conditional stability of solitary waves propagating in elastic rods abstract the problem of dynamic stability of solitary wave solutions of the equations describing bending oscillations of inextensible elastic rods is treated the governing equations describe sufficiently large displacements though we are restricted to small strains we show that under the condition of well posedness of the initial value problem in some specific sense the family of solitary wave solutions of the mentioned equations is stable for the planar elastic rod the framework of the analysis is largely based on the spectral properties of the linearized hamiltonian h we show that for planar oscillations h is positively semidefinite subject to a certain constraint which implies the stability

classical solutions of nonlinear beam equations existence and stabilization in this paper we consider the large amplitude planar motion of a cantilevered beam with a feedback force and or torque proportional and acting opposite to the velocity angular velocity respectively applied at the free end we derive nonlinear equations of motion for such a beam based upon certain natural geometric assumptions we then prove the existence of classical solutions for these equations and show that all classical solutions are uniformly exponentially stable

clutter invariant atr one of the central problems in automated target recognition is to accommodate the infinite variety of clutter in real military environments the principle focus of our paper is on the construction of metric spaces where the metric measures the distance between objects of interest invariant to the infinite variety of clutter such metrics are formulated using second order random field models our results indicate that this approach significantly improves detection classification rates of targets in clutter

texture synthesis and nonparametric resampling of random fields this paper introduces a nonparametric algorithm for bootstrapping a stationary random field and proves certain consistency properties of the algorithm for the case of mixing random fields the motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general nonparametric bootstrapping of stationary random fields we give a formal resampling scheme for the heuristic texture algorithm and prove that it produces a consistent estimate of the joint distribution of pixels in a window of certain size under mixing and regularity conditions on the random field the joint distribution of pixels is the quantity of interest here because theories of human perception of texture suggest that two textures with the same joint distribution of pixel values in a suitably chosen window will appear similar to a human thus we provide theoretical justification for an algorithm that has already been very successful in practice and suggest an explanation for its perceptually good results

minimax entropy principle and its application to texture modeling this article proposes a general theory and methodology called the minimax entropy principle for building statistical models for images or signals in a variety of applications this principle consists of two parts the first is the maximum entropy principle for feature binding or fusion for a given set of observed feature statistics a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them the second part is the minimum entropy principle for feature selection among all plausible sets of feature statistics we choose the set whose maximum entropy distribution has the minimum entropy computational and inferential issues in both parts are addressed in particular a feature pursuit procedure is proposed for approximately selecting the optimal set of features the minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics and an information criterion for feature pursuit is derived the minimax entropy principle is applied to texture modeling where a novel markov random field mrf model called frame filter random field and minimax entropy is derived and encouraging results are obtained in experiments on a variety of texture images the relationship between our theory and the mechanisms of neural computation is also discussed

multi multiplier ambient space formulations of constrained dynamical systems with an application to elastodynamics various formulations of the equations of motion for both finite and infinite dimensional constrained lagrangian dynamical systems are studied the different formulations correspond to different ways of enforcing constraints through multiplier fields all the formulations considered are posed on ambient spaces whose members are unrestricted by the need to satisfy constraint equations but each formulation is shown to possess an invariant set on which the constraint equations and physical balance laws are satisfied the stability properties of the invariant set within its ambient space are shown to be different in each case we use the specific model problem of linearized incompressible elastodynamics to compare properties of three different ambient space formulations we establish the well posedness of one formulation in the particular case of a homogeneous isotropic body subject to specified tractions on its boundary

texture segmentation using voronoi polygons textures are defined in terms of primitives called tokens a texture segmentation algorithm based on the voronoi tessellation is discussed the algorithm first builds the voronoi tessellation of the tokens that make up the textured image it then computes a feature vector for each voronoi polygon these feature vectors are used in a probabilistic relaxation labeling on the tokens to identify the interior and the border regions of the textures some experimental results are shown

parameter estimation for optimal object recognition theory andapplication object recognition systems involve parameters such as thresholds bounds and weights these parameters have to be tuned before the system can perform successfully a common practice is to choose such parameters manually on an it add hoc basis which is a disadvantage this paper presents a novel theory of parameter estimation for optimization based object recognition where the optimal solution is defined as the global minimum of an energy function the theory is based on supervised learning from examples it correctness and it instability are established as criteria for evaluating the estimated parameters a correct estimate enables the labeling implied in each exemplary configuration to be encoded in a unique global energy minimum the instability is the ease with which the minimum is replaced by a non exemplary configuration after a perturbation the optimal estimate minimizes the instability algorithms are presented for computing correct and minimal instability estimates the theory is applied to the parameter estimation for mrf based recognition and promising results are obtained

constraint satisfaction neural networks for image segmentation abstract constraint satisfaction neural networks csnns are proposed for image recognition which is the process to identify objects of interest in an image the image recognition problem is formulated as a constraint satisfaction problem csp the regions resulting from a signal based image segmentation algorithm can be considered as objects and their entities as labels in the csp the proposed neural network is multi layered and the function of each layer is to identify one physical entity label from the input regions objects through cascading these layers each label can be assigned to the corresponding region s attention is focused on recognizing x ray ct computed tomography images of human heads e g anatomic structure in a medical image the proposed csnn is capable of identifying the components of a brain in a preliminarily segmented image the major components in a human head include bone ventricle and gyrus therefore three layers are needed for this task each layer is constructed based on the principles proposed in kohonen s self organizing feature maps and the optimal linear associative memories and their weights are trained by the features of each entity in the prestored model the experimental results show that the proposed approach is very promising

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

pixon based image segmentation with markov random fields image segmentation is an essential processing step for many image analysis applications we propose a novel pixon based adaptive scale method for image segmentation the key idea of our approach is that a pixon based image model is combined with a markov random field mrf model under a bayesian framework we introduce a new pixon scheme that is more suitable for image segmentation than the fuzzy pixon scheme the anisotropic diffusion equation is successfully used to form the pixons in our new pixon scheme experimental results demonstrate that our algorithm performs fairly well and computational costs decrease dramatically compared with the pixel based mrf algorithm

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

convergence of a second order scheme for the nonlinear dynamical equations of elastic rods a second order energy preserving finite difference scheme to approximate the partial differential equations governing planar twist free motions of inextensible unshearable elastic rods is presented and analyzed

on the estimation of markov random field parameters we examine the histogram method for estimating the parameters associated with a markov random field this method relies on the estimation of the local interaction sums from histogram data we derive an estimator for these quantities that is optimal in a well defined sense furthermore we show that the final step of the histogram method the solution of a least squares problem can be done substantially faster than one might expect if no equation culling is used we also examine the use of weighted least squares and see that this seems to lead to better estimates even with small amounts of data

an unconstrained hamiltonian formulation for incompressible fluid flow the equations governing the time evolution of an ideal fluid in material coordinates are expressed as an unconstrained canonical hamiltonian system the incompressibility of the flow is consequent upon certain first integrals of the motion the variable conjugate to the configuration field is not the usual linear momentum but is instead a quantity that is related to linear momentum through an auxiliary scalar field whose time derivative is the pressure the definition of the hamiltonian involves a minimization with respect to this auxiliary field the method of derivation may be generally applied to obtain unconstrained hamiltonian descriptions of lagrangian field equations subject to pointwise constraints

optimization of integer wavelet transforms based on difference correlation structures in this paper a novel lifting integer wavelet transform based on difference correlation structure dccs liwt is proposed first we establish a relationship between the performance of a linear predictor and the difference correlations of an image the obtained results provide a theoretical foundation for the following construction of the optimal lifting filters then the optimal prediction lifting coefficients in the sense of least square prediction error are derived dccs liwt puts heavy emphasis on image inherent dependence a distinct feature of this method is the use of the variance normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources the proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations experimental evaluation shows that the proposed method produces better results than the other well known integer transforms for the lossless image compression

rate distortion modeling for multiscale binary shape coding based on markov random fields the purpose of this paper it to explore the relationship between the rate distortion characteristics of multiscale binary shape and markov random field mrf parameters for coding it is important that the input parameters that will be used to define this relationship be able to distinguish between the same shape at different scales as well as different shapes at the same scale we consider an mrf model referred to as the chien model which accounts for high order spatial interactions among pixels we propose to use the statistical moments of the chien model as input to a neural network to accurately predict the rate and distortion of the binary shape when coded at various scales

inverse optimal design of input to state stabilizing nonlinear controllers we show that input to state stabilizability as defined by sontag 1989 1995 is both necessary and sufficient for the solvability of a hamilton jacobi isaacs equation associated with a meaningful differential game problem similar to but more general than the nonlinear h sub spl infin problem the significance of the result stems from the fact that constructive solutions to the input to state stabilization problem are available presented in the paper and that as shown here inverse optimal controllers possess margins on input to state stability against a certain class of input unmodeled dynamics rather than completion of squares the main tools in our analysis are legendre fenchel transformations and the general form of young s inequality

on a parameter estimation method for gibbs markov random fields this correspondence is about a gibbs markov random field gmrf parameter estimation technique proposed by derin and elliott 1987 we will refer to this technique as the histogramming h method first the relation of the h method to the conditional maximum likelihood method is considered second a bias reduction based modification of the h method is proposed to improve its performance especially in the case of small amounts of image data

nonlinear scaling of i iss lyapunov functions while nonlinear scalings of lyapunov functions are also lyapunov functions we provide examples that the same statement does not necessarily hold for input to state stable iss lyapunov functions or for integral iss iiss lyapunov functions we provide sufficient conditions under which a nonlinear scaling of an iss or iiss lyapunov function is also an iss or iiss lyapunov function we also introduce a generalization of the iiss lyapunov function which we term a dissipative iiss lyapunov function that allows for a larger class of nonlinear scalings so that nonlinear scalings of dissipative iiss lyapunov functions are again dissipative iiss lyapunov functions

a characterization of integral input to state stability the notion of input to state stability iss is now recognized as a central concept in nonlinear systems analysis it provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite l sup 2 gains it plays a central role in recursive design coprime factorizations controllers for nonminimum phase systems and many other areas in this paper a newer notion that of integral input to state stability iiss is studied the notion of iiss generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states in that sense generalizing the linear h sup 2 theory it allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance we obtain several necessary and sufficient characterizations of the iiss property expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations

hamiltonian dynamics of an elastica and the stability of solitary waves a method is presented for deriving unconstrained hamiltonian systems of partial differential equations equivalent to given constrained lagrangian systems the method is applied to the theory of planar finite amplitude motions of inextensible and unshearable elastic rods the constraints of inextensibility and unshearability become integrals of motion in the hamiltonian formulation

stability of solitary waves in nonlinear composite media the system of equations for planar waves in elastic composite media in the presence of anisotropy is considered in anisotropic case two two parametric families of solitary waves are found in an explicit form in case of the absence of anisotropy these two families coalesce into the unique three parametric family the solitary wave solutions are found to be orbitally stable in a certain range of their phase speeds range of stability both in an anisotropic as well as in an isotropic materials it is also shown that the initial value problem for the governing equations is locally well posed which is needed to prove the stability result the local well posedness of the initial value problem along with stability of solitary waves implies global existence result provided the initial data lie in a neighbourhood of a stable solitary wave this complements the previous results of blow up for this type of equations

classification of rotated and scaled textured images using gaussian markov random field models consideration is given to the problem of classifying a test textured image that is obtained from one of c possible parent texture classes after possibly applying unknown rotation and scale changes to the parent texture the training texture images parent classes are modeled by gaussian markov random fields gmrfs to classify a rotated and scaled test texture the rotation and scale changes are incorporated in the texture model through an appropriate transformation of the power spectral density of the gmrf for the rotated and scaled image a bona fide likelihood function that shows the explicit dependence of the likelihood function on the gmrf parameters as well as on the rotation and scale parameters is derived although in general the scaled and or rotated texture does not correspond to a finite order gmrf it is possible nonetheless to write down a likelihood function for the image data the likelihood function of the discrete fourier transform of the image data corresponds to that of a white nonstationary gaussian random field with the variance at each pixel i j being a known function of the rotation the scale the gmrf model parameters and i j the variance is an explicit function of the appropriately sampled power spectral density of the gmrf the estimation of the rotation and scale parameters is performed in the frequency domain by maximizing the likelihood function associated with the discrete fourier transform of the image data cramer rao error bounds on the scale and rotation estimates are easily computed a modified bayes decision rule is used to classify a given test image into one of c possible texture classes the classification power of the method is demonstrated through experimental results on natural textures from the brodatz album

state dependent scaling problems and stability of interconnected iiss and iss systems this paper addresses the problem of establishing stability of nonlinear interconnected systems this paper introduces a mathematical formulation of the state dependent scaling problems whose solutions directly provide lyapunov functions proving stability properties of interconnected dissipative systems in a unified manner stability criteria are interpreted as sufficient conditions for the existence of solutions to the state dependent scaling problems computing solutions to the problems is straightforward for systems covered by classical stability criteria it however could be too difficult for systems with strong nonlinearity the main purpose of this paper is to demonstrate the effectiveness beyond formal applicability by focusing on interconnected integral input to state stable iiss systems and input to state stable iss systems this paper derives small gain type theorems for interconnected systems involving iiss systems from the state dependent scaling formulation this paper provides solutions and lyapunov functions explicitly the new framework seamlessly generalizes the iss small gain theorem and classical stability criteria such as the lp small gain theorem the passivity theorems the circle and popov criteria state dependence of the scaling is crucial for effective treatment of essential nonlinearities while constants are sufficient for classical nonlinearities

on the dynamics of rods in the theory of kirchhoff and clebsch we discuss here the dynamical equations of a theory of elastic rods that is due to kmcm ioff 1 2 and cl bsc 3 4 this properly invariant theory is applicable to motions in which the strains relative to an undistorted configuration remain small although rotations may be large it is constructed to be a first order theory i e a theory that is complete to within an error of order two in an appropriate dimensionless measure of thickness curvature twist and extension in a first order theory of thin rods one can treat the rod as inextensible and we do so here at the outset thus at each time t the arc length parameter s for the axial curve t is employed as a material coordinate i e a parameter whose value at a material point is constant in time and not only the resultant of the shearing forces on a cross section but also the tension in the rod are reactive quantities not given by constitutive equations consider for a moment a rod that is naturally prismatic and dynamically symmetric i e a rod that in an undistorted stress free configuration is a cylinder whose directrix although not necessarily a circle bounds a figure with equal principal moments of inertia a motion of the rod is said to be planar and twist flee i e a motion of pure flexure if it is such that t lies at all times in a fixed plane which contains a principal axis of inertia of each cross section for such a motion we employ a fixed cartesian coordinate system on and for consistency with a discussion of more general motions to be given later in this paper we call the abscissa z and the ordinate x we may write fz s t fx s t for the z and x components of the resultant force f at time t on the cross section with arc length coordinate s the motion of the rod may be described by giving the z x coordinates of the points on t as functions of s and t with o s t the counterclockwise angle from the z axis to the tangent of t at s we have

passive error concealment for wavelet coded i frames with an inhomogeneous gauss markov random field model in video communication over lossy packet networks e g the internet packet loss errors can severely damage the transmitted video the damaged video can largely be repaired with passive error concealment where neighboring information is used to estimate missing information we address the problem of passive error concealment for wavelet coded data with dispersive packetization the reported techniques of this kind have many problems and usually fail in the reconstruction of high frequency content this paper presents a novel locally adaptive error concealment method for subband coded i frames based on an inhomogeneous gaussian markov random field model we estimate the parameters of this model from a local context of each lost coefficient and we interpolate the lost coefficients accordingly the results demonstrate a significant improvement over the reported related methods both in terms of objective performance measures and visually the biggest improvement of the proposed method compared to the state of the art in the field is the correct reconstruction of high frequency information such as textures and edges

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

modeling of ultrasound speckle with application in flaw detection in metals rf ultrasound backscatter speckle is modeled by a parametric noncausal gaussian markov field that appears to capture the speckle structure well is consistent with the first order marginal statistics of the complex amplitude speckle and explains the homogeneous coarseness appearance of the speckle in terms of a homogeneous colored random field with a definite correlation structure the markov property results in the compact parametrization of the backscatter echo field by a few parameters and constitutes a huge reduction in the representation and analysis complexity of the backscatter image use is made of the intensity as well as phase information associated with the acoustic image by analyzing and modeling the acoustic rf data rather than the intensity data the additional phase information associated with the rf data allows for the statistics of the complex backscatter echo field or equivalently that of the rf field to be completely specified the approach provides a coherent theoretical basis for the design of statistical tests for detecting targets embedded in the speckle image for the case where the speckle model parameters are either a priori known or unknown

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

the hamiltonian structure of nonlinear elasticity the material and convective representations of solids rods and plates it is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation for example in the analysis of rotating structures the coupling of the equations for geometrically inexact models obtained by linearization or other approximations with those for rotating rigid bodies can easily lead to misleading artificial softening effects that can significantly alter numerical results see simo and vuquoc 1986c especially equations 3 and 5 in this paper we consider fully nonlinear geometrically exact models for rods plates and shells which take into account shear and torsion as well as the usual bending effects in traditional rod and plate models these models can be obtained either from the three dimensional theory by a systematic use of projection methods see e g antman 1972 and naghdi 1972 or by a direct approach within the context of cosserat continuum remarkably the two approaches lead to essentially the same form of the governing field equations in the present context we have chosen as a model problem a particular rod model which may be regarded as an extension of the classical kirchhoff love model see love 1944 to include shear deformations as in

numerical integration of constrained hamiltonian systems using dirac brackets we study the numerical properties of the equations of motion of constrained systems derived with dirac brackets this formulation is compared with one based on the extended hamiltonian as concrete examples a pendulum in cartesian coordinates and a chain molecule are treated

high dimensional ising model selection using l1 regularized logistic regression we consider the problem of estimating the graph associated with a binary ising markov random field we describe a method based on l1 regularized logistic regression in which the neighborhood of any given node is estimated by performing logistic regression subject to an l1 constraint the method is analyzed under high dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n our main results provide sufficient conditions on the triple n p d and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously with coherence conditions imposed on the population fisher information matrix we prove that consistent neighborhood selection can be obtained for sample sizes n d3log p with exponentially decaying error when these same conditions are imposed directly on the sample matrices we show that a reduced sample size of n d2log p suffices for the method to estimate neighborhoods consistently although this paper focuses on the binary graphical models we indicate how a generalization of the method of the paper would apply to general discrete markov random fields

bispectral analysis and model validation of texture images statistical approaches to texture analysis and synthesis have largely relied upon random models that characterize the 2 d process in terms of its first and second order statistics and therefore cannot completely capture phase properties of random fields that are non gaussian and or asymmetric in this paper higher than second order statistics are used to derive and implement 2 d gaussianity linearity and spatial reversibility tests that validate the respective modeling assumptions the nonredundant region of the 2 d bispectrum is correctly defined and proven a consistent parameter estimator for nonminimum phase asymmetric noncausal 2 d arma models is derived by minimizing a quadratic error polyspectrum matching criterion simulations on synthetic data are performed and the results of the bispectral analysis on real textures are reported

texture synthesis using 2 d noncausal autoregressive models the purpose of this paper is to illustrate the usefulness of two dimensional noncausal autoregressive ncar models for the synthesis of textures these models characterize the gray level at a pixel as a linear combination of gray levels at nearby locations in all directions and an additive white noise variable we first show that the class of ncar models is capable of generating a wide variety of image patterns posessing the local replication attribute an essential ingredient of many natural textures it is also shown that the theoretical variograms of many ncar models possess an oscillatory behavior a characteristic of the variograms of many natural textures next we give experimental results of synthesis of 64 64 textures resembling several real textures in the brodatz album the synthetic textures generated by 16 parameter ncar models retain most the visual characteristics of the original textures the variograms of the original and synthetic textures are also similar

sasi a generic texture descriptor for image retrieval in this paper a generic texture descriptor namely statistical analysis of structural information sasi is introduced as a representation of texture sasi is based on statistics of clique autocorrelation coefficients calculated over structuring windows sasi defines a set of clique windows to extract and measure various structural properties of texture by using a spatial multi resolution method experimental results performed on various image databases indicate that sasi is more successful then the gabor filter descriptors in capturing small granularities and discontinuities such as sharp corners and abrupt changes due to the flexibility in designing the clique windows sasi reaches higher average retrieval rates compared to gabor filter descriptors however the price of this performance is increased computational complexity

a markov random field model based approach to image interpretation an image is segmented into a collection of disjoint regions that form the nodes of an adjacency graph and image interpretation is achieved through assigning object labels or interpretations to the segmented regions or nodes using domain knowledge extracted feature measurements and spatial relationships between the various regions the interpretation labels are modeled as a markov random field mrf on the corresponding adjacency graph and the image interpretation problem is then formulated as a maximum a posteriori map estimation rule given domain knowledge and region based measurements simulated annealing is used to find this best realization or optimal map interpretation this approach also provides a systematic method for organizing and representing domain knowledge through appropriate design of the clique functions describing the gibbs distribution representing the pdf of the underlying mrf a general methodology is provided for the design of the clique functions results of image interpretation experiments on synthetic and real world images are described

image representation using block pattern models and its image processing applications an image representation scheme using a set of block pattern models bpms consisting of three categories constant oriented and irregular is introduced algorithms for model classification model parameter estimation and image reconstruction from model parameters are presented and these provide the necessary vehicles for applying the proposed representation scheme to various image processing tasks the applications of the proposed models in image coding image zooming and image smoothing are described satisfactory coded images have been obtained at bit rates between 0 5 approximately 0 6 b p p bits per pixel with a high rate realization and between 0 3 approximately 0 5 b p p with a low rate realization the high rate realization has a simple structure suitable for real time implementation the methods for image zooming and smoothing are similar where both adapt the processing for each pixel according to the model of its neighborhood by using directional filters in oriented regions edges and lines are rendered sharper in a smoother manner than with conventional linear filtering approaches which leads to significant improvement in perceived image quality

bayesian segmentation via asymptotic partition functions asymptotic approximations to the partition function of gaussian random fields are derived textures are characterized via gaussian random fields induced by stochastic difference equations determined by finitely supported stationary linear difference operators adjusted to be nonstationary at the boundaries it is shown that as the scale of the underlying shape increases the log normalizer converges to the integral of the log spectrum of the operator inducing the random field fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator induced random field model matrix analysis techniques are proposed for handling textures with variable orientation examples of texture parameters estimated from training data via asymptotic maximum likelihood are shown isotropic models involving powers of the laplacian and directional models involving partial derivative mixtures are explored parameters are estimated for mitochondria and actin myocin complexes in electron micrographs and clutter in forward looking infrared images deformable template models are used to infer the shape of mitochondria in electron micrographs with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds

texture segmentation using gaussian markov random fields and neural oscillator networks we propose an image segmentation method based on texture analysis our method is composed of two parts the first part determines a novel set of texture features derived from a gaussian markov random fields gmrf model unlike a gmrf based approach our method does not employ model parameters as features or require the extraction of features for a fixed set of texture types a priori the second part is a 2d array of locally excitatory globally inhibitory oscillator networks legion after being filtered for noise suppression features are used to determine the local couplings in the network when legion runs the oscillators corresponding to the same texture tend to synchronize whereas different texture regions tend to correspond to distinct phases in simulations a large system of differential equations is solved for the first time using a recently proposed method for integrating relaxation oscillator networks we provide results on real texture images to demonstrate the performance of our method

statistical texture characterization from discrete wavelet representations we conjecture that texture can be characterized by the statistics of the wavelet detail coefficients and therefore introduce two feature sets 1 the wavelet histogram signatures which capture all first order statistics using a model based approach and 2 the wavelet co occurrence signatures which reflect the coefficients second order statistics the introduced feature sets outperform the traditionally used energy best performance is achieved by combining histogram and co occurrence signatures

texture classification using spectral histograms based on a local spatial frequency representation we employ a spectral histogram as a feature statistic for texture classification the spectral histogram consists of marginal distributions of responses of a bank of filters and encodes implicitly the local structure of images through the filtering stage and the global appearance through the histogram stage the distance between two spectral histograms is measured using spl chi sup 2 statistic the spectral histogram with the associated distance measure exhibits several properties that are necessary for texture classification a filter selection algorithm is proposed to maximize classification performance of a given dataset our classification experiments using natural texture images reveal that the spectral histogram representation provides a robust feature statistic for textures and generalizes well comparisons show that our method produces a marked improvement in classification performance finally we point out the relationships between existing texture features and the spectral histogram suggesting that the latter may provide a unified texture feature

nonlinear dynamical theory of the elastica the dynamical behaviour of a slender rod is analyzed here in terms of a generalization of euler s elastica theory the model includes a linear stress strain relation but nonlinear geometric terms properties of the rod may vary along its length and various boundary conditions are considered a rotational inertia term that is neglected in many theories is retained and is essential to the analysis by use of the equivalence of an energy and a sobolev norm and by reformulation of the equations as a semilinear system global existence of solutions is proved for any smooth initial data equilibrium solutions that are stable in the static sense of minimizing the potential energy are then proved to be stable in the dynamic sense due to liapounov

universal construction of feedback laws achieving iss and integral iss disturbance attenuation we study nonlinear systems with both control and disturbance inputs the main problem addressed in the paper is design of state feedback control laws that render the closed loop system integral input to state stable iiss with respect to the disturbances we introduce an appropriate concept of control lyapunov function iiss clf whose existence leads to an explicit construction of such a control law the same method applies to the problem of input to state stabilization converse results and techniques for generating iiss clfs are also discussed

two dimensional linear prediction model based decorrelation method a unified feature extraction scheme the two dimensional 2 d linear prediction model based decorrelation method is presented by applying 2 d causal linear prediction model to decorrelate a textured image the very heavy computation load required when using a whitening operator to decorrelate the image or the significant information loss when using the gradient operator to approximately whiten the image is avoided the texture model based decorrelation provides three sets of features to perform texture classification the coefficients of the 2 d linear prediction the moments of error residuals and the autocorrelation values an optimum feature selection scheme using modified branch and bound method was introduced to reduce information redundancy after feature selection 100 classification accuracy was achieved for a 20 class texture problem experiments show that this feature extraction scheme is truly information lossless effective and fast

binary partitioning perceptual grouping and restoration with semidefinite programming we introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints the approach is tuning parameter free and computes high quality combinatorial solutions using interior point methods convex programming and a randomized hyperplane technique apart from a symmetry condition no assumptions such as metric pairwise interactions are made with respect to the objective criterion as a consequence the approach can be applied to a wide range of problems applications to unsupervised partitioning figure ground discrimination and binary restoration are presented along with extensive ground truth experiments from the viewpoint of relaxation of the underlying combinatorial problem we show the superiority of our approach to relaxations based on spectral graph theory and prove performance bounds

a study of gaussian mixture models of color and texture features for image classification and segmentation the aims of this paper are two fold to define gaussian mixture models gmms of colored texture on several feature spaces and to compare the performance of these models in various classification tasks both with each other and with other models popular in the literature we construct gmms over a variety of different color and texture feature spaces with a view to the retrieval of textured color images from databases we compare supervised classification results for different choices of color and texture features using the vistex database and explore the best set of features and the best gmm configuration for this task in addition we introduce several methods for combining the color and structure information in order to improve the classification performances we then apply the resulting models to the classification of texture databases and to the classification of man made and natural areas in aerial images we compare the gmm model with other models in the literature and show an overall improvement in performance

correction to rotation and gray scale transform invariant texture classification using spiral resampling subband decomposition and hidden markov model this paper proposes a new texture classification algorithm that is invariant to rotation and gray scale transformation first we convert two dimensional 2 d texture images to one dimensional 1 d signals by spiral resampling then we use a quadrature mirror filter qmf bank to decompose sampled signals into subbands in each band we take high order autocorrelation functions as features features in different bands which form a vector sequence are then modeled as a hidden markov model bmm during classification the unknown texture is matched against all the models and the best match is taken as the classification result simulations showed that the highest correct classification rate for 16 kinds of texture was 95 14

a new texture generation method based on pseudo dct coefficients in this paper a new method for generating different texture images is presented this method involves a simple transform from a certain one dimensional 1 d signal to an expected two dimensional 2 d image unlike traditional methods the input signal is generated by a simple 1 d function in our work instead of a sample texture we first transform the 1 d input signal into frequency domain using fast fourier transform based on the sufficient analysis in 2 d discrete cosine transform dct domain where each of the coefficients expresses a texture feature in a certain direction the 2 d pseudo dct coefficients are then constructed by appropriately rearranging the fourier coefficients in terms of their frequency components finally the corresponding texture image can be produced by 2 d inverse dct algorithm we applied the proposed method to generate several stochastic textures i e cloud illumination and sand and several structural texture images experimental results indicate the good performance of the proposed method

image modeling using inverse filtering criteria with application to textures statistical approaches to image modeling have largely relied upon random models that characterize the 2 d process in terms of its first and second order statistics and therefore cannot completely capture phase properties of random fields that are non gaussian this constrains the parameters of noncausal image models to be symmetric and therefore the underlying random field to be spatially reversible research indicates that this assumption may not be always valid for texture images in this paper higher than second order statistics are used to derive and implement two classes of inverse filtering criteria for parameter estimation of asymmetric noncausal autoregressive moving average arma image models with known orders contrary to existing approaches fir inverse filters are employed and image models with zeros on the unit bicircle can be handled one of the criteria defines the smallest set of cumulant lags necessary for identifiability of these models to date consistency of these estimators is established and their performance is evaluated with monte carlo simulations as well as texture classification and synthesis experiments

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners

relationships between subclasses of integral input to state stability a certain qualitative equivalence has been recently demonstrated between integral input to state stability iiss and a nonlinear mathcal l 2 gain property furthermore it has been observed that the properties of strong iiss and nonlinear mathcal l 2 gain are preserved when multiple systems satisfying the respective property are connected in cascade this technical note clarifies the relationships between various input to state stability and non linear mathcal l p gain properties