finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

lattice based random jammed configurations for hard particles a nontrivial subset of the jammed packings for rigid disks and spheres are those that can be obtained by sequential removal of particles from periodic crystalline arrays this paper considers the enumeration problems presented by such packings that are based on the close packed triangular disk lattice and the face centered and body centered cubic sphere lattices three distinct categories of packings have been distinguished depending on their behavior with respect to nonoverlap geometric constraints and or externally imposed virtual displacements locally jammed collectively jammed and strictly jammed each of these possesses an upper limiting vacancy concentration beyond which no packings of the types considered can exist for each of the three lattices specific vacancy clusters have been identified whose presence would destroy local jamming and some of the corresponding patterns that would destroy collective jamming in the triangular disk lattice have also been found within the allowable range of vacancy concentration for each case the number of distinct jammed packings is expected to rise exponentially with system size by using the concept of local attrition factors approximate enumerations have been constructed for the three lattice classes of locally jammed packings in the interests of later extension of this work we stress that at least some aspects of these enumeration problems might benefit from the formal transcription to a lattice gas ising model representation with vacancy interactions chosen to enforce the packing category of interest

a wavelet based joint estimator of the parameters of long range dependence a joint estimator is presented for the two parameters that define the long range dependence phenomenon in the simplest case the estimator is based on the coefficients of a discrete wavelet decomposition improving a wavelet based estimator of the scaling parameter abry and veitch 1998 as well as extending it to include the associated power parameter an important feature is its conceptual and practical simplicity consisting essentially in measuring the slope and the intercept of a linear fit after a discrete wavelet transform is performed a very fast o n operation under well justified technical idealizations the estimator is shown to be unbiased and of minimum or close to minimum variance for the scale parameter and asymptotically unbiased and efficient for the second parameter through theoretical arguments and numerical simulations it is shown that in practice even for small data sets the bias is very small and the variance close to optimal for both parameters closed form expressions are given for the covariance matrix of the estimator as a function of data length and are shown by simulation to be very accurate even when the technical idealizations are not satisfied comparisons are made against two maximum likelihood estimators in terms of robustness and computational cost the wavelet estimator is found to be clearly superior and statistically its performance is comparable we apply the tool to the analysis of ethernet teletraffic data completing an earlier study on the scaling parameter alone

on the universality of geometrical and transport exponents of rigidity percolation we develop a three parameter position space renormalization group method and investigate the universality of geometrical and transport exponents of rigidity vector percolation in two dimensions to do this we study site bond percolation in which sites and bonds are randomly and independently occupied with probabilitiess andb respectively the global flow diagram of the renormalization transformation is obtained which shows that thegeometrical exponents of the rigid clusters in both site and bond percolation belong to the same universality class and possibly that of random scalar percolation however if we use the same renormalization transformation to calculate the critical exponents of the elastic moduli of the system in bond and site percolation we find them to be very different although the corresponding values of the correlation length exponent are the same this indicates that the critical exponent of the elastic moduli of rigidity percolation may not be universal which is consistent with some of the recent numerical simulations

rigidity of random networks of stiff fibers in the low density limit rigidity percolation is analyzed in two dimensional random networks of stiff fibers as fibers are randomly added to the system there exists a density threshold q q min above which a rigid stress bearing percolation cluster appears this threshold is found to be above the connectivity percolation threshold q q c such that q min 1 1698 0 0004 q c the transition is found to be continuous and in the universality class of the two dimensional central force rigidity percolation on lattices at percolation threshold the rigid backbone of the percolating cluster was found to break into rigid clusters whose number diverges in the limit of infinite system size when a critical bond is removed the scaling with system size of the average size of these clusters was found to give a new scaling exponent delta 1 61 0 04

enhanced gradient based algorithm for the estimation of fingerprint orientation fields an accurate estimation of fingerprint orientation fields is an essential step in the overall fingerprint recognition process conventional gradient based approaches are popular but very sensitive to noise in this paper we propose a novel implementation to improve the performance of gradient based methods the enhanced algorithm chooses the best orientation estimate from four overlapping neighborhoods of every image block where the voting scheme is based on the reliability measures we test our algorithm on real fingerprint images the experiment results suggest that our enhanced algorithm achieves visibly better noise resistance with modest computation time in comparison with other gradient based methods

combinatorial models of rigidity and renormalization we first introduce the percolation problems associated with the graph theoretical concepts of k l sparsity and make contact with the physical concepts of ordinary and rigidity percolation we then devise a renormalization transformation for k l percolation problems and investigate its domain of validity in particular we show that it allows an exact solution of k l percolation problems on hierarchical graphs for k l 2k we introduce and solve by renormalization such a model which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions depending on the values of the parameters

from rational bubbles to crashes we study and generalize in various ways the model of rational expectation re bubbles introduced by blanchard and watson in the economic literature bubbles are argued to be the equivalent of goldstone modes of the fundamental rational pricing equation associated with the symmetry breaking introduced by non vanishing dividends generalizing bubbles in terms of multiplicative stochastic maps we summarize the result of lux and sornette that the no arbitrage condition imposes that the tail of the return distribution is hyperbolic with an exponent 1 we then outline the main results of malevergne and sornette who extend the re bubble model to arbitrary dimensions d a number d of market time series are made linearly interdependent via d d stochastic coupling coefficients we derive the no arbitrage condition in this context and with the renewal theory for products of random matrices applied to stochastic recurrence equations we extend the theorem of lux and sornette to demonstrate that the tails of the unconditional distributions associated with such d dimensional bubble processes follow power laws with the same asymptotic tail exponent 1 for all assets the distribution of price differences and of returns is dominated by the same power law over an extended range of large returns although power law tails are a pervasive feature of empirical data the numerical value 1 is in disagreement with the usual empirical estimates 3 we then discuss two extensions the crash hazard rate model and the non stationary growth rate model of the re bubble model that provide two ways of reconciliation with the stylized facts of financial data

rigidity percolation in a field rigidity percolation with g degrees of freedom per site is analyzed on randomly diluted erdos renyi graphs with average connectivity gamma in the presence of a field h in the gamma h plane the rigid and flexible phases are separated by a line of first order transitions whose location is determined exactly this line ends at a critical point with classical critical exponents analytic expressions are given for the densities n f of uncanceled degrees of freedom and gamma r of redundant bonds upon crossing the coexistence line gamma r and n f are continuous although their first derivatives are discontinuous we extend for the case of nonzero field a recently proposed hypothesis namely that the density of uncanceled degrees of freedom is a free energy for rigidity percolation analytic expressions are obtained for the energy entropy and specific heat some analogies with a liquid vapor transition are discussed particularizing to zero field we find that the existence of a g 1 core is a necessary condition for rigidity percolation with g degrees of freedom at the transition point gamma c maxwell counting of degrees of freedom is exact on the rigid cluster and on the g 1 rigid core i e the average coordination of these subgraphs is exactly 2g although gamma c the average coordination of the whole system is smaller than 2g gamma c is found to converge to 2g for large g i e in this limit maxwell counting is exact globally as well

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

exponents of operator self similar random fields abstract if x c e t and c h x t have the same finite dimensional distributions for some pair of linear operators e and h we say that the random vector field x t is operator self similar the exponents e and h are not unique in general due to symmetry this paper characterizes the possible set of range exponents h for a given domain exponent and conversely the set of domain exponents e for a given range exponent

application of logical transport to determine the directed and isotropic percolation thresholds the authors present a monte carlo algorithm based on logical transport which determines the effective isotropic percolation and directed percolation thresholds of finite size lattices they apply the algorithm to bond and site directed percolation in two dimensions and determine the asymptotic percolation thresholds by finite size scaling

automatic detection of the boundary of the calcaneus from ultrasound parametric images using an active contour model clinical assessment presents a computerized method for automated detection of the boundary of the os calcis on in vivo ultrasound parametric images using an active dynamic contour model the initial contour defined without user interaction is an iso contour extracted from the textural feature space the contour is deformed through the action of internal and external forces until stability is reached the external forces which characterize image features are a combination of gray level information and second order textural features arising from local cooccurrence matrices the broadband ultrasound attenuation bua value is then averaged within the contour obtained the method was applied to 381 clinical images the contour was correctly detected in the great majority of the cases for the short term reproducibility study the mean coefficient of variation was equal to 1 81 for bua values and 4 95 for areas in the detected region women with osteoporosis had a lower bua than age matched controls p 0 0005 in healthy women the age related decline was 0 45 db mhz yr in the group of healthy post menopausal women years since menopause weight and age were significant predictors of bua these results are comparable to those obtained when averaging bua values in a small region of interest

nonlocal percolation and partial ordering in the dilute baxter wu model the zero temperature limit of the dilute baxter wu model is studied in the context of percolation theory the percolation model describing the propagation of order is identified and shown to possess a nonlocal mechanism for the propagation of that order a monte carlo study of this model is performed using the nonlocal cluster identification algorithm developed by fried and schick 1992 the author also shows that the mechanism responsible for nonlocal percolation allows for the possibility of the propagation of partial order at intermediate impurity concentration a partially ordered phase is found and its structure is discussed

a mean field theory of the elastic granular disc model in two dimensions the author has constructed a stephen type mean field theory for the elastic granular disc model in two dimensions and calculated the mean field value of two crossover exponents phi 1 and phi 2 which describe the ways in which the two point elastic susceptibility and the angle angle correlation function scale with the distance respectively the author has found that phi 1 2 and phi 2 1 the possible relation of phi 1 and phi 2 to the bulk modulus exponent f is discussed

fractional brownian motion a maximum likelihood estimator and its application to image texture fractals have been shown to be useful in characterizing texture in a variety of contexts use of this methodology normally involves measurement of a parameter h which is directly related to fractal dimension in this work the basic theory of fractional brownian motion is extended to the discrete case it is shown that the power spectral density of such a discrete process is only approximately proportional to f a instead of in direct proportion as in the continuous case an asymptotic cramer rao bound is derived for the variance of an estimate of h subsequently a maximum likelihood estimator mle is developed to estimate h it is shown that the variance of this estimator nearly achieves the minimum bound a generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the mle when the discrete fractional brownian process is contaminated with additive gaussian noise the results show that even at signal to noise ratios of 30 db significant errors in estimation of h can result when noise is present the mle is then applied to x ray images of the human calcaneus to demonstrate how the line to line formulation can be applied to the two dimensional case these results indicate that it has strong potential for quantifying texture

a new adaptive framework for unbiased orientation estimation in textured images this paper focuses on directional texture analysis we propose a new approach for orientation estimation this approach hinges on two classes of convolution masks i e the gradient and the valleyness operators we provide a framework for their optimization regarding bias reduction and noise robustness as the gradient and the valleyness operators are complementary we propose a combination named gv joe this combination consists in using the gradient on inflexion pixels the valleyness on crests and valleys and a linear mixture of both elsewhere we implement an adaptive selection of the size of our operators in order to take into account the variations of the texture scale in the image we apply our approach both on synthetic and natural textures these experiments show that when used separately both classes of operators are more accurate than classical derivative approaches in noisy cases the gv joe implementation improves the robustness of our operators without affecting their accuracy moreover compared to well known orientation estimators it gives the best estimates in the most difficult cases i e for high frequency textures and low snr

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

area and length minimizing flows for shape segmentation a number of active contour models have been proposed that unify the curve evolution framework with classical energy minimization techniques for segmentation such as snakes the essential idea is to evolve a curve in two dimensions or a surface in three dimensions under constraints from image forces so that it clings to features of interest in an intensity image the evolution equation has been derived from first principles as the gradient flow that minimizes a modified length functional tailored to features such as edges however because the flow may be slow to converge in practice a constant hyperbolic term is added to keep the curve surface moving in the desired direction we derive a modification of this term based on the gradient flow derived from a weighted area functional with image dependent weighting factor when combined with the earlier modified length gradient flow we obtain a partial differential equation pde that offers a number of advantages as illustrated by several examples of shape segmentation on medical images in many cases the weighted area flow may be used on its own with significant computational savings

fingerprint ridge orientation field reconstruction using the best quadratic approximation by orthogonal polynomials in two discrete variables this paper proposes a novel algorithm for reconstructing the fingerprint orientation field fof the basic idea of the algorithm is to reconstruct the ridge orientation by using the best quadratic approximation by orthogonal polynomials in two discrete variables we first estimate the local region orientation by the linear projection analysis lpa based on the vector set of point gradients and then reconstruct the ridge orientation field using the best quadratic approximation by orthogonal polynomials in two discrete variables in the sine domain in this way we solve the problem that is difficult to accurately extract low quality fingerprint image orientation fields the experiments with the database of fvc 2004 show that compared to the state of the art fingerprint orientation estimation algorithms the proposed method is more accurate and more robust against noise and is able to better estimate the fof of low quality fingerprint images with large areas of noise

self similar anisotropic texture analysis the hyperbolic wavelet transform contribution textures in images can often be well modeled using self similar processes while they may simultaneously display anisotropy the present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of gaussian anisotropic selfsimilar processes it will be first shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2d discrete wavelet transform with the hyperbolic wavelet transform which permits the use of different dilation factors along the horizontal and vertical axes defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized this discrepancy defines a rotation angle second we show that this rotation angle can be jointly estimated third a nonparametric bootstrap based procedure is described which provides confidence intervals in addition to the estimates themselves and enables us to construct an isotropy test procedure which can be applied to a single texture image fourth the robustness and versatility of the proposed analysis are illustrated by being applied to a large variety of different isotropic and anisotropic self similar fields as an illustration we show that a true anisotropy built in self similarity can be disentangled from an isotropic self similarity to which an anisotropic trend has been superimposed

multifractality tests using bootstrapped wavelet leaders multifractal analysis which mostly consists of measuring scaling exponents is becoming a standard technique available in most empirical data analysis toolboxes making use of the most recent theoretical results it is based here on the estimation of the cumulants of the log of the wavelet leaders an elaboration on the wavelet coefficients these log cumulants theoretically enable discrimination between mono and multifractal processes as well as between simple log normal multifractal models and more advanced ones the goal of the present contribution is to design nonparametric bootstrap hypothesis tests aiming at testing the nature of the multifractal properties of stochastic processes and empirical data bootstrap issues together with six declinations of test designs are analyzed their statistical performance significances powers and p values are assessed and compared by means of monte carlo simulations performed on synthetic stochastic processes whose multifractal properties and log cumulants are known theoretically a priori we demonstrate that the joint use of wavelet leaders log cumulants and bootstrap procedures enable us to obtain a powerful tool for testing the multifractal properties of data this tool is practically effective and can be applied to a single observation of data with finite length

critical behaviour of anisotropic superelastic central force percolation the authors study central force percolation on a triangular lattice where the bonds are springs that can freely rotate around the nodes all bonds in one preferred direction are infinitely rigid in the other two directions a proportion p of the springs chosen at random are infinitely rigid while the rest have a finite strength for this specific problem the threshold at which the network becomes infinitely rigid corresponds to the usual bond percolation threshold of a square lattice and is therefore exactly equal to 0 5 they use a transfer matrix algorithm to study the elastic modulus of strips of width ranging from 2 to 32 and length 105 they obtain an estimate of the critical exponent relative to the scaling of the elastic moduli with the strip width 0 99 or 0 03 close to s v for the corresponding isotropic electric problem

rigid animals in three dimensions the number of rigid clusters c n is enumerated for the central force model on a site diluted fcc lattice the exponent vr governing the growth of the radius of gyration of the rigid animal is also calculated it is found that c n approximately n0 333n and vr 0 32 or 0 02

rigidity transition in two dimensional random fiber networks rigidity percolation is analyzed in two dimensional random fibrous networks the model consists of central forces between the adjacent crossing points of the fibers two strategies are used to incorporate rigidity adding extra constraints between second nearest crossing points with a probability p sn and welding individual crossing points by adding there four additional constraints with a probability p weld and thus fixing the angles between the fibers these additional constraints will make the model rigid at a critical probability p sn p sn c and p weld p weld c respectively accurate estimates are given for the transition thresholds and for some of the associated critical exponents the transition is found in both cases to be in the same universality class as that of the two dimensional central force rigidity percolation in diluted lattices

a geometrical interpretation of the chaotic state of inhomogeneous deterministic cellular automata abstract we propose a geometrical interpretation of the chaotic state of inhomogeneous cellular automata from the rules of the cellular automaton we construct a network the percolating phase of this network coincides with the chaotic phase of the cellular automaton we also report numerical tests of these ideas on several cellular automata

encoding of a priori information in active contour models the theory of active contours models the problem of contour recovery as an energy minimization process the computational solutions based on dynamic programming require that the energy associated with a contour candidate can be decomposed into an integral of local energy contributions in this paper we propose a grammatical framework that can model different local energy models and a set of allowable transitions between these models the grammatical encodings are utilized to represent a priori knowledge about the shape of the object and the associated signatures in the underlying images the variability encountered in numerical experiments is addressed with the energy minimization procedure which is embedded in the grammatical framework we propose an algorithmic solution that combines a nondeterministic version of the knuth morris pratt algorithm for string matching with a time delayed discrete dynamic programming algorithm for energy minimization the numerical experiments address practical problems encountered in contour recovery such as noise robustness and occlusion

segmentation of external force field for automatic initialization and splitting of snakes active contours or snakes have been extensively utilized in handling image segmentation and classification problems in traditional active contour models snake initialization is performed manually by users and topological changes such as splitting of the snake cannot be automatically handled in this paper we introduce a new method to solve the snake initialization and splitting problem based on an area segmentation approach the external force field is segmented first and then the snake initialization and splitting can be automatically performed by using the segmented external force field such initialization and splitting produces multiple snakes each of which is within the capture range associated to an object and will be evolved to the object boundary the external force used in this paper is a gradient vector flow with an edge preserving property epgvf which can prevent the snakes from passing over weak boundaries to segment the external force field we represent it with a graph and a graph theory approach can be taken to determine the membership of each pixel experimental results establish the effectiveness of the proposed approach

maximum independent set on diluted triangular lattices core percolation and maximum independent set on random graphs have recently been characterized using the methods of statistical physics here we present a statistical physics study of these problems on bond diluted triangular lattices core percolation critical behavior is found to be consistent with the standard percolation values though there are strong finite size effects a transfer matrix method is developed and applied to find accurate values of the density and degeneracy of the maximum independent set on lattices of limited width but large length an extrapolation of these results to the infinite lattice limit yields high precision results which are tabulated these results are compared to results found using both vertex based and edge based local probability recursion algorithms which have proven useful in the analysis of hard computational problems such as the satisfiability problem

scalar and vectorial percolation in compressed expanded graphite dc electrical conductivity and elastic moduli of cubic samples made of two kinds of compressed expanded graphite are measured as a function of their apparent density different percolation thresholds at which the physical properties under study are found to vanish are determined the accuracy of the values is confirmed by the application of the usual scaling laws above but near these thresholds the corresponding critical exponents are indeed found to be very close to their universal values the relationships between the connectivity dc i e scalar and rigidity dr i e vectorial critical densities are discussed it is shown that the ratio dr dc is always almost equal to 8 5 which fact may be accounted by the so called kirkwood keating kk model to our knowledge it is the first time that such a constant value is observed in real materials the kk model is also consistent with critical exponents of elasticity found in both kind of samples hence compressed expanded graphite appears to behave like a disordered heterogeneous medium in which elastic forces are mostly of central nature but include also bond bending contributions

rigid backbone a new geometry for percolation understood in both cases from the nodes linksblobs picture of percolation clusters in fact it is fair to say that in the vast majority of percolation problems encountered to date even continuum percolation 6 the basic geometric features of the percolation clusters such as the scaling of the number of singly connected bonds are identical and the differences arise only at the level of the dynamics for the class of models of interest here however geometric connection the existence of a bond does not imply complete elastic connection because the number of constraints associated with the existence of a bond is smaller than the number of degrees of freedom associated with the sites it connects the percolation threshold is higher8 than that of the corresponding standard percolation problem thorpe6 has suggested the name rigidity percolation for this class of models distinguishing it from the elasticity percolation universality class mentioned above in this paper we study the simplest rigidity percolation model namely the two dimensional central force model 8 ex

wavelet based estimations of fractional brownian sheet least squares versus maximum likelihood abstract the scaling behavior or self similarity and long range dependence has been studied in numerous fields such as computer telecommunication hydrology and economics and can be characterized by the hurst parameter h fractional brownian sheet plays an important role in modeling the scaling behavior in multi dimensional signals a wavelet based maximum likelihood estimator for the hurst parameter h h 1 h d of fractional brownian sheet is proposed it is asymptotically normal and compared with the wavelet based least squares estimators introduced in the previous article from theoretical analysis and numerical simulation the theoretical results show that the proposed estimator has the same asymptotic covariance as the least squares estimator of which the weight is equal to the number of available wavelet coefficients and the convergence rates of two estimators are both o 1 i 1 d t i t i is sample length in the i th dimension the simulation results show that the proposed estimator performs better than the least squares estimators in bias and costs less runtime than the generalized least squares estimator realized by the two step method

markov random field models for directional field and singularity extraction in fingerprint images a bayesian formulation is proposed for reliable and robust extraction of the directional field in fingerprint images using a class of spatially smooth priors the spatial smoothness allows for robust directional field estimation in the presence of moderate noise levels parametric template models are suggested as candidate singularity models for singularity detection the parametric models enable joint extraction of the directional field and the singularities in fingerprint impressions by dynamic updating of feature information this allows for the detection of singularities that may have previously been missed as well as better aligning the directional field around detected singularities a criteria is presented for selecting an optimal block size to reduce the number of spurious singularity detections the best rates of spurious detection and missed singularities given by the algorithm are 4 9 and 7 1 respectively based on the nist 4 database

deformable contour method a constrained optimization approach in this paper a class of deformable contour methods using a constrained optimization approach of minimizing a contour energy function satisfying an interior homogeneity constraint is proposed the class is defined by any positive potential function describing the contour interior characterization an evolutionary strategy is used to derive the algorithm a similarity threshold tv can be used to determine the interior size and shape of the contour sensitivity and significance of tv and a spreadness measure are also discussed and shown experiments on noisy images and the convergence to a minimum energy gap contour are included the developed method has been applied to a variety of medical images from ct abdominal section mri image slices of brain brain tumor a pig heart ultrasound image sequence to visual blood cell images as the results show the algorithm can be adapted to a broad range of medical images containing objects with vague complex and or irregular shape boundary inhomogeneous and noisy interior and contour with small gaps

identification of rational expectations models abstract this paper deals with the problem of the identification of simultaneous rational expectations re models in the case of re models with current expectations of the endogenous variables the necessary and sufficient conditions for the global identification are derived explicitly in terms of the structural parameters and the linear homogenous identifying restrictions it is shown that in the absence of a priori restrictions on the processes generating the exogenous variables and the disturbances re models and general distributed lag models are observationally equivalent in the case of re models with future expectations of the endogenous variables a general solution that highlights the non uniqueness problem and from which other solutions such as forward or backward solutions can be obtained is derived it is shown that untestable and often quite arbitrary restrictions are needed if re models with future expectations are to be identifiable certain order conditions similar to those obtained for the identification of re models with current expectations are also derived for this case

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

multiple resolution texture analysis and classification textures are classified based on the change in their properties with changing resolution the area of the gray level surface is measured at serveral resolutions this area decreases at coarser resolutions since fine details that contribute to the area disappear fractal properties of the picture are computed from the rate of this decrease in area and are used for texture comparison and classification the relation of a texture picture to its negative and directional properties are also discussed

a statistical test for the time constancy of scaling exponents a statistical test is described for determining if scaling exponents vary over time it is applicable to diverse scaling phenomena including long range dependence and exactly self similar processes in a uniform framework without the need for prior knowledge of the type in question it is based on the special properties of wavelet based estimates of the scaling exponent strongly motivating an idealized inference problem the equality or otherwise of means of independent gaussian variables with known variances a uniformly most powerful invariant test exists for this problem and is described a separate uniformly most powerful invariant test is also given for when the scaling exponent undergoes a level change the power functions of both tests are given explicitly and compared using simulation the effect in practice of deviations from the idealizations made of the statistical properties of the wavelet detail coefficients are analyzed and found to be small the tests inherit the significant robustness and computational advantages of the underlying wavelet based estimator a detailed methodology is given describing its use in practical situations the use and benefits of the test are illustrated on the bellcore ethernet data sets

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

bond diluted rigid animals for central force model an exact enumeration of rigid clusters is analysed using pade approximants the number of bond diluted rigid clusters with n b bonds is found to grow like n theta b b 2 165 or 0 005 n b with theta b 0 988 a value different from that of site diluted rigid animals

continuous force field analysis for generalized gradient vector flow field we propose a modification of the generalized gradient vector flow field techniques based on a continuous force field analysis at every iteration the generalized gradient vector flow method obtains a new improved vector field however the numerical procedure always employs the original image to calculate the gradients used in the source term the basic idea developed in this paper is to use the resulting vector field to obtain an improved edge map and use it to calculate a new gradient based source term the improved edge map is evaluated by new continuous force field analysis techniques inspired by a preceding discrete version the approach leads to a better convergence and better segmentation accuracy as compared to several conventional gradient vector flow type methods

rigid clusters enumeration animal counting techniques suggest that the fraction of rigid animals among all animals with s sites on a triangular lattice varied roughly as s1 2 0 46 or 0 01 s

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

biased motion adaptive temporal filtering for speckle reduction in echocardiography describes a new fully motion adaptive spatio temporal filtering technique to reduce the speckle in ultrasound images the advantages of this approach are demonstrated in echocardiographic boundary detection and in comparison with other techniques the first stage of many automated echocardiographic image interpretation schemes is filtering to reduce the amount of speckle noise the authors show how the two dimensional least mean squares tdlms filter can be configured as a motion compensated filter for a time sequence of ultrasound images that eliminates the blurring associated with direct averaging for an image corrupted by multiplicative speckle noise the mode of the intensity distribution approximates the maximum likelihood estimator in consequence the temporal filter s output is biased towards the mode from the mean using information contained within the speckle itself a new adaptive algorithm for controlling the filter s convergence is also included to evaluate performance application to simulated phantom and an in vivo test sequence of the carotid artery are considered in comparison with other techniques the effect of filtering on edges is of great importance as these are used by subsequent image interpretation schemes quantitative measurements demonstrate the effectiveness of the biased tdlms filter for both noise reduction and edge preservation echocardiographic images have a high noise content and suffer from poor contrast despite this challenging environment the biased tdlms filter is shown to produce images that are better inputs for subsequent feature extraction the benefits for echocardiographic images are highlighted by considering the problems of mitral valve analysis and extraction of the left atrium boundary

an efficient algorithm for testing the generic rigidity of graphs in the plane given a structure made up of n sites connected by b bars the problem of recognizing which subsets of sites form rigid units is not a trivial one because of the non local character of rigidity in central force systems even though this is a very old problem of statics no simple algorithms are available for it so the most usual approach has been to solve the elastic equations which is very time consuming for large systems recently an integer algorithm was proposed for this problem in two dimensions using matching methods from graph theory and laman s theorem for two dimensional graphs the method is relatively simple but its time complexity grows as in the worst case and almost as fast on practical cases so that an improvement is highly desirable in this paper we describe a further elaboration of that procedure which relies upon the description of the system as a collection of rigid bodies connected by bars instead of sites connected by bars sets of rigidly connected objects are replaced by a unique body and this is done recursively as more rigid connections between bodies are discovered at larger scales as a consequence of this rescaling transformation our algorithm has much improved average behaviour even when its worst case complexity remains the time complexity of the body bar algorithm is found to scale as for the randomly diluted triangular lattice while the original site bar version scales as for the same problem

cagan type rational expectation model on complex discrete time domains abstract in this article we derive a solution for a linear stochastic model on a complex time domain in this type of models the time domain can be any collection of points along the real number line so these models are suitable for problems where events do not occur at evenly spaced time intervals we present examples based on well known results from economics and finance to illustrate how our model generalizes and extends conventional dynamic models

detection and inpainting of facial wrinkles using texture orientation fields and markov random field modeling facial retouching is widely used in media and entertainment industry professional software usually require a minimum level of user expertise to achieve the desirable results in this paper we present an algorithm to detect facial wrinkles imperfection we believe that any such algorithm would be amenable to facial retouching applications the detection of wrinkles imperfections can allow these skin features to be processed differently than the surrounding skin without much user interaction for detection gabor filter responses along with texture orientation field are used as image features a bimodal gaussian mixture model gmm represents distributions of gabor features of normal skin versus skin imperfections then a markov random field model is used to incorporate the spatial relationships among neighboring pixels for their gmm distributions and texture orientations an expectation maximization algorithm then classifies skin versus skin wrinkles imperfections once detected automatically wrinkles imperfections are removed completely instead of being blended or blurred we propose an exemplar based constrained texture synthesis algorithm to inpaint irregularly shaped gaps left by the removal of detected wrinkles imperfections we present results conducted on images downloaded from the internet to show the efficacy of our algorithms

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

anisotropic discrete dual tree wavelet transform for improved classification of trabecular bone this paper deals with a new anisotropic discrete dual tree wavelet transform addtwt to characterize the anisotropy of bone texture more specifically we propose to extend the conventional discrete dual tree wavelet transform ddtwt by using the anisotropic basis functions associated with the hyperbolic wavelet transform instead of isotropic spectrum supports a texture classification framework is adopted to assess the performance of the proposed transform the generalized gaussian distribution is used to model the distribution of the sub band coefficients the estimated vector of parameters for each image is then used as input for the support vector machine classifier experiments were conducted on synthesized anisotropic fractional brownian motion fields and on a real database composed of osteoporotic patients and control cases results show that the addtwt outperforms most of the competing anisotropic transforms with an area under curve rate of 93

motion field and optical flow qualitative properties it is shown that the motion field the 2 d vector field which is the perspective projection on the image plane of the 3 d velocity field of a moving scene and the optical flow defined as the estimate of the motion field which can be derived from the first order variation of the image brightness pattern are in general different unless special conditions are satisfied therefore dense optical flow is often ill suited for computing structure from motion and for reconstructing the 3 d velocity field by algorithms which require a locally accurate estimate of the motion field a different use of the optical flow is suggested it is shown that the smoothed optical flow and the motion field can be interpreted as vector fields tangent to flows of planar dynamical systems stable qualitative properties of the motion field which give useful informations about the 3 d velocity field and the 3 d structure of the scene usually can be obtained from the optical flow the idea is supported by results from the theory of structural stability of dynamical systems

pixel level singular point detection from multi scale gaussian filtered orientation field singular point as a global feature plays an important role in fingerprint recognition inconsistent detection of singular points apparently gives an affect to fingerprint alignment classification and verification accuracy this paper proposes a novel approach to pixel level singular point detection from the orientation field obtained by multi scale gaussian filters initially a robust pixel level orientation field is estimated by a multi scale averaging framework then candidate singular points in pixel level are extracted from the complex angular gradient plane derived directly from the pixel level orientation field the candidate singular points are finally validated via a cascade framework comprised of nested poincare indices and local feature based classification experimental results over the fvc 2000 db2 confirm that the proposed method achieves robust and accurate orientation field estimation and consistent pixel level singular point detection the experimental results exhibit a low computational cost with better performance thus the proposed method can be employed in real time fingerprint recognition

wavelet based texture retrieval using generalized gaussian density and kullback leibler distance we present a statistical view of the texture retrieval problem by combining the two related tasks namely feature extraction fe and similarity measurement sm into a joint modeling and classification scheme we show that using a consistent estimator of texture model parameters for the fe step followed by computing the kullback leibler distance kld between estimated models for the sm step is asymptotically optimal in term of retrieval error probability the statistical scheme leads to a new wavelet based texture retrieval method that is based on the accurate modeling of the marginal distribution of wavelet coefficients using generalized gaussian density ggd and on the existence a closed form for the kld between ggds the proposed method provides greater accuracy and flexibility in capturing texture information while its simplified form has a close resemblance with the existing methods which uses energy distribution in the frequency domain to identify textures experimental results on a database of 640 texture images indicate that the new method significantly improves retrieval rates e g from 65 to 77 compared with traditional approaches while it retains comparable levels of computational complexity

recursive solution methods for dynamic linear rational expectations models abstract this paper develops recursive solution methods for linear rational expectations models the underlying structural model is transformed into a state space representation which can then be used to solve the model and to form the gaussian likelihood function the recursive solution method has several advantages over other approaches first the set of solutions to the model are summarized by a set of parameters that appear in the state space representation but are unspecified by the structural model next the likelihood function is formed as a byproduct of the solution to the model finally modifications in the likelihood function necessary to incorporate complications arising from temporal aggregation dynamic errors in variables etc are straightforward

kalman filter approach to solution of rational expectations models abstract the solution of forward looking dynamical models for economical systems consists in finding a suitable expression of the forcing term describing the agents expectations on the future behaviour of the involved economical variables in this paper such a control function is estimated by a kalman filtering technique which allows us to exploit just the current informations the solution obtained is shown to be an asymptotically stationary process with finite steady state covariance

statistical region snake based segmentation adapted to different physical noise models algorithms for object segmentation are crucial in many image processing applications during past years active contour models snakes have been widely used for finding the contours of objects this segmentation strategy is classically edge based in the sense that the snake is driven to fit the maximum of an edge map of the scene we propose a region snake approach and we determine fast algorithms for the segmentation of an object in an image the algorithms developed in a maximum likelihood approach are based on the calculation of the statistics of the inner and the outer regions defined by the snake it has thus been possible to develop optimal algorithms adapted to the random fields which describe the gray levels in the input image if we assume that their probability density function family are known we demonstrate that this approach is still efficient when no boundary s edge exists in the image we also show that one can obtain fast algorithms by transforming the summations over a region for the calculation of the statistics into summations along the boundary of the region finally we will provide numerical simulation results for different physical situations in order to illustrate the efficiency of this approach

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

elastic property of the self avoiding random walk calculates the end to end elastic susceptibility for the bond bending model on the self avoiding random walk the numerical result shows clearly that the central force term is irrelevant when the bond bending term is present the result also indicates that when the elastic constant of the bond bending term is set equal to infinity the elastic network is governed by the conductivity exponent of the random resistor network

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

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

percolation in media with columnar disorder we study a generalization of site percolation on a simple cubic lattice where not only single sites are removed randomly but also entire parallel columns of sites we show that typical clusters near the percolation transition are very anisotropic with different scaling exponents for the sizes parallel and perpendicular to the columns below the critical point there is a griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power law tails with continuously varying non universal powers this region is very similar to the griffiths phase in subcritical directed percolation with frozen disorder in the preferred direction and the proof follows essentially the same arguments as in that case but in contrast to directed percolation in disordered media the number of active growth sites in a growing cluster at criticality shows a power law while the probability of a cluster to continue to grow shows logarithmic behavior

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

the use of optical flow for the analysis of non rigid motions this paper analysis the 2d motion field on the image plane produced by the 3d motion of a plane undergoing simple deformations when the deformation can be represented by a planar linear vector field the projected vector field i e the 2d motion field of the deformation is at most quadratic this 2d motion field has one singular point with eigenvalues identical to those of the singular point describing the deformation as a consequence the nature of the singular point of the deformation is a projective invariant when the plane moves and experiences a linear deformation at the same time the associated 2d motion field is at most quadratic with at most 3 singular points in the case of a normal rototranslation i e when the angular velocity is normal to the plane and of a linear deformation the 2d motion field has one singular point and substantial information on the rigid motion and on the deformation can be recovered from it experiments with image sequences of planes moving and undergoing linear deformations show that the proposed analysis can provide accurate results in addition experiments with deformable objects such as water oil textiles and rubber show that the proposed approach can provide information on more general 3d deformations

detecting singular patterns in 2d vector fields using weighted laurent polynomial in this paper we propose a method for detecting patterns of interest in vector fields our method detects patterns in a scale and rotation invariant manner it works by approximating the vector field data locally using a laurent polynomial weighted by radial basis functions the proposed representation is able to model both analytic and non analytic flow fields invariance to scale and rotation is achieved by combining the linearity properties of the model coefficients and a scale space parameter of the radial basis functions promising detection results are obtained on a variety of fluid flow sequences

comparison of rigidity and connectivity percolation in two dimensions using a recently developed algorithm for generic rigidity of two dimensional graphs we analyze rigidity and connectivity percolation transitions in two dimensions on lattices of linear size up to l 4096 we compare three different universality classes the generic rigidity class the connectivity class and the generic open quotes braced square net close quotes gbsn we analyze the spanning cluster density p sub infinity the backbone density p sub b and the density of dangling ends p sub d in the generic rigidity gr and connectivity cases the load carrying component of the spanning cluster the backbone is ital fractal at p sub c so that the backbone density behaves as b approximately p minus p sub c sup beta sup prime for p gt p sub c we estimate beta sub gr sup prime 0 25 plus minus 0 02 for generic rigidity and beta sub c sup prime 0 467 plus minus 0 007 for the connectivity case we find the correlation length exponents nu sub gr 1 16 plus minus 0 03 for generic rigidity compared to the exact value for connectivity nu sub c 4 3 in contrast the gbsn undergoes a first order rigidity transition with the backbone density being extensive at p sub c and undergoing a jump discontinuity on reducing ital p across the transition we define a model which tunes continuously between the gbsn and gr classes and show that the gr class is typical copyright ital 1999 italmore the american physical society less

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

rigidity percolation by next nearest neighbor bonds on generic and regular isostatic lattices we study rigidity percolation transitions in two dimensional central force isostatic lattices including the square and the kagome lattices as next nearest neighbor bonds braces are randomly added to the system in particular we focus on the differences between regular lattices which are perfectly periodic and generic lattices with the same topology of bonds but whose sites are at random positions in space we find that the regular square and kagome lattices exhibit a rigidity percolation transition when the number of braces is llnl where l is the linear size of the lattice this transition exhibits features of both first order and second order transitions the whole lattice becomes rigid at the transition and a diverging length scale also exists in contrast we find that the rigidity percolation transition in the generic lattices occur when the number of braces is very close to the number obtained from maxwell s law for floppy modes which is l the transition in generic lattices is a very sharp first order like transition at which the addition of one brace connects all small rigid regions in the bulk of the lattice leaving only floppy modes on the edge we characterize these transitions using numerical simulations and develop analytic theories capturing each transition our results relate to other interesting problems including jamming and bootstrap percolation

1 d expansion for k core percolation the physics of k core percolation pertains to those systems whose constituents require a minimum number of k connections to each other in order to participate in any clustering phenomenon examples of such a phenomenon range from orientational ordering in solid ortho para mathrm h 2 mixtures to the onset of rigidity in bar joint networks to dynamical arrest in glass forming liquids unlike ordinary k 1 and biconnected k 2 percolation the mean field k ensuremath geqslant 3 core percolation transition is both continuous and discontinuous i e there is a jump in the order parameter accompanied with a diverging length scale to determine whether or not this hybrid transition survives in finite dimensions we present a 1 d expansion for k core percolation on the d dimensional hypercubic lattice we show that to order 1 d 3 the singularity in the order parameter and in the susceptibility occur at the same value of the occupation probability this result suggests that the unusual hybrid nature of the mean field k core transition survives in high dimensions

computerized flow field analysis oriented texture fields an approach to the solution of signal to symbol transformation in the domain of flow fields such as oriented texture fields and velocity vector fields is discussed the authors use the geometric theory of differential equations to derive a symbol set based on the visual appearance of phase portraits which are a geometric representation of the solution curves of a system of differential equations they also provide the computational framework to start with a given flow field and derive its symbolic representation specifically they segment the given texture derive its symbolic representation and perform a quantitative reconstruction of the salient features of the original texture based on the symbolic descriptors results of applying this technique to several real texture images are presented this technique is useful in describing complex flow visualization pictures defects in lumber processing defects in semiconductor wafer inspection and optical flow fields

region based strategies for active contour models the variational method has been introduced by kass et al 1987 in the field of object contour modeling as an alternative to the more traditional edge detection edge thinning edge sorting sequence since the method is based on a pre processing of the image to yield an edge map it shares the limitations of the edge detectors it uses in this paper we propose a modified variational scheme for contour modeling which uses no edge detection step but local computations instead only around contour neighborhoods as well as an anticipating strategy that enhances the modeling activity of deformable contour curves many of the concepts used were originally introduced to study the local structure of discontinuity in a theoretical and formal statement by leclerc zucker 1987 but never in a practical situation such as this one the first part of the paper introduces a region based energy criterion for active contours and gives an examination of its implications as compared to the gradient edge map energy of snakes then a simplified optimization scheme is presented accounting for internal and external energy in separate steps this leads to a complete treatment which is described in the last sections of the paper 4 and 5 the optimization technique used here is mostly heuristic and is thus presented without a formal proof but is believed to fill a gap between snakes and other useful image representations such as split and merge regions or mixed line labels image fields

systematic methods for the computation of the directional fields and singular points of fingerprints the first subject of the paper is the estimation of a high resolution directional field of fingerprints traditional methods are discussed and a method based on principal component analysis is proposed the method not only computes the direction in any pixel location but its coherence as well it is proven that this method provides exactly the same results as the averaged square gradient method that is known from literature undoubtedly the existence of a completely different equivalent solution increases the insight into the problem s nature the second subject of the paper is singular point detection a very efficient algorithm is proposed that extracts singular points from the high resolution directional field the algorithm is based on the poincare index and provides a consistent binary decision that is not based on postprocessing steps like applying a threshold on a continuous resemblance measure for singular points furthermore a method is presented to estimate the orientation of the extracted singular points the accuracy of the methods is illustrated by experiments on a live scanned fingerprint database

the bond bending model in three dimensions the author discusses the bond bending model in three dimensions he argues that for this model loops are very important in all length scales and the rigidity percolation is non local exhibiting similar behaviour to the central force model

exact relations between elastic and electrical response of d dimensional percolating networks with angle bending forces arguments are presented to demonstrate that exact equality relations exist between the critical exponents which characterize the macroscopic conductivity e and the macroscopic elastic stiffness moduli c e of percolating systems of any dimensionality using the notation e p t c e p t for the critical behavior of a randomly diluted system slightly above the percolation threshold p c p p p c 0 and e p s c e p s for the critical behavior of a random mixture of normal and perfectly conducting or normal and perfectly rigid constituents slightly below that threshold p p p c 0 we show that t t 2 and s s where is the percolation correlation length critical exponent p p 0

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

vector field analysis for oriented patterns presents a method based on the properties of vector fields for the estimation of a set of symbolic descriptors node saddle star node improper node center and spiral from linear orientation fields planar first order phase portraits are used to model the linear orientation fields a weighted linear estimator is developed to estimate linear phase portraits using only the flow orientation a classification scheme for planar first order phase portraits based on their local properties curl divergence and deformation is developed the authors present results of experiments on noise added synthetic flow patterns and real oriented textures

rational expectations in dynamic linear models analysis of the solutions in this paper we analyze the solutions of linear econometric models with rational expectations more precisely we describe in detail the set of all the solutions in particular this set is shown to be much larger than the sets previously considered we also study various criteria of selection in this set of solutions and we examine to what extent these criteria redtiuce the set of the solutions

the perceptual organization of texture flow a contextual inference approach locally parallel dense patterns sometimes called texture flows define a perceptually coherent structure of particular significance to perceptual organization we argue that with applications ranging from image segmentation and edge classification to shading analysis and shape interpretation texture flows deserve attention equal to edge segment grouping and curve completion this paper develops the notion of texture flow from a geometrical point of view to argue that local measurements of such structures must incorporate two curvatures we show how basic theoretical considerations lead to a unique model for the local behavior of the flow and to a notion of texture flow good continuation this in turn translates to a specification of consistency constraints between nearby flow measurements which we use for the computation of globally piecewise coherent structure through the contextual framework of relaxation labeling we demonstrate the results on synthetic and natural images

extracting image orientation feature by using integration operator this paper presents an orientation operator to extract image local orientation features we show that a proper employment of image integration leads to an unbiased orientation estimate based on which an orientation operator is proposed the resulting discrete operator has flexibility in the scale selection as the scale change does not violate the bias minimization criteria an analytical formula is developed to compare orientation biases of various discrete operators the proposed operator shows lower bias than eight well known gradient operators experiments further demonstrate higher orientation accuracy of the proposed operator than these gradient operators

vascular segmentation of phase contrast magnetic resonance angiograms based on statistical mixture modeling and local phase coherence in this paper we present an approach to segmenting the brain vasculature in phase contrast magnetic resonance angiography pc mra according to our prior work we can describe the overall probability density function of a pc mra speed image as either a maxwell uniform mu or maxwell gaussian uniform mgu mixture model an automatic mechanism based on kullback leibler divergence is proposed for selecting between the mgu and mu models given a speed image volume a coherence measure namely local phase coherence lpc which incorporates information about the spatial relationships between neighboring flow vectors is defined and shown to be more robust to noise than previously described coherence measures a statistical measure from the speed images and the lpc measure from the phase images are combined in a probabilistic framework based on the maximum a posteriori method and markov random fields to estimate the posterior probabilities of vessel and background for classification it is shown that segmentation based on both measures gives a more accurate segmentation than using either speed or flow coherence information alone the proposed method is tested on synthetic flow phantom and clinical datasets the results show that the method can segment normal vessels and vascular regions with relatively low flow rate and low signal to noise ratio e g aneurysms and veins