optimal boundary detection on grey tone image the paper is devoted to the problem of optimal boundary detection for a two object image the objects have different average brightnesses under conditions of stationary noise there is no a priori information about the average brightness of the objects the type and parameters of noise density distribution functions the shapes of the objects or the boundary length however the location of an initial point belonging to an object contour is presumed to be known it is shown that an unknown contour line can only be found among level lines a graph is constructed from a group of level lines passing through the initial point the problem of finding the optimal path on the graph is solved according to a pre defined quality criterion the investigation included previously known criteria maximization of gradient sums the average gradient maximization as well as some proposed by the authors average risk minimization as applied to a segmentation task and alternative choice the efficiency of the criteria is tested on a set of image models with different signal to noise ratios an effective suboptimal tracking algorithm is developed for practical tasks of grey tone image segmentation

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

some experiments with simulated annealing for coloring graphs abstract methods of thermodynamical simulation have been used for several famous combinatorial optimization problems for graph coloring i e partition of the node set into as few independent sets as possible we describe a method of simulation such an approach is combined with other techniques for graph coloring experiments on random graphs show evidence that this combination gives better results than anyone of the original non combined methods

improving inductive logic programming by using simulated annealing in inductive logic programming ilp algorithms that are purely of the bottom up or top down type encounter several problems in practice since a majority of them are greedy ones these algorithms stop when finding clauses in local optima according to the quality measure used for evaluating the results moreover when learning clauses one by one the induced clauses become less and less interesting as the algorithm is progressing to cover few remaining examples in this paper we propose a simulated annealing framework to overcome these problems using a refinement operator we define neighborhood relations on clauses and on hypotheses i e sets of clauses with these relations and appropriate quality measures we show how to induce clauses in a coverage approach or to induce hypotheses directly by using simulated annealing algorithms we discuss the necessary conditions on the refinement operators and the evaluation measures to increase the effectiveness of the algorithm implementations included a parallelized version of the algorithm are described and experimentation results in terms of convergence of the method and in terms of accuracy are presented

relevance of soft modes for order parameter fluctuations in the two dimensional xy model we analyse the spin wave approximation for the two dimensional xy model directly in reciprocal space in this limit the model is diagonal and the normal modes are statistically independent despite this simplicity non trivial critical properties are observed and exploited we confirm that the observed asymmetry for the probability density function for order parameter fluctuations comes from the divergence of the mode amplitudes across the brillouin zone we show that the asymmetry is a many body effect despite the importance played by the zone centre the precise form of the function is dependent on the details of the microscopic generating function for the modes we discuss the relevance of this to more complex or non equilibrium systems where similar distributions are observed

cooling schedules for optimal annealing a monte carlo optimization technique called simulated annealing is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima the level of randomization is determined by a control parameter t called temperature which tends to zero according to a deterministic cooling schedule we give a simple necessary and sufficient condition on the cooling schedule for the algorithm state to converge in probability to the set of globally minimum cost states in the special case that the cooling schedule has parametric form tt c log1 t the condition for convergence is that c be greater than or equal to the depth suitably defined of the deepest local minimum which is not a global minimum state

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

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

a regularized contrast statistic for object boundary estimation implementation and statistical evaluation we propose an optimization approach to the estimation of a simple closed curve describing the boundary of an object represented in an image the problem arises in a variety of applications such as template matching schemes for medical image registration a regularized optimization formulation with an objective function that measures the normalized image contrast between the inside and outside of a boundary is proposed numerical methods are developed to implement the approach and a set of simulation studies are carried out to quantify statistical performance characteristics one set of simulations models emission computed tomography ect images a second set considers images with a locally coherent noise pattern in both cases the error characteristics are found to be quite encouraging the approach is highly automated which offers some practical advantages over currently used technologies in the medical imaging field

optimizing antenna array geometry for interference suppression the determination of an optimum antenna array geometry for suppressing interference is addressed an optimization problem is derived whose solution yields an optimum array geometry for a given interference environment a specific example is solved via the simulated annealing optimization algorithm and results are presented for arrays of varying configurations

a class of self interacting processes with applications to games and reinforced random walks this paper studies a class of non markovian and nonhomogeneous stochastic processes on a finite state space relying on a recent paper by benaim hofbauer and sorin siam j control optim 44 2005 pp 328 348 it is shown that under certain assumptions the asymptotic behavior of occupation measures can be described in terms of a certain set valued deterministic dynamical system this provides a unified approach to simulated annealing type processes and permits the study of new models of vertex reinforced random walks and new models of learning in games such as markovian fictitious play

a general approach for token correspondence abstract this paper presents a generalization of the correspondence approach of i k sethi and r jain ieee trans pattern anal mech intell 9 56 73 1987 by extending the path coherence criterion to high dimensional vector spaces where tokens are represented as points two algorithms for obtaining correspondence of tokens are described experimental results for line and region tokens are presented to demonstrate the general purpose nature of the proposed correspondence approach

a note on the finite time behavior of simulated annealing simulated annealing has proven to be a very successful heuristic for various combinatorial optimization problems it is a randomized algorithm that attempts to find the global optimum with high probability by local exchanges in this paper we give a new proof of the convergence of simulated annealing by applying results about rapidly mixing markov chains with this proof technique it is possible to obtain better bounds for the finite time behavior of simulated annealing than previously known

a stochastic method for bayesian estimation of hidden markov random field models with application to a color model we propose a new stochastic algorithm for computing useful bayesian estimators of hidden markov random field hmrf models that we call exploration selection estimation ese procedure the algorithm is based on an optimization algorithm of o francois called the exploration selection e s algorithm the novelty consists of using the a posteriori distribution of the hmrf as exploration distribution in the e s algorithm the ese procedure computes the estimation of the likelihood parameters and the optimal number of region classes according to global constraints as well as the segmentation of the image in our formulation the total number of region classes is fixed but classes are allowed or disallowed dynamically this framework replaces the mechanism of the split and merge of regions that can be used in the context of image segmentation the procedure is applied to the estimation of a hmrf color model for images whose likelihood is based on multivariate distributions with each component following a beta distribution meanwhile a method for computing the maximum likelihood estimators of beta distributions is presented experimental results performed on 100 natural images are reported we also include a proof of convergence of the e s algorithm in the case of nonsymmetric exploration graphs

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

cooling down levy flights let l t be a levy flights process with a stability index 0 2 and u be an external multi well potential a jump diffusion z satisfying a stochastic differential equation dz t u z t dt t dl t describes an evolution of a levy particle of an instant scale t in an external force field the scale is supposed to decrease polynomially fast i e t t for some 0 we discover two different decrease regimes if 1 fast cooling the levy particle gets trapped in one of the potential wells

reduced complexity hmm filtering with stochastic dominance bounds a convex optimization approach this paper uses stochastic dominance principles to construct upper and lower sample path bounds for hidden markov model hmm filters we consider an hmm consisting of an x state markov chain with transition matrix p by using convex optimization methods for nuclear norm minimization with copositive constraints we construct low rank stochastic matrices underline p and bar p so that the optimal filters using underline p bar p provably lower and upper bound with respect to a partially ordered set the true filtered distribution at each time instant since underline p and bar p are low rank say r the computational cost of evaluating the filtering bounds is o x r instead of o x 2 a monte carlo importance sampling filter is presented that exploits these upper and lower bounds to estimate the optimal posterior finally explicit bounds are given on the variational norm between the true posterior and the upper and lower bounds in terms of the dobrushin coefficient

a parallel algorithm for detecting dominant points on multiple digital curves abstract a new parallel algorithm is proposed for detecting corners of multiple planar curves or shapes this algorithm is based on an analysis of morphological residues and corner characteristics the method is different from traditional chain code based corner detection algorithms which associate with a chain coding and floating point computation for multiple objects in an image the proposed algorithm treats them uniformly and applies simultaneously on curves and shapes of multiple objects the experiments demonstrate that the algorithm can be effectively executed on an simd parallel computer a boundary constrained morphological method is presented for filling closed curves into shapes which are subsequently used for corner detection

stochastic optimization on continuous domains with finite time guarantees by markov chain monte carlo methods we introduce bounds on the finite time performance of markov chain monte carlo mcmc algorithms in solving global stochastic optimization problems defined over continuous domains it is shown that mcmc algorithms with finite time guarantees can be developed with a proper choice of the target distribution and by studying their convergence in total variation norm this work is inspired by the concept of finite time learning with known accuracy and confidence developed in statistical learning theory

ergodicity in parametric nonstationary markov chains an application to simulated annealing methods a nonstationary markov chain is weakly ergodic if the dependence of the state distribution on the starting state vanishes as time tends to infinity a chain is strongly ergodic if it is weakly ergodic and converges in distribution in this paper we show that the two ergodicity concepts are equivalent for finite chains under rather general and widely verifiable conditions we discuss applications to probabilistic analyses of general search methods for combinatorial optimization problems simulated annealing

an edge detection algorithm using multi state adalines abstract an edge detection algorithm using multi state adaptive linear neurons adalines is presented although the tri state adaline is only considered in this work general multi state input vectors with extreme values are shown to be linearly separable from the rest of the vectors with the same dimension the input state of each adaline is defined using the local mean in a predefined mask in addition to the binary input states 1 the 0 input state is introduced for controlling the noise effect if the input pattern matches one of the predefined edge patterns the corresponding pixel is detected as an edge pixel experimental results are shown where the proposed detector is compared with both the canny and log edge detectors

convergence to global minima for a class of diffusion processes abstract we prove that there exists a gain function t t t 0 such that the solution of the sde d x t t grad u x t d t t d b t settles down on the set of global minima of u in particular the existence of a gain function t t 0 so that yt satisfying d y t t grad u y t d t d b t converges to the set of the global minima of u is verified then we apply the results to the robbins monro and the kiefer wolfowitz procedures which are of particular interest in statistics

phase transition and landscape statistics of the number partitioning problem the phase transition in the number partitioning problem npp i e the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution is investigated by examining the energy landscape of this classic optimization problem this is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure termed a barrier tree the leaves and internal nodes of which represent respectively the minima and the lowest energy saddles connecting those minima here we apply several measures of shape balance and symmetry as well as of branch lengths barrier heights to the barrier trees that result from the landscape of the npp aiming at identifying traces of the easy hard transition we find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights only the difficulty measure given by the maximum value of the ratio between the barrier height and the energy surplus of local minima succeeded in detecting traces of the phase transition in the tree in addition we show that the barrier trees associated with the npp are very similar to random trees contrasting dramatically with trees associated with the p spin glass and random energy models we also examine critically a recent conjecture on the equivalence between the npp and a truncated random energy model

temperature dependence of universal fluctuations in the two dimensional harmonic xy model we compute exact analytical expressions for the skewness and kurtosis in the two dimensional harmonic xy model these quantities correspond to the third and fourth normalized moments of the probability density function pdf of the magnetization of the model from their behavior we conclude that they depend explicitly on the system temperature even in the thermodynamic limit and hence the pdf itself must depend on it our results correct the hypothesis called universal fluctuations they confirm and extend previous results which showed a t dependence of the pdf including perturbative expansions within the xy model up to first order in temperature

convergence analysis of self adaptive equalizers a theoretical analysis of self adaptive equalization for data transmission is carried out starting from known convergence results for the corresponding trained adaptive filter the development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel thanks to the boundedness of the decision function used for data recovery it can be proved that the algorithm is bounded strong convergence results can be reached when a perfect noiseless equalizer exists the algorithm will converge to it if the eye pattern is initially open otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined some of them will result in a poor error rate the case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical trained algorithm the stronger the noise the greater the difference is one of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over

stochastic relaxation on partitions with connected components and its application to image segmentation we present a new method of segmentation in which images are segmented in partitions with connected components we give computationally inexpensive algorithms for probability simulation and simulated annealing on the space of partitions with connected components of a general graph in particular hastings algorithms 1970 and generalized metropolis algorithms are defined to avoid heavy computation to achieve segmentation we propose a hierarchical approach which at each step minimizes a cost function on the space of partitions with connected components of a graph the algorithm is applied to segment gray level color and textured images

edge detection using two dimensional local structure information abstract local intensity discontinuities commonly referred to as edges are important attributes of an image many imaging scenarios produce image regions exhibiting complex two dimensional 2d local structure such as when several edges meet to form corners and vertices traditional derivative based edge operators which typically assume that an edge can be modeled as a one dimensional 1d piecewise smooth step function give misleading results in such situations leclerc and zucker introduced the concept of local structure as an aid for locating intensity discontinuities they proposed a detailed procedure for detecting discontinuities in a 1d function they had only given a preliminary version of their scheme however for 2d images three related edge detection methods are proposed that draw upon 2d local structural information the first method greatly expands upon leclerc and zucker s 2d method the other two methods employ a mechanism similar to that used by the maximum homogeneity filter a filter used for image enhancement all three methods permit the detection of multiple edges at a point and have the flexibility to detect edges at differing spatial and angular acuity results show that the methods typically perform better than other operators

temperature dependent fluctuations in the two dimensional xy model we present a detailed investigation of the probability density function pdf of order parameter fluctuations in the finite two dimensional xy 2dxy model in the low temperature critical phase of this model the pdf approaches a universal non gaussian limit distribution in the limit t 0 our analysis resolves the question of temperature dependence of the pdf in this regime for which conflicting results have been reported we show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously derived graphical expansion this is confirmed by numerical simulations on two controlled approximations to the 2dxy model the harmonic and harmonic xy models the harmonic model has no kosterlitz thouless berezinskii ktb transition and the pdf becomes progressively less skewed with increasing temperature until it closely approximates a gaussian function above t approximate to 4 pi near to that temperature we find some evidence of a phase transition although our observations appear to exclude a thermodynamic singularity

an edge detection technique using genetic algorithm based optimization abstract in this paper we present a genetic algorithm based optimization technique for edge detection the problem of edge detection is formulated as one of choosing a minimum cost edge configuration the edge configurations are viewed as two dimensional chromosomes with fitness values inversely proportional to their costs the design of the crossover and the mutation operators in the context of the two dimensional chromosomal representation is described the knowledge augmented mutation operator which exploits knowledge of the local edge structure is shown to result in rapid convergence the incorporation of meta level operators and strategies such as the elitism strategy the engineered conditioning operator and adaptation of mutation and crossover rates in the context of edge detection are discussed and are shown to improve the convergence rate the genetic algorithm with various combinations of meta level operators is tested on synthetic and natural images the performance of the genetic algorithm based cost minimization technique is compared both qualitatively and quantitatively with local search based and simulated annealing based cost minimization approaches the genetic algorithm based technique is shown to perform very well in terms of robustness to noise rate of convergence and quality of the final edge image

boundary detection by constrained optimization a statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions the model is a joint probability distribution for the array of pixel gray levels and an array of labels in boundary finding the labels are binary zero or one representing the absence or presence of boundary elements in partitioning the label values are generic two labels are the same when the corresponding scene locations are considered to belong to the same region the distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels using the kolmogorov smirnov nonparametric measures of difference between the distributions of these features the number of model parameters is minimized by forbidding label configurations which are assigned probability zero the maximum a posteriori estimator of boundary placements and partitionings is examined the forbidden states introduce constraints into the calculation of these configurations stochastic relaxation methods are extended to accommodate constrained optimization

sharp asymptotics for fixation times in stochastic population genetics models at low mutation probabilities this article describes new models in population genetics that extend the neutral wright fisher model by including strong selection and mutation fixation times are studied in the limit of small mutation probabilities within the framework of markov chains with rare transitions the main result outlines the role of the discrete geometry of the fitness landscape and provides a mean for estimating the expected number of generations for an individual with better fitness value to appear some connections to evolutionary algorithms are discussed as well

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

nonstationary markov chains and convergence of the annealing algorithm we study the asymptotic behavior as timet of certain nonstationary markov chains and prove the convergence of the annealing algorithm in monte carlo simulations we find that in the limitt a nonstationary markov chain may exhibit phase transitions nonstationary markov chains in general and the annealing algorithm in particular lead to biased estimators for the expectation values of the process we compute the leading terms in the bias and the variance of the sample means estimator we find that the annealing algorithm converges if the temperaturet t goes to zero no faster thanc log t t0 ast with a computable constantc andt0 the initial time the bias and the variance of the sample means estimator in the annealing algorithm go to zero likeo t 1 e for some 0 e 1 with e 0 only in very special circumstances our results concerning the convergence of the annealing algorithm and the rate of convergence to zero of the bias and the variance of the sample means estimator provide a rigorous procedure for choosing the optimal annealing schedule this optimal choice reflects the competition between two physical effects a the adiabatic effect whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state and b the super cooling effect whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state s but may do so extremely slowly

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

simulated annealing via sobolev inequalities we use sobolev inequalities to study the simulated annealing algorithm this approach takes advantage of the local time reversibility of the process and yields the optimal freezing schedule as well as quantitative information about the rate at which the process is tending to its ground state

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

a combined multistart annealing algorithm for continuous global optimization the application of simulated annealing to the global optimization of a function on a compact subset of rd is discussed for the langevin algorithm the class of convergent schedules depends on some a priori knowledge about the form of the function it is shown that this problem disappears by using the simplest annealing algorithm of jump type which can also be improved by performing local searches between two consecutive jump times the resulting algorithm is essentially a multistart technique controlled by an annealing schedule

diffusion for global optimization in r n we seek a global minimum of u mathbb r n to mathbb r the solution to d dt x t nabla u x t will find local minima using the idea of simulated annealing we consider th

a markovian model for contour grouping abstract classical methods of contour extraction do not always allow the detection of all the contours for instance the contours obtained by a canny deriche filter have some gaps especially at corners or at t junctions in this paper we present an algorithm which restores incomplete contours we model the image by a markov random field in order to complete the contours several criteria are defined and introduced in an energy function which has to be optimized the deterministic icm iterated conditional mode relaxation algorithm is implemented to minimize this energy function the result is a contour image consisting of closed contours this method has been tested on different images which present different types of difficulties indoors outdoors satellite spot industrial and medical images

quantitative error measures for edge detection how to measure the performance of an edge detection method is an open problem many performance measures have been presented in the literature however there seems to be no agreement on the best option and there exist no practical studies of the features of some of the most recent measures in this work we make a comprehensive overview of the different proposals followed by a practical comparison of the most representative measures on synthetic as well as natural edge images

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

new bounds for binary covering arrays using simulated annealing covering arrays cas are combinatorial structures specified as a matrix of n rows and k columns over an alphabet on v symbols such that for each set of t columns called the strength of the array every t tuple of symbols is covered recently they have been used to represent interaction test suites for software testing given that they provide economical sized test cases while still preserving important fault detection capabilities this paper introduces an improved implementation of a simulated annealing algorithm called isa for constructing cas of strengths three through six over a binary alphabet i e binary cas extensive experimentation is carried out using 127 well known benchmark instances for assessing its performance with respect to an existing simulated annealing implementation a greedy method and five state of the art algorithms the results show that our algorithm attains 104 new bounds and equals the best known solutions for the other 23 instances consuming reasonable computational time furthermore the implications of using these results as ingredients to recursive constructions are also analyzed

proposals for chunking and tabu search chunking grouping basic units of information to create higher level units is a critical aspect of human intelligence we identify special types of chunking to enhance tabu search memory structures producing improved problem solving ability and giving useful supporting information for decision makers tabu search as proposed by glover orsa journal on computing 1 3 1989 190 2 1 1990 4 has proven to be a very effective meta heuristic for hard optimization problems the search is typically based on a local improvement scheme that involves alteration of one or more attributes of fully specified solutions at each iteration in this paper we describe the use of and search for groupings of solution attributes although they are most natural in the context of the tabu search paradigm many of the proposals can also be employed in genetic algorithms and simulated annealing based algorithms chunking enables a number of search improvements including a general purpose metric for decision vectors the paper develops theory and proposals for learning about chunks and using them computational experience to date is summarized to support the contention that chunking can be an important part of effective optimization algorithms

asymptotic behavior of some linear differential systems abstract consider the following chasing game in r amongbparticles whose trajectories are governed by the following differential equations fori s 1 2 b f i t j i q ij t f j t f i t wherefi t is the position at timetof the particleiandqij t which measures the instantaneous rate that particleiis attracted toward particlej is given byqij t pij t u i j forj i the rate function t is positive with limt t 0 u i j 0 is the cost function indicating the level of difficulty fromitojand the nonnegative numberspijfori jreflect the neighborhood structure of the particles particles are attracted to one another but such attraction becomes weaker as time goes on a sufficient condition on t is given for allfi t converging to a common finite limit

generalized deterministic annealing we develop a general formalism for computing high quality low cost solutions to nonconvex combinatorial optimization problems expressible as distributed interacting local constraints for problems of this type generalized deterministic annealing gda avoids the performance related sacrifices of current techniques gda exploits the localized structure of such problems by assigning k state neurons to each optimization variable the neuron values correspond to the probability densities of k state local markov chains and may be updated serially or in parallel the markov model is derived from the markov model of simulated annealing sa although it is greatly simplified theorems are presented that firmly establish the convergence properties of gda as well as supplying practical guidelines for selecting the initial and final temperatures in the annealing process a benchmark image enhancement application is provided where the performance of gda is compared to other optimization methods the empirical data taken in conjunction with the formal analytical results suggest that gda enjoys significant performance advantages relative to current methods for combinatorial optimization

approximating the permanent a randomised approximation scheme for the permanent of a 0 1s presented the task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph the latter is accomplished by simulating a markov chain whose states are the matchings in the graph for a wide class of 0 1 matrices the approximation scheme is fully polynomial i e runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output this class includes all dense matrices those that contain sufficiently many 1 s and almost all sparse matrices in some reasonable probabilistic model for 0 1 matrices of given density for the approach sketched above to be computationally efficient the markov chain must be rapidly mixing informally it must converge in a short time to its stationary distribution a major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing apparently the first such result for a markov chain with genuinely c

on detecting edges an edge in an image corresponds to a discontinuity in the intensity surface of the underlying scene it can be approximated by a piecewise straight curve composed of edgels i e short linear edge elements each characterized by a direction and a position the approach to edgel detection here is to fit a series of one dimensional surfaces to each window kernel of the operator and accept the surface description which is adequate in the least squares sense and has the fewest parameters a one dimensional surface is one which is constant along some direction the tanh is an adequate basis for the stepedge and its combinations are adequate for the roofedge and the line edge the proposed method of step edgel detection is robust with respect to noise for step size noise 2 5 it has subpixel position localization position and an angular localization better than 10 further it is designed to be insensitive to smooth shading these results are demonstrated by some simple analysis statistical data and edgelimages also included is a comparison of performance on a real image with a typical operator difference of gaussians the results indicate that the proposed operator is superior with respect to detection localization and resolution

simulated annealing for convex optimization we apply the method known as simulated annealing to the following problem in convex optimization minimize a linear function over an arbitrary convex set where the convex set is specified only by a membership oracle using distributions from the boltzmann gibbs family leads to an algorithm that needs only o n phases for instances in rn this gives an optimization algorithm that makes o n4 5 calls to the membership oracle in the worst case compared to the previous best guarantee of o n5 the benefits of using annealing here are surprising because such problems have no local minima that are not also global minima hence we conclude that one of the advantages of simulated annealing in addition to avoiding poor local minima is that in these problems it converges faster to the minima that it finds we also give a proof that under certain general conditions the boltzmann gibbs distributions are optimal for annealing on these convex problems

a limit theorem for a class of inhomogeneous markov processes pour un processus de markov xh irreductible et aperiodique avec un espace d etats fini et avec un taux de transition q ij t x t devient homogene dans le cas q ij t q ij et admet une loi limite qui est independante de x o le but de cet article est de demontrer qu un resultat similaire peut etre obtenu dans le cas de processus de markov non homogenes avec un certain type de taux de transition

finding point correspondences using simulated annealing abstract identifying corresponding points between two recordings of a point set has always been an important problem in stereo vision applications we describe this matching problem in terms of cost minimization and present an algorithm to approach the minimal cost mapping using simulated annealing the algorithm calculates the costs to match all possible point pairs and tries to minimize the sum of the costs of all matched points starting from an initial mapping it uses a random rearrangement scheme to alter the mapping towards the optimal minimal cost mapping

cluster algorithm renormalization group study of universal fluctuations in the two dimensional ising model in this paper we propose a method to study critical systems numerically which combines collective mode algorithms and renormalization group on the lattice this method is an improved version of the monte carlo renormalization group in the sense that it has all the advantages of cluster algorithms as an application we considered the 2d ising model and studied whether scale invariance or universality are possible underlying mechanisms responsible for the approximate universal fluctuations close to a so called bulk temperature t l universal fluctuations were first proposed in the work of bramwell holdsworth and pinton nature london 396 552 1998 and stated that the probability density function of a global quantity for very dissimilar systems such as a confined turbulent flow and a two dimensional 2d magnetic system properly normalized to the first two moments becomes similar to the universal distribution originally obtained for magnetization in the 2d xy model in the low temperature region the results for the critical exponents and the renormalization group flow of the probability density function are very accurate and show no evidence to support that the approximate common shape of the pdf should be related to both scale invariance or universal behavior

scaling and commonality in anomalous fluctuation statistics in models for turbulence and ferromagnetism recently portelli et al 2003 phys rev lett 90 104501 have semi numerically obtained a functional form of the probability distribution of fluctuations in the total energy flow in a model for fluid turbulence this follows earlier work suggesting that fluctuations in the total magnetization in the 2d xy model for a ferromagnet also follow this distribution here starting from the scaling ansatz that is the basis of the turbulence model we analytically derive the functional form of this distribution and find its single control parameter that depends upon the scaling exponents and system size of the model our analysis allows us to identify this explicitly with that of the xy model and suggest a possible generalization

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

analysis of adaptive step size sa algorithms for parameter tracking we present proofs and data for adaptive step size algorithms for tracking time varying parameters when recursive stochastic approximation type algorithms are used a classical problem in adaptive control and communication theory concerns the tracking of the best fit of a given form when the statistics or the parameters change slowly a major and yet unresolved problem has been the choice of the step sizes in the tracking algorithm an algorithm for adapting the step size using the same system measurements which are used for the tracking was suggested by benveniste and various examples worked out by brossier the numerical results were very encouraging but proofs were lacking these proofs are supplied here together with supporting numerical data the proofs are based on recent results in stochastic approximation the adaptive step size technique works very well indeed much supporting analysis is presented particularly concerning the interpretation of certain stationary processes as stationary pathwise derivatives finite difference forms are also treated these are mathematically simpler and can be applied to a wide variety of systems even when the system is not well modeled the data shows that they work well

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

magnetic fluctuations in the classical xy model the origin of an exponential tail in a complex system we study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the mathrm xy model of finite size in two dimensions this system is critical over the whole of the low temperature phase it is shown analytically and without recourse to the scaling hypothesis that in this case the distribution is non gaussian and of universal form independent of both system size and critical exponent ensuremath eta an exact expression for the generating function of the distribution is obtained which is transformed and compared with numerical data from high resolution molecular dynamics and monte carlo simulations the asymptotes of the distribution are calculated and found to be of exponential and double exponential form the calculated distribution is fitted to three standard functions a generalization of gumbel s first asymptote distribution from the theory of extremal statistics a generalized log normal distribution and a ensuremath chi 2 distribution the calculation is extended to general dimension and an exponential tail is found in all dimensions less than 4 despite the fact that critical fluctuations are limited to d 2 these results are discussed in the light of similar behavior observed in models of interface growth and for dissipative systems driven into a nonequilibrium steady state

metropolis type annealing algorithms for global optimization in r d the convergence of a class of metropolis type markov chain annealing algorithms for global optimization of a smooth function u cdot on mathbb r d is established no prior information is assumed as to what bounded region contains a global minimum the analysis contained herein is based on writing the metropolis type algorithm in the form of a recursive stochastic algorithm x k 1 x k a k nabla u x k xi k b k w k where w k is a standard white gaussian sequence xi k are random variables and a k a k b k sqrt b sqrt k log log k for k large convergence results for x k are then applied from our previous work siam journal on control and optimization 29 1991 pp 999 1018 since the analysis of x k is based on the asymptotic behavior of the related langevin type markov diffusion annealing algorithm dy t nabla u y t dt c t dw t where w cdot is a standard wiener process and c t

a cost minimization approach to edge detection using simulated annealing the authors cast edge detection as a problem in cost minimization this is achieved by the formulation of a cost function that evaluates the quality of edge configurations the function is a linear sum of weighted cost factors the cost factors capture desirable characteristics of edges such as accuracy in localization thinness and continuity edges are detected by finding the edge configurations that minimize the cost function the authors give a mathematical description of edges and analyze the cost function in terms of the characteristics of the edges in minimum cost configurations through the analysis guidelines are provided on the choice of weights to achieve certain characteristics of the detected edges the cost function is minimized by the simulated annealing method a set of strategies is presented for generating candidate states and to devise a suitable temperature schedule

constrained nonlinear optimization approaches to color signal separation separating a color signal into illumination and surface reflectance components is a fundamental issue in color reproduction and constancy this can be carried out by minimizing the error in the least squares ls fit of the product of the illumination and the surface spectral reflectance to the actual color signal when taking in account the physical realizability constraints on the surface reflectance and illumination the feasible solutions to the nonlinear ls problem should satisfy a number of linear inequalities four distinct novel optimization algorithms are presented to employ these constraints to minimize the nonlinear ls fitting error the first approach which is based on ritter s superlinear convergent method luengerger 1980 provides a computationally superior algorithm to find the minimum solution to the nonlinear ls error problem subject to linear inequality constraints unfortunately this gradient like algorithm may sometimes be trapped at a local minimum or become unstable when the parameters involved in the algorithm are not tuned properly the remaining three methods are based on the stable and promising global minimizer called simulated annealing the annealing algorithm can always find the global minimum solution with probability one but its convergence is slow to tackle this a cost effective variable separable formulation based on the concept of golub and pereyra 1973 is adopted to reduce the nonlinear ls problem to be a small scale nonlinear ls problem the computational efficiency can be further improved when the original boltzman generating distribution of the classical annealing is replaced by the cauchy distribution

weak convergence and asymptotic properties of adaptive filters with constant gains the basic adaptive filtering algorithm x n 1 epsilon x n epsilon epsilon y n y n x n epsilon psi n is analyzed using the theory of weak convergence apart from some very special cases the analysis is hard when done for each fixed epsilon 0 but the weak convergence techniques are set up to provide much information for small epsilon the relevant facts from the theory are given define x epsilon cdot by x epsilon t x n epsilon on n epsilon n epsilon epsilon then weak distributional convergence of x epsilon cdot and of x epsilon cdot t epsilon is proved under very weak assumptions where t epsilon rightarrow infty as epsilon rightarrow 0 the normalized errors x n epsilon theta sqrt epsilon are analyzed where theta is a stable point for the mean algorithm the asymptotic properties of a projection algorithm are developed where the x n epsilon are truncated at each iteration if they fall outside of a given set

performance analysis of general tracking algorithms a general family of tracking algorithms for linear regression models is studied it includes the familiar least mean square gradient approach recursive least squares and kalman filter based estimators the exact expressions for the quality of the obtained estimates are complicated approximate and easy to use expressions for the covariance matrix of the parameter tracking error are developed these are applicable over the whole time interval including the transient and the approximation error can be explicitly calculated

continuous time tracking algorithms involving two time scale markov chains this work is concerned with least mean squares lms algorithms in continuous time for tracking a time varying parameter process a distinctive feature is that the true parameter process is changing at a fast pace driven by a finite state markov chain the states of the markov chain are divisible into a number of groups within each group the transitions take place rapidly among different groups the transitions are infrequent introducing a small parameter into the generator of the markov chain leads to a two time scale formulation the tracking objective is difficult to achieve nevertheless a limit result is derived yielding algorithms for limit systems moreover the rates of variation of the tracking error sequence are analyzed under simple conditions it is shown that a scaled sequence of the tracking errors converges weakly to a switching diffusion in addition a numerical example is provided and an adaptive step size algorithm developed

the time complexity of maximum matching by simulated annealing the random heuristic search algorithm called simulated annealing is considered for the problem of finding the maximum cardinality matching in a graph it is shown that neither a basic form of the algorithm nor any other algorithm in a fairly large related class of algorithms can find maximum cardinality matchings such that the average time required grows as a polynomial in the number of nodes of the graph in contrast it is also shown for arbitrary graphs that a degenerate form of the basic annealing algorithm obtained by letting temperature be a suitably chosen constant produces matchings with nearly maximum cardinality in polynomial average time

jump surface estimation edge detection and image restoration surface estimation is important in many applications when conventional smoothing procedures e g running averages local polynomial kernel smoothing procedures smoothing spline procedures are used for estimating jump surfaces from noisy data jumps are blurred at the same time when noise is removed in recent years new smoothing methodologies have been proposed in the statistical literature for detecting jumps in surfaces and for estimating jump surfaces with jumps preserved we provide a review of these methodologies because a monochrome image can be considered a jump surface of the image intensity function with jumps at the outlines of objects edge detection and image restoration problems in image processing are closely related to the jump surface estimation problem in statistics we also review major methodologies on edge detection and image restoration and discuss connections and differences among these methods and related methods in the statistical literature

corrections to universal fluctuations in correlated systems the two dimensional xy model generalized universality as recently proposed postulates a universal non gaussian form of the probability density function pdf of certain global observables for a wide class of highly correlated systems of finite volume n studying the two dimensional xy model we link its validity to renormalization group properties it would be valid if there were a single dimension 0 operator but the actual existence of several such operators leads to t dependent corrections the pdf is the fourier transform of the partition function z q of an auxiliary theory which differs by a dimension 0 perturbation with a very small imaginary coefficient iq n from a theory which is asymptotically free in the infrared we compute the pdf from a systematic loop expansion of ln z q

markov chains with rare transitions and simulated annealing we consider approximate stationary markov chains in which the entries of the one step transition probability matrix are known to be of different orders of magnitude and whose structure that is the orders of magnitude of the transition probabilities does not change with time for such markov chains we present a method for generating order of magnitude estimates for the t step transition probabilities for any t we then notice that algorithms of the simulated annealing type may be represented by markov chains which are approximately stationary over fairly long time intervals using our results we obtain a characterization of the convergent cooling schedules for the most general class of algorithms of the simulated annealing type

unsupervised image segmentation using an unlabeled region process abstract the segmentation of a gray scale image of regions of uniform or slowly varying intensity is discussed a gibbsian representation is given for a partition of a lattice with no labels the homogeneity of each segment is measured by the sample variance of observations in a region merging algorithm the posterior probability of the segmentation is gradually increased it is shown how to simulate partitions with the gibbs sampler and how to combine information in simulated segmentations when the segments cannot be grouped into genuine classes the segmentation methods are preferable to classification by iterated conditional modes icm or by the maximizer of posterior marginals mpm

universal magnetic fluctuations with a field induced length scale we calculate the probability density function for the order parameter fluctuations in the low temperature phase of the two dimensional mathrm xy model of magnetism near the line of critical points a finite correlation length ensuremath xi is introduced with a small magnetic field h and an expression for ensuremath xi h is developed by treating nonlinear contributions to the field energy using a hartree approximation we find analytically a series of universal non gaussian distributions of the finite size scaling form p m l ensuremath xi ensuremath sim l ensuremath beta ensuremath nu p l ml ensuremath beta ensuremath nu ensuremath xi l and present a function of the form p x ensuremath sim mathrm exp x ensuremath mathrm exp x a h that gives the probability density functions to an excellent approximation we propose a h as an indirect measure of the length scale of correlations in a wide range of complex systems