion invariant texture distance as well as rules for 3 d rigid motion invariant texture discrimination classification and experimental results demonstrating the capabilities of the proposed 3 d rigid motion texture discrimination rules when applied in a multiscale setting even on very general 3 d texture models

amenability a survey for statistical applications of hunt stein and related conditions on groups a number of conditions on groups have appeared in the literature of invariant statistical models in connection with minimaxity approximation of invariant bayes priors by proper priors the relationship between bayesian and classical inference ergodic theorems and other matters in the last decade rapid development has occurred in the field and many of these conditions are now known to be equivalent we survey the subject make the equivalences explicit and list some groups of statistical interest which do and also some which do not have these properties in particular it is shown that the existence of the asymptotically invariant sequence of probabilities in the hypothesis of the hunt stein theorem is equivalent to amenability a condition that has been much studied by functional analysts

brief review of invariant texture analysis methods this paper considers invariant texture analysis texture analysis approaches whose performances are not affected by translation rotation affine and perspective transform are addressed existing invariant texture analysis algorithms are carefully studied and classified into three categories statistical methods model based methods and structural methods the importance of invariant texture analysis is presented first each approach is reviewed according to its classification and its merits and drawbacks are outlined the focus of possible future work is also suggested

statistical properties of discretizations of a class of chaotic dynamical systems computer simulations of dynamical systems contain discretizations where finite machine arithmetic replaces continuum state spaces in some circumstances complicated theoretical behavior has a tendency to collapse to trivial and degenerate behavior as a result of discretizations various statistical estimators associated with such collapsing effects often seem to depend on the corresponding discretization in a random way behavior of some statistical properties of collapse is discussed results of computer modeling of mappings x 1 1 2x l x 0 1 l 2 are presented

machine iteration of a linear function local behaviour abstract we study analytically the behaviour of a discrete linear iteration near its fixed point in the case of truncation we also calculate the conditions needed for spurious multiple fixed points and for period two cycles we find that neither of these two errors can be reduced with better machine precision

limit cycles in a quadratic discrete iteration i study the truncated logistic equation as a map of d integers the number of limit cycles and the size of longest cycle are averaged exhaustively over many values of d for parameter values a beyond the first accumulation point fits of these quantities are compared with estimates obtained from random maps the results suggest some form of self organization i also present some analytical results on the existence and position of fixed points and a fast matrix method to enumerate limit cycles of arbitrary length for given a and d

image classification by a two dimensional hidden markov model for block based classification an image is divided into blocks and a feature vector is formed for each block by grouping statistics extracted from the block conventional block based classification algorithms decide the class of a block by examining only the feature vector of this block and ignoring context information in order to improve classification by context an algorithm is proposed that models images by two dimensional 2 d hidden markov models hmms the hmm considers feature vectors statistically dependent through an underlying state process assumed to be a markov mesh which has transition probabilities conditioned on the states of neighboring blocks from both horizontal and vertical directions thus the dependency in two dimensions is reflected simultaneously the hmm parameters are estimated by the em algorithm to classify an image the classes with maximum a posteriori probability are searched jointly for all the blocks applications of the hmm algorithm to document and aerial image segmentation show that the algorithm outperforms cart sup tm lvq and bayes vq

filtering for texture classification a comparative study in this paper we review most major filtering approaches to texture feature extraction and perform a comparative study filtering approaches included are laws masks 1980 ring wedge filters dyadic gabor filter banks wavelet transforms wavelet packets and wavelet frames quadrature mirror filters discrete cosine transform eigenfilters optimized gabor filters linear predictors and optimized finite impulse response filters the features are computed as the local energy of the filter responses the effect of the filtering is highlighted keeping the local energy function and the classification algorithm identical for most approaches for reference comparisons with two classical nonfiltering approaches co occurrence statistical and autoregressive model based features are given we present a ranking of the tested approaches based on extensive experiments

analysis of multichannel narrow band filters for image texture segmentation a model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework several different arguments are applied leading to the conclusion that the two dimensional gabor filters possess strong optimality properties for this task properties of the multiple channel segmentation approach are analyzed in particular perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low pass postfilter prior to making region assignments the difficult problems of space variant textures and multiple component textures are also considered local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number

robust continuous time smoothers without two sided stochastic integrals we consider the problem of fixed interval smoothing of a continuous time partially observed nonlinear stochastic dynamical system existing results for such smoothers require the use of two sided stochastic calculus the main contribution of the paper is to present a robust formulation of the smoothing equations under this robust formulation the smoothing equations are nonstochastic parabolic partial differential equations with random coefficients and hence the technical machinery associated with two sided stochastic calculus is not required furthermore the robust smoothed state estimates are locally lipschitz in the observations which is useful for numerical simulation as examples finite dimensional robust versions of the benes and hidden markov model smoothers and smoothers for piecewise linear dynamics are derived these finite dimensional smoothers do not involve stochastic integrals

asymptotic convergence rate of the em algorithm for gaussian mixtures it is well known that the convergence rate of the expectation maximization em algorithm can be faster than those of convention first order iterative algorithms when the overlap in the given mixture is small but this argument has not been mathematically proved yet this article studies this problem asymptotically in the setting of gaussian mixtures under the theoretical framework of xu and jordan 1996 it has been proved that the asymptotic convergence rate of the em algorithm for gaussian mixtures locally around the true solution is o e0 5 e where e 0 is an arbitrarily small number o x means that it is a higher order infinitesimal as x 0 and e is a measure of the average overlap of gaussians in the mixture in other words the large sample local convergence rate for the em algorithm tends to be asymptotically superlinear when e tends to zero

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

the vocabulary and grammar of color patterns we determine the basic categories and the hierarchy of rules used by humans in judging similarity and matching of color patterns the categories are 1 overall color 2 directionality and orientation 3 regularity and placement 4 color purity 5 complexity and heaviness these categories form the pattern vocabulary which is governed by the grammar rules both the vocabulary and the grammar were obtained as a result of a subjective experiment experimental data were interpreted using multidimensional scaling techniques yielding the vocabulary and the hierarchical clustering analysis yielding the grammar rules finally we give a short overview of the existing techniques that can be used to extract and measure the elements of the vocabulary

accelerated iterative reconstruction for positron emission tomography based on the em algorithm for maximum likelihood estimation the em method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography pet the result is an iterative algorithm for image reconstruction that is finding increasing use in pet due to its attractive theoretical and practical properties its major disadvantage is the large amount of computation that is often required due to the algorithm s slow rate of convergence this paper presents an accelerated form of the em algorithm for pet in which the changes to the image as calculated by the standard algorithm are multiplied at each iteration by an overrelaxation parameter the accelerated algorithm retains two of the important practical properties of the standard algorithm namely the selfnormalization and nonnegativity of the reconstructed images experimental results are presented using measured data obtained from a hexagonal detector system for pet the likelihood function and the norm of the data residual were monitored during the iterative process according to both of these measures the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm for two different sets of data important theoretical properties remain to be investigated namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator

invariant strings and pattern recognizing properties of one dimensional cellular automata a cellular automaton is a discrete dynamical system whose evolution is governed by a deterministic rule involving local interactions it is shown that given an arbitrary string of values and an arbitrary neighborhood size representing the range of interaction a simple procedure can be used to find the rules of that neighborhood size under which the string is invariant the set of nearestneighbor rules for which invariant strings exist is completely specified as is the set of strings invariant under each such rule for any automaton rule an associated filtering rule is defined for which the only attractors are spatial sequences consisting of concatenations of invariant strings a result is provided defining the rule of minimum neighborhood size for which an arbitrarily chosen string is the unique invariant string the applications of filtering rules to pattern recognition problems are discussed

structural texture similarity metrics for image analysis and retrieval we develop new metrics for texture similarity that accounts for human visual perception and the stochastic nature of textures the metrics rely entirely on local image statistics and allow substantial point by point deviations between textures that according to human judgment are essentially identical the proposed metrics extend the ideas of structural similarity and are guided by research in texture analysis synthesis they are implemented using a steerable filter decomposition and incorporate a concise set of subband statistics computed globally or in sliding windows we conduct systematic tests to investigate metric performance in the context of known item search the retrieval of textures that are identical to the query texture this eliminates the need for cumbersome subjective tests thus enabling comparisons with human performance on a large database our experimental results indicate that the proposed metrics outperform peak signal to noise ratio psnr structural similarity metric ssim and its variations as well as state of the art texture classification metrics using standard statistical measures

enumeration of limit cycles in noncylindrical cellular automata recently a method has been developed by jen to enumerate limit cycles in cellular automata ca with periodic boundary conditions this involves operations on a connectivity matrix whose elements are related to the invariance of a site in a particular neighborhood to application of the ca rule we extend this method to the case of fixed boundary conditions of interest in simulations in this case translational invariance is lost and the enumeration procedure is much more tedious than with periodic boundary conditions we show examples for a fixed point a period two and a period three enumeration in considerable detail and give results in agreement with simulations for the number of fixed points and period two cycles in selected two state nearest neighbor ca rules

diversity combining for ds ss systems with time varying correlated fading branches diversity combining of multiple time varying and correlated fading branches is investigated for direct sequence spread spectrum systems the correlated branches are modeled and estimated jointly as a vector autoregressive var process the joint estimation is shown to provide performance gain over separate estimation of the fading branches the parameter matrices of the var model are estimated via the method of expectation maximization em with two algorithms the first algorithm using results from kalman smoothing provides a closed form solution to the maximization problem in the iterative em procedure however the iterative em kalman algorithm operates repeatedly on a batch of training data and results in large storage requirements and long processing delays to overcome these disadvantages a new algorithm with only forward time recursions is proposed that approximates the iterative em solution and efficiently adapts to slowly changing doppler spreads as a result the new algorithm significantly reduces memory and training sequence requirements through computer simulations a near ideal bit error rate performance is found for both algorithms and the efficacy of the new adaptive algorithm for channels with changing doppler spreads is demonstrated