dynamical behavior of lotka volterra competition systems non autonomous bistable case and the effect of telegraph noise this article is concerned with the study of trajectory behavior of lotka volterra competition bistable systems and systems with telegraph noises we proved that for bistable systems there exists a unique solution bounded above and below by positive constants the oscillatory situation of systems with telegraph noises is pointed out

bayesian image restoration an application to edge preserving surface recovery bayesian methods for recovering a 2 d surface are discussed it is assumed that there is a textural image that can be modeled by a markov random field and that the original surface is composed of different surfaces each of which is associated with one textural state both parametric and nonparametric methods are used to enforce smoothness of these surfaces iterative procedures are examined for simultaneous restoration of the textural image and estimation of underlying parameters from the estimated textural image and the estimated parameters an estimate for the original surface is obtained two illustrative examples are presented

binary restoration of thin objects in multidimensional imagery we present a method for restoration of noisy tomographic images for detecting thin objects such as explosives use of a weighted mean square estimate optimizes the solution to place emphasis on the infrequent but significant local structure associated with thin objects experimental results show successful restoration at very high noise levels

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

globally convergent iterative numerical schemes for nonlinear variational image smoothing and segmentation on a multiprocessor machine we investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel a general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown we characterize various edge preserving regularization methods from the image processing literature involving auxiliary variables as special cases of this general framework as a by product global convergence can be proven under conditions slightly weaker than these stated in the literature efficient krylov subspace solvers for the linear parts of these schemes have been implemented on a multiprocessor machine the performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed up factors are reported

edge preserving tomographic reconstruction with nonlocal regularization tomographic image reconstruction using statistical methods can provide more accurate system modeling statistical models and physical constraints than the conventional filtered backprojection fbp method because of the ill posedness of the reconstruction problem a roughness penalty is often imposed on the solution to control noise to avoid smoothing of edges which are important image attributes various edge preserving regularization methods have been proposed most of these schemes rely on information from local neighborhoods to determine the presence of edges in this paper we propose a cost function that incorporates nonlocal boundary information into the regularization method we use an alternating minimization algorithm with deterministic annealing to minimize the proposed cost function jointly estimating region boundaries and object pixel values we apply variational techniques implemented using level sets methods to update the boundary estimates then using the most recent boundary estimate we minimize a space variant quadratic cost function to update the image estimate for the positron emission tomography transmission reconstruction application we compare the bias variance tradeoff of this method with that of a conventional penalized likelihood algorithm with local huber roughness penalty

pedestrian detection in images via cascaded l1 norm minimization learning method a new cascaded l1 norm minimization learning clml method for pedestrian detection in images is proposed in this paper the proposed clml method which is designed from the perspective of vapnic s theory in the statistical learning integrates feature selection with classifier construction via solving meaningful optimization models the method incorporates three stages weak classifier learning strong classifier learning and the cascaded classifier construction in the weak classifier learning the l1 norm minimization learning lml and min max penalty function model are presented in the strong classifier learning an integer programming optimization model is built equaling the reformulation of lml in the integer space finally a cascade of lml classifiers is constructed to promote detection speed during the classifier learning and pedestrian detection histograms of oriented gradients of variable sized blocks v hog are used as feature descriptors experimental results on the inria and sdl human datasets show that the proposed method achieves a higher performance and speed than the state of the art methods

message passing approach for recurrent state epidemic models on networks epidemic processes are common out of equilibrium phenomena of broad interdisciplinary interest recently dynamic message passing dmp has been proposed as an efficient algorithm for simulating epidemic models on networks and in particular for estimating the probability that a given node will become infectious at a particular time to date dmp has been applied exclusively to models with one way state changes as opposed to models like sis and sirs where nodes can return to previously inhabited states because many real world epidemics can exhibit such recurrent dynamics we propose a dmp algorithm for complex recurrent epidemic models on networks our approach takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source and thus avoids echo chamber effects where a pair of adjacent nodes each amplify the probability that the other is infectious we demonstrate that this approach well approximates results obtained from monte carlo simulation and that its accuracy is often superior to the pair approximation which also takes second order correlations into account moreover our approach is more computationally efficient than the pair approximation especially for complex epidemic models the number of variables in our dmp approach grows as 2mk where m is the number of edges and k is the number of states as opposed to mk 2 for the pair approximation we suspect that the resulting reduction in computational effort as well as the conceptual simplicity of dmp will make it a useful tool in epidemic modeling especially for high dimensional inference tasks

threshold dynamics and ergodicity of an sirs epidemic model with markovian switching abstract this work studies the threshold dynamics and ergodicity of a stochastic sirs epidemic model with the disease transmission rate driven by a semi markov process the semi markov process used in this paper for describing a randomly changing environment is a very large extension of the most common markov regime switching process we define a basic reproduction number for the semi markov regime switching environment and show that its position with respect to 1 determines the extinction or persistence of the disease in the case of disease persistence we give mild sufficient conditions for ensuring the existence and absolute continuity of the invariant probability measure under the same conditions we also prove the global attractivity of the limit set of the system and the convergence in total variation norm of the transition probability to the invariant measure compared with the existing results in the markov regime switching environment the results generalized require almost no additional conditions

dynamics of a multigroup sis epidemic model with standard incidence rates and markovian switching abstract in this paper we investigate a multigroup sis epidemic model with standard incidence rates and markovian switching first of all we establish sufficient conditions for extinction of the diseases then we obtain sufficient conditions for persistence in the mean of the diseases in addition in the case of persistence we obtain sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic lyapunov function with regime switching

dynamics in a stochastic heroin model with seasonal variation abstract in this paper a stochastic non autonomous heroin model is formulated we obtain sufficient conditions for extinction and permanence in mean with probability one of the positive solutions in addition we prove that there exists at least one positive periodic solution under some conditions finally numerical simulations are performed to illustrate our theoretical results

a stochastic model of aids and condom use in this paper we introduce stochasticity into a model of aids and condom use via the technique of parameter perturbation which is standard in stochastic population modelling we show that the model established in this paper possesses non negative solutions as desired in any population dynamics we also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system

ergodic property of a lotka volterra predator prey model with white noise higher order perturbation under regime switching abstract in this paper we investigate a classical lotka volterra predator prey model with telephone noise and a higher order perturbation of white noise the existence of a unique positive solution is discussed and sufficient conditions for the existence of an ergodic stationary distribution is established some simulation figures are presented to illustrate the analytical findings

gauss markov measure field models for low level vision we present a class of models derived from classical discrete markov random fields that may be used for the solution of ill posed problems in image processing and in computational vision they lead to reconstruction algorithms that are flexible computationally efficient and biologically plausible to illustrate their use we present their application to the reconstruction of the dominant orientation and direction fields to the classification of multiband images and to image quantization and filtering

modal matching for correspondence and recognition modal matching is a new method for establishing correspondences and computing canonical descriptions the method is based on the idea of describing objects in terms of generalized symmetries as defined by each object s eigenmodes the resulting modal description is used for object recognition and categorization where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects in general modes provide a global to local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison in contrast to previous techniques which required correspondence to be computed with an initial or prototype shape modal matching utilizes a new type of finite element formulation that allows for an object s eigenmodes to be computed directly from available image information this improved formulation provides greater generality and accuracy and is applicable to data of any dimensionality correspondence results with 2d contour and point feature data are shown and recognition experiments with 2d images of hand tools and airplanes are described

stability of a stochastic sir system abstract we propose a stochastic sir model with or without distributed time delay and we study the stability of disease free equilibrium the numerical simulation of the stochastic sir model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found

optimal signal design for multi parameter estimation problems in this paper the optimal stochastic design of multiple parameters is investigated for an array of fixed estimators both in the absence and presence of an average power constraint two different performance criteria are considered the total bayes risk criterion and the maximum bayes risk criterion it is obtained that in the presence of k parameters and the average power constraint the optimal stochastic parameter design results in randomization time sharing among at most two and k 1 different signals for the total bayes risk and the maximum bayes risk criteria respectively the average transmitted signal powers corresponding to the optimal parameter design approaches are specified and the characterization of the optimal approaches is provided in various scenarios in addition sufficient conditions are derived to specify when the stochastic parameter design or the deterministic parameter design is optimal finally numerical examples are presented to investigate the theoretical results and to illustrate performance improvements achieved via the proposed approaches

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

stationary distribution and extinction of sir model with nonlinear incident rate under markovian switching abstract taking into account of both white and colored noises a stochastic epidemic model with nonlinear incident rate under regime switching is formulated based on this model we investigate the dynamic behaviors such as ergodicity and extinction of the sir model with beddington deangelis incidence rate and markov switching first we study the existence of the unique positive solution of system 1 3 secondly by using lyapunov functions we prove that the system has a ergodic stationary distribution under certain sufficient conditions then we obtain the conditions for extinction finally numerical simulations are employed to illustrate our theoretical analysis

feature guided biased gaussian mixture model for image matching in this article we propose a feature guided biased gaussian mixture model fgbg for image matching we formulate the matching task as a maximum a posteriori map problem by seeing one point set as the centroid of a gaussian mixture model gmm and the other point set as the data a thin plate spline tps transformation between the two point sets is learnt so that the gmm can best fit the data our main contribution is to assign each gaussian mixture component a different weight this is where our model differs from the traditional self governed balanced gaussian mixture model sgbg whose gaussian mixture components have equal coefficients the new weight is defined as a value related to feature similarity which can be computed by simply decomposing a distance matrix in the feature space in this way both feature similarity and spatial arrangement are considered the feature descriptor is introduced as a reasonable prior to guide the matching and the spatial transformation offers a global constraint so that local ambiguity can be alleviated we solve this map problem in a framework similar to 16 in which deterministic annealing and the expectation maximization em algorithms are used we show that our fgbg algorithm is robust to outliers deformation and rotation extensive experiments on self collected and the latest open access data sets show that fgbg can boost the number of correct matches

optimal noise benefits in neyman pearson and inequality constrained statistical signal detection we present theorems and an algorithm to find optimal or near optimal ldquostochastic resonancerdquo sr noise benefits for neyman pearson hypothesis testing and for more general inequality constrained signal detection problems the optimal sr noise distribution is just the randomization of two noise realizations when the optimal noise exists for a single inequality constraint on the average cost the theorems give necessary and sufficient conditions for the existence of such optimal sr noise in inequality constrained signal detectors there exists a sequence of noise variables whose detection performance limit is optimal when such noise does not exist another theorem gives sufficient conditions for sr noise benefits in neyman pearson and other signal detection problems with inequality cost constraints an upper bound limits the number of iterations that the algorithm requires to find near optimal noise the appendix presents the proofs of the main results

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

noise enhanced parameter estimation this paper investigates the phenomenon of noise enhanced systems for a general parameter estimation problem when the estimator is fixed and known the estimation performance before and after the addition of noise are evaluated performance comparisons are made between the original estimators and noise enhanced estimators based on different criteria the form of the optimal noise probability density function pdf is determined the results are further extended to the general case where the noise is introduced to the system via a transformation for the case where the estimator is fixed and unknown approaches are also proposed to find the optimum noise finally two illustrative examples are presented where the performance comparison is made between the optimal noise modified estimator and gaussian noise modified estimator

optimal stochastic parameter design for estimation problems in this study the aim is to perform optimal stochastic parameter design in order to minimize the cost of a given estimator optimal probability distributions of signals corresponding to different parameters are obtained in the presence and absence of an average power constraint it is shown that the optimal parameter design results in either a deterministic signal or a randomization between two different signal levels in addition sufficient conditions are obtained to specify the cases in which improvements over the deterministic parameter design can or cannot be achieved via the stochastic parameter design numerical examples are presented in order to provide illustrations of theoretical results

dynamics of a stochastic lotka volterra model perturbed by white noise abstract this paper continues the study of mao et al investigating two aspects of the equation d x t diag x 1 t x n t b a x t d t x t d w t t 0 the first of these is to slightly improve results in x mao s sabais e renshaw asymptotic behavior of stochastic lotka volterra model j math anal 287 2003 141 156 concerning with the upper growth rate of the total quantity i 1 n x i t of species by weakening hypotheses posed on the coefficients of the equation the second aspect is to investigate the lower growth rate of the positive solutions by using lyapunov function technique and using a changing time method we prove that the total quantity i 1 n x i t always visits any neighborhood of the point 0 and we simultaneously give estimates for this lower growth rate

removal of compression artifacts using projections onto convex sets and line process modeling we present a new image recovery algorithm to remove in addition to blocking ringing artifacts from compressed images and video this new algorithm is based on the theory of projections onto convex sets pocs a new family of directional smoothness constraint sets is defined based on line processes modeling of the image edge structure the definition of these smoothness sets also takes into account the fact that the visibility of compression artifacts in an image is spatially varying to overcome the numerical difficulty in computing the projections onto these sets a divide and conquer dac strategy is introduced according to this strategy new smoothness sets are derived such that their projections are easier to compute the effectiveness of the proposed algorithm is demonstrated through numerical experiments using motion picture expert group based mpeg based coders decoders codecs

the application of mean field theory to image motion estimation previously markov random field mrf model based techniques have been proposed for image motion estimation since motion estimation is usually an ill posed problem various constraints are needed to obtain a unique and stable solution the main advantage of the mrf approach is its capacity to incorporate such constraints for instance motion continuity within an object and motion discontinuity at the boundaries between objects in the mrf approach motion estimation is often formulated as an optimization problem and two frequently used optimization methods are simulated annealing sa and iterative conditional mode icm although the sa is theoretically optimal in the sense of finding the global optimum it usually takes many iterations to converge the icm on the other hand converges quickly but its results are often unsatisfactory due to its hard decision nature previously the authors have applied the mean field theory to image segmentation and image restoration problems it provides results nearly as good as sa but with much faster convergence the present paper shows how the mean field theory can be applied to mrf model based motion estimation this approach is demonstrated on both synthetic and real world images where it produced good motion estimates

modelling the effect of telegraph noise in the sirs epidemic model using markovian switching abstract we discuss the effect of introducing telegraph noise which is an example of an environmental noise into the susceptible infectious recovered susceptible sirs model by examining the model using a finite state markov chain mc first we start with a two state mc and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence we then explain how the results can be generalised to a finite state mc the results for the sir susceptible infectious removed model with markovian switching ms are a special case numerical simulations are produced to confirm our theoretical results

an edge based algorithm for discontinuity adaptive color image smoothing abstract we present a new scheme to increase the performance of edge preserving image smoothing algorithm from the parameter tuning of a markov random field mrf function this method is based on an automatic control of the image smoothing strength in the mrf function in which the parameter control of the function depends on edge magnitude resulted from discontinuities of image intensity without any binary decision for the edge magnitude direct use of full edge magnitude could improve the performance of discontinuity preserving image smoothing technique

noise enhancement in robust estimation of location in this paper we investigate the noise benefits to maximum likelihood type estimators m estimator for the robust estimation of a location parameter two distinct noise benefits are shown to be accessible under these conditions with symmetric heavy tailed noise distributions the asymptotic efficiency of the estimation can be enhanced by injecting extra noise into the m estimators with an asymmetric contaminated noise model having a convex cumulative distribution function we demonstrate that addition of noise can reduce the maximum bias of the median estimator these findings extend the analysis of stochastic resonance effects for noise enhanced signal and information processing

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

genetic algorithms for ambiguous labelling problems abstract consistent labelling problems frequently have more than one solution most work in the field has aimed at disambiguating early in the interpretation process using only local evidence this paper starts with a review of the literature on labelling problems and ambiguity based on this review we propose a strategy for simultaneously extracting multiple related solutions to the consistent labelling problem in a preliminary experimental study we show that an appropriately modified genetic algorithm is a robust tool for finding multiple solutions to the consistent labelling problem these solutions are related by common labellings of the most strongly constrained junctions we have proposed three run time measures of algorithm performance the maximum fitness of the genetic algorithm s population its shannon entropy and the total hamming distance between its distinct members the results to date indicate that when the shannon entropy falls below a certain threshold new solutions are unlikely to emerge and that most of the diversity in the population disappears within the first few generations

signal recovery with cost constrained measurements we are concerned with the problem of optimally measuring an accessible signal under a total cost constraint in order to estimate a signal which is not directly accessible an important aspect of our formulation is the inclusion of a measurement device model where each device has a cost depending on the number of amplitude levels that the device can reliably distinguish we also assume that there is a cost budget so that it is not possible to make a high amplitude resolution measurement at every point we investigate the optimal allocation of cost budget to the measurement devices so as to minimize estimation error this problem differs from standard estimation problems in that we are allowed to design the number and noise levels of the measurement devices subject to the cost constraint our main results are presented in the form of tradeoff curves between the estimation error and the cost budget although our primary motivation and numerical examples come from wave propagation problems our formulation is also valid for other measurement problems with similar budget limitations where the observed variables are related to the unknown variables through a linear relation we discuss the effects of signal to noise ratio distance of propagation and the degree of coherence correlation of the waves on these tradeoffs and the optimum cost allocation our conclusions not only yield practical strategies for designing optimal measurement systems under cost constraints but also provide insights into measurement aspects of certain inverse problems

a stochastic differential equation sis epidemic model in this paper we extend the classical susceptible infected susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation sde for the number of infectious individuals i t we then prove that this sde has a unique global positive solution i t and establish conditions for extinction and persistence of i t we discuss perturbation by stochastic noise in the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance the results are illustrated by computer simulations including two examples based on real life diseases

single image defogging by multiscale depth fusion restoration of fog images is important for the deweathering issue in computer vision the problem is ill posed and can be regularized within a bayesian context using a probabilistic fusion model this paper presents a multiscale depth fusion mdf method for defog from a single image a linear model representing the stochastic residual of nonlinear filtering is first proposed multiscale filtering results are probabilistically blended into a fused depth map based on the model the fusion is formulated as an energy minimization problem that incorporates spatial markov dependence an inhomogeneous laplacian markov random field for the multiscale fusion regularized with smoothing and edge preserving constraints is developed a nonconvex potential adaptive truncated laplacian is devised to account for spatially variant characteristics such as edge and depth discontinuity defog is solved by an alternate optimization algorithm searching for solutions of depth map by minimizing the nonconvex potential in the random field the mdf method is experimentally verified by real world fog images including cluttered depth scene that is challenging for defogging at finer details the fog free images are restored with improving contrast and vivid colors but without over saturation quantitative assessment of image quality is applied to compare various defog methods experimental results demonstrate that the accurate estimation of depth map by the proposed edge preserved multiscale fusion should recover high quality images with sharp details

the threshold dynamics in a stochastic sis epidemic model with vaccination and nonlinear incidence under regime switching abstract in this paper a stochastic sis epidemic model with vaccination and nonlinear incidence under regime switching is investigated this model concerned about white noise and color noise a new technique to deal with the nonlinear incidence and vaccination for the stochastic epidemic models is introduced the sufficient conditions on the extinction and the permanence in the mean with probability one are established by constructing new lyapunov functions with regime switching

probabilistic relaxation and the hough transform abstract we discuss the recent developments in probabilistic relaxation which is used as a tool for contextual sensory data interpretation the relationship of this technique with the hough transform is then established focusing on the generalised hough transform ght we show that the label probability updating formula of the probabilistic relaxation process exploiting binary relations between object primitives under the assumption that the primitives convey weak context exhibits very close similarity to the voting function employed by a computationally efficient ght we argue that the relationship could be exploited by importing the positive features of the respective techniques to benefit one another specific suggestions for enhancing the respective techniques are mentioned they include the adoption of the representational efficiency of the hough transform to reduce the computational complexity of probabilistic relaxation vice versa in the case of the generalised hough transform it is pointed out that the effect of an unknown object transformation could be dealt with by means of a parallel cooperative interpretation rather than by means of an exhaustive search through the parameter space of a transformation group this has implications in terms of both the storage and computational requirements of the ght it also opens the possibility of using the ght for detecting objects subject to more complex transformations such as affine or perspective the relationship also suggests the possibility of using alternative voting functions which may speed up the object detection process

toward color image segmentation in analog vlsi algorithm and hardware standard techniques for segmenting color images are based on finding normalized rgb discontinuities color histogramming or clustering techniques in rgb or cie color spaces the use of the psychophysical variable hue in hsi space has not been popular due to its numerical instability at low saturations in this article we propose the use of a simplified hue description suitable for implementation in analog vlsi we demonstrate that if theintegrated white condition holds hue is invariant to certain types of highlights shading and shadows this is due to theadditive shift invariance property a property that other color variables lack the more restrictive uniformly varying lighting model associated with themultiplicative scale invariance property shared by both hue and normalized rgb allows invariance to transparencies and to simple models of shading and shadows using binary hue discontinuities in conjunction with first order type of surface interpolation we demonstrate these invariant properties and compare them against the performance of rgb normalized rgb and cie color spaces we argue that working in hsi space offers an effective method for segmenting scenes in the presence of confounding cues due to shading transparency highlights and shadows based on this work we designed and fabricated for the first time an analog cmos vlsi circuit with on board phototransistor input that computes normalized color and hue

correctness of local probability propagation in graphical models with loops graphical models such as bayesian networks and markov networks represent joint distributions over a set of variables by means of a graph when the graph is singly connected local propagation rules of the sort proposed by pearl 1988 are guaranteed to converge to the correct posterior probabilities recently a number of researchers have empirically demonstrated good performance of these same local propagation schemes on graphs with loops but a theoretical understanding of this performance has yet to be achieved for graphical models with a single loop we derive an analytical relationship between the probabilities computed using local propagation and the correct marginals using this relationship we show a category of graphical models with loops for which local propagation gives rise to provably optimal maximum a posteriori assignments although the computed marginals will be incorrect we also show how nodes can use local information in the messages they receive in order to correct their computed marginals we discuss how these results can be extended to graphical models with multiple loops and show simulation results suggesting that some properties of propagation on single loop graphs may hold for a larger class of graphs specifically we discuss the implication of our results for understanding a class of recently proposed error correcting codes known as turbo codes

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

a field model for human detection and tracking the large shape variability and partial occlusions challenge most object detection and tracking methods for nonrigid targets such as pedestrians this paper presents a new approach based on a two layer statistical field model that characterizes the prior of the complex shape variations as a boltzmann distribution and embeds this prior and the complex image likelihood into a markov field a probabilistic variational analysis of this model reveals a set of fixed point equations characterizing the equilibrium of the field it leads to computationally efficient methods for calculating the image likelihood and for training the model based on that effective algorithms for detecting nonrigid objects are developed this new approach has several advantages first it is intrinsically suitable for capturing local nonrigidity in addition due to the distributed likelihood this approach is robust to partial occlusions moreover the two layer structure provides large flexibility of modeling the image observations which makes the new method robust to clutters extensive experiments demonstrate its effectiveness

convexity properties in binary detection problems the author investigates the convexity properties of error probability in the detection of binary valued scalar signals corrupted by additive noise it is shown that the error probability of the maximum likelihood receiver is a convex function of the signal power when the noise has a unimodal distribution based on this property the results of the optimal time sharing strategies of transmitters and jammers and of the optimal use of multiple channels are obtained

parallel and deterministic algorithms from mrfs surface reconstruction deterministic approximations to markov random field mrf models are derived one of the models is shown to give in a natural way the graduated nonconvexity gnc algorithm proposed by a blake and a zisserman 1987 this model can be applied to smooth a field preserving its discontinuities a class of more complex models is then proposed in order to deal with a variety of vision problems all the theoretical results are obtained in the framework of statistical mechanics and mean field techniques a parallel iterative algorithm to solve the deterministic equations of the two models is presented together with some experiments on synthetic and real images

detector randomization and stochastic signaling for minimum probability of error receivers optimal receiver design is studied for a communications system in which both detector randomization and stochastic signaling can be performed first it is proven that stochastic signaling without detector randomization cannot achieve a smaller average probability of error than detector randomization with deterministic signaling for the same average power constraint and noise statistics then it is shown that the optimal receiver design results in a randomization between at most two maximum a posteriori probability map detectors corresponding to two deterministic signal vectors numerical examples are provided to explain the results

asymptotic properties of switching diffusion epidemic model with varying population size the purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical sis epidemic model with standard incidence and varying population size the stochastic model studied here includes white vector noise and telegraph noise modeled by markovian switching we established conditions for extinction both in probability one and in pth moment we also established the persistence of disease under different conditions on the intensities of noises and the parameters of the model furthermore we showed the existence of a stationary distribution and derive expressions for its mean and variance the presented results are demonstrated by numerical simulations

noise benefits in combined nonlinear bayesian estimators this paper investigates the benefits of intentionally adding noise to a bayesian estimator which comprises a linear combination of a number of individual bayesian estimators that are perturbed by mutually independent noise sources and multiplied by a set of adjustable weighting coefficients we prove that the bayes risk for the mean square error mse criterion is minimized when the same optimum weighting coefficients are assigned to the identical estimators in the combiner this property leads to a simplified analysis of the noise benefit to the mse of the combined bayesian estimator even when the number of individual estimators tends to infinity it is shown that for a sufficiently large number of individual estimators the mse of the designed bayesian estimator approaches a plateau for a wide range of added noise levels this robust feature facilitates the incorporation of the added noise into the design of bayesian estimators without tuning the noise level for an easily implementable bayesian estimator composed of quantizers the benefit of the symmetric scale family noise is demonstrated and the optimal noise probability density function is approximated by solving a constrained nonlinear optimization problem we further extend this potential bayesian estimator to the nonlinear filter design finally examples of the noise benefits in random parameter estimation and nonlinear filtering support the theoretical analyses

a markov model for blind image separation by a mean field em algorithm this paper deals with blind separation of images from noisy linear mixtures with unknown coefficients formulated as a bayesian estimation problem this is a flexible framework where any kind of prior knowledge about the source images and the mixing matrix can be accounted for in particular we describe local correlation within the individual images through the use of markov random field mrf image models these are naturally suited to express the joint pdf of the sources in a factorized form so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained our model also includes edge variables to preserve intensity discontinuities mrf models have been proved to be very efficient in many visual reconstruction problems such as blind image restoration and allow separation and edge detection to be performed simultaneously we propose an expectation maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix the sources and their edge maps we tested this procedure on both synthetic and real images in the fully blind case i e no prior information on mixing is exploited and found that a source model accounting for local autocorrelation is able to increase robustness against noise even space variant furthermore when the model closely fits the source characteristics independence is no longer a strict requirement and cross correlated sources can be separated as well

filters random fields and maximum entropy frame towards a unified theory for texture modeling this article presents a statistical theory for texture modeling this theory combines filtering theory and markov random field modeling through the maximum entropy principle and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view our theory characterizes the ensemble of images i with the same texture appearance by a probability distribution f i on a random field and the objective of texture modeling is to make inference about f i given a set of observed texture examples in our theory texture modeling consists of two steps 1 a set of filters is selected from a general filter bank to capture features of the texture these filters are applied to observed texture images and the histograms of the filtered images are extracted these histograms are estimates of the marginal distributions of f i this step is called feature extraction 2 the maximum entropy principle is employed to derive a distribution p i which is restricted to have the same marginal distributions as those in 1 this p i is considered as an estimate of f i this step is called feature fusion a stepwise algorithm is proposed to choose filters from a general filter bank the resulting model called frame filters random fields and maximum entropy is a markov random field mrf model but with a much enriched vocabulary and hence much stronger descriptive ability than the previous mrf models used for texture modeling gibbs sampler is adopted to synthesize texture images by drawing typical samples from p i thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled experiments on a variety of 1d and 2d textures are described to illustrate our theory and to show the performance of our algorithms these experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework

hierarchical unsupervised learning with growing via phase transitions we address unsupervised learning subject to structural constraints with particular emphasis placed on clustering with an imposed decision tree structure most known methods are greedy optimizing one node of the tree at a time to minimize a local cost by constrast we develop a joint optimization method derived based on information theoretic principles and closely related to known methods in statistical physics the approach is inspired by the deterministic annealing algorithm for unstructured data clustering which was based on maximum entropy inference the new approach is founded on the principle of minimum cross entropy using informative priors to approximate the unstructured clustering solution while imposing the structural constraint the resulting method incorporates supervised learning principles applied in an unsupervised problem setting in our approach the tree grows by a sequence of bifurcations that occur while optimizing an effective free energy cost at decreasing temperature scales thus estimates of the tree size and structure are naturally obtained at each temperature in the process examples demonstrate considerable improvement over known methods

the ergodicity and extinction of stochastically perturbed sir and seir epidemic models with saturated incidence abstract in this paper we include stochastic perturbations into sir and seir epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number r 0 the long time behavior of the two stochastic systems is studied mainly we utilize stochastic lyapunov functions to show under some conditions the solution has the ergodic property as r 0 1 while exponential stability as r 0 1 at last we make simulations to conform our analytical results

evolution of predator prey systems described by a lotka volterra equation under random environment abstract in this paper we consider the evolution of a system composed of two predator prey deterministic systems described by lotka volterra equations in random environment it is proved that under the influence of telegraph noise all positive trajectories of such a system always go out from any compact set of int r 2 with probability one if two rest points of the two systems do not coincide in case where they have the rest point in common the trajectory either leaves from any compact set of int r 2 or converges to the rest point the escape of the trajectories from any compact set means that the system is neither permanent nor dissipative

population dynamical behavior of lotka volterra system under regime switching in this paper we investigate a lotka volterra system under regime switching dx t diag x 1 t x n t b r t a r t x t dt s r t db t where b t is a standard brownian motion the aim here is to find out what happens under regime switching we first obtain the sufficient conditions for the existence of global positive solutions stochastic permanence and extinction we find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the markov chain the limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients finally the main results are illustrated by several examples

stability of sirs system with random perturbations epidemiological models with bilinear incidence rate si usually have an asymptotically stable trivial equilibrium corresponding to the disease free state or an asymptotically stable non trivial equilibrium i e interior equilibrium corresponding to the endemic state in this paper we consider an epidemiological model which is an sirs model with or without distributed time delay influenced by random perturbations we present the stability conditions of the disease free equilibrium of the associated stochastic sirs system

edge preserving image denoising and estimation of discontinuous surfaces in this paper we are interested in the problem of estimating a discontinuous surface from noisy data a novel procedure for this problem is proposed based on local linear kernel smoothing in which local neighborhoods are adapted to the local smoothness of the surface measured by the observed data the procedure can therefore remove noise correctly in continuity regions of the surface and preserve discontinuities at the same time since an image can be regarded as a surface of the image intensity function and such a surface has discontinuities at the outlines of objects this procedure can be applied directly to image denoising numerical studies show that it works well in applications compared to some existing procedures

theory of the stochastic resonance effect in signal detection part ii variable detectors in part i of this paper ldquotheory of the stochastic resonance effect in signal detection part i fixed detectors rdquo ieee transactions on signal processing vol 55 no 7 pt 1 pp 3172 3184 the mechanism of the stochastic resonance sr effect for a fixed detector has been examined this paper analyzes the stochastic resonance sr effect under the condition that the detector structure or its parameters can also be changed the detector optimization problem with sr noise under both neyman pearson and bayesian criteria is examined in the bayesian approach when the prior probabilities are unknown the minimax approach is adopted the form of the optimal noise pdf along with the corresponding detector as well as the maximum achievable performance are determined the developed theory is then applied to a general class of weak signal detection problems under the assumptions that the sample size n is large enough and the test statistics satisfies the conditions of central limit theorem the optimal sr noise is shown to be a constant vector and independent of the signal strength for both neyman pearson and bayesian criteria illustrative examples are presented where performance comparisons are made between the original detector and the optimal sr noise modified detector for different types of sr noise

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance

the sis epidemic model with markovian switching abstract population systems are often subject to environmental noise motivated by takeuchi et al 7 we will discuss in this paper the effect of telegraph noise on the well known sis epidemic model we establish the explicit solution of the stochastic sis epidemic model which is useful in performing computer simulations we also establish the conditions for extinction and persistence for the stochastic sis epidemic model and compare these with the corresponding conditions for the deterministic sis epidemic model we first prove these results for a two state markov chain and then generalise them to a finite state space markov chain computer simulations based on the explicit solution and the euler maruyama scheme are performed to illustrate our theory we include a more realistic example using appropriate parameter values for the spread of s t r e p t o c o c c u s p n e u m o n i a e in children