pattern recognition by graph matching using the potts mft neural networks this paper is concerned with programming of the potts mean field theory neural networks for pattern recognition by homomorphic mapping of the attributed relational graphs arg in order to generate the homomorphic mapping from the scene relational graph to the model graph we make use of the recently introduced suganthan technical report nanyang technical university 1994 compatibility functions in relation to the hopfield network an efficient pose clustering algorithm is used to separate and localize different occurrences of any particular object model in the scene the pose clustering algorithm also eliminates spurious hypotheses generated by the network and resolves ambiguities in the final interpretation the performance of the proposed approach to pattern recognition by homomorphism is demonstrated using a number of line patterns silhouette images and circle patterns

exit problems associated with affine reflection groups we obtain a formula for the distribution of the first exit time of brownian motion from the alcove of an affine weyl group in most cases the formula is expressed compactly in terms of pfaffians expected exit times are derived in the type widetilde a case the results extend to other markov processes we also give formulas for the real eigenfunctions of the dirichlet and neumann laplacians on alcoves observing that the hot spots conjecture of j rauch is true for alcoves

intrinsic ultracontractivity and eigenfunction estimates for schrodinger operators let d be a domain in rn n 2 and let h h0 v where h0 is a divergence form uniformly elliptic operator with dirichlet boundary conditions and v is in the kato class intrinsic ultracontractivity is proved for the semigroup of h when d is holder domain of order 0 or a uniformly holder domain of order for 0 2 for every 2 there exists a uniformly holder domain of order for which the dirichlet laplacian is not intrinsically ultracontractive for a large class of domains it is shown that the heat kernels for h0 and h decay at the same rate at the boundary applications are given to the lifetime of conditioned brownian motion some of our results seem to be new even for smooth domains

image sequence analysis using relational structures abstract time varying images are usually analyzed to obtain a description of the observed objects and of their actions an abstraction process is necessary which converts the input images into symbolic descriptions the attributes of image symbols and the relationship between symbols are computed from the sampled intensity or colour measurements relational structures are a formal tool to describe not only the symbolic image representation but furthermore stored models as prototypes of objects and objects as instantiations of such prototypes following this paradigm an essential task of image sequence analysis is the generation of mappings between images to establish the correspondence relationship and between images and prototypes to identify objects different types of morphisms between relational structures rs morphisms are proposed together with an approach for computing them by searching for cliques in a compatibility graph of hypothetical assignments of elements from both structures the common formalism presented here aims at a unification of methods for those steps necessary to instantiate objects and follow them through the sequence one practical reason for this attempt is to make relational database systems available to store and retrieve the large amount of data whidch might be generated during the exploration of a real world image sequence

a consistent metric for performance evaluation of multi object filters the concept of a miss distance or error between a reference quantity and its estimated controlled value plays a fundamental role in any filtering control problem yet there is no satisfactory notion of a miss distance in the well established field of multi object filtering in this paper we outline the inconsistencies of existing metrics in the context of multi object miss distances for performance evaluation we then propose a new mathematically and intuitively consistent metric that addresses the drawbacks of current multi object performance evaluation metrics

discrete optimization by relational constraint satisfaction in pattern matching a basic problem is to determine one or more vectors x that maximize an objective function which is a sum of functions of components of x when this problem is solved by dynamic programming cpu time and storage requirements grow explosively as the amount of intervariable interaction in the objective function increases this explosion may be reduced by departing from the traditional dynamic programming method of eliminating successive variables and instead determining a constraint relation between each variable and all others with which it interacts discrete relaxation is used to accelerate a backtrack search to find all vectors that satisfy all such constraints optimization is achieved by evaluating the objective function for all such vectors this new method of optimization has been experimentally compared with a classical dynamic programming algorithm running with the same pseudorandomly generated objective functions

an elementary solution of gessel s walks in the quadrant abstract around 2000 ira gessel conjectured that the number of lattice walks in the quadrant n 2 starting and ending at the origin 0 0 and taking their steps in had a simple hypergeometric form in the following decade this problem was recast in the systematic study of walks with small steps that is steps in 1 0 1 2 confined to the quadrant the generating functions of such walks are archetypal solutions of partial discrete differential equations a complete classification of quadrant walks according to the nature of their generating function algebraic d finite or not is now available but gessel s walks remained mysterious because they were the only model among the 23 d finite ones that had not been given an elementary solution instead gessel s conjecture was first proved using an inventive computer algebra approach in 2008 a year later the associated three variate generating function was proved to be algebraic by a computer algebra tour de force this was re proved recently using elaborate complex analysis machinery we give here an elementary and constructive proof our approach also solves other quadrant models with multiple steps recently proved to be algebraic via computer algebra

renormalization group analysis of some dynamical systems with noise we formulate a renormalization group analysis for the study of the accumulation of period doubling in the presence of noise the main tool is a renormalization of the time evolution of the noise the critical indices depend on the nature of the noise but are given by thermodynamic quantities describing the large deviations of the lyapunov exponent of the linearized random renormalization

brownian motion in cones we study the asymptotic behavior of brownian motion and its conditioned process in cones using an infinite series representation of its transition density a concise probabilistic interpretation of this series in terms of the skew product decomposition of brownian motion is derived and used to show properties of the transition density

the lifetime of conditioned brownian motion in certain lipschitz domains for certain lipschitz domains d we obtain a series expansion for the distribution of the lifetime d of conditioned brownian motion on d from this we determine mathop lim limits t to infty text t 1 text log text p x h tau d text t mathop lim limits t to infty text t 1 text log text p x tau d text t text lambda d text where d is the first eigenvalue of 1 2 on d

random walks in cones we study the asymptotic behavior of a multidimensional random walk in a general cone we find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone the main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments for the proof of tail asymptotics and integral limit theorems we use a strong approximation of random walks by brownian motion for the proof of local limit theorems we suggest a rather simple approach which combines integral theorems for random walks in cones with classical local theorems for unrestricted random walks we also discuss some possible applications of our results to ordered random walks and lattice path enumeration

the first exit time of a brownian motion from an unbounded convex domain consider the first exit time d of a d 1 dimensional brownian motion from an unbounded open domain d set x y rd 1 dvtxy f x x rd starting at vspace 0 5pt x0 f x0 1 rd 1 for some x0 rd where the function f x on rd is convex and f x as the euclidean norm x very general estimates for the asymptotics of log pr d t are given by using gaussian techniques in particular for f x exp x p p 0 limt t 1 logt 2 plog pr d t j2 2 where d 2 2 and j is the smallest positive zero of the bessel function j

brownian motion in a quasi cone we determine precise logarithmic asymptotics of the probability of a large exit time for brownian motion in a quasi cone this answers a question formally posed by lifshits and shi bernoulli 8 745 765 2002 but first studied by li ann probab 31 1078 1096 2001

higher order pdes and symmetric stable processes we describe a connection between the semigroup of a symmetric stable process with rational index and higher order partial differential equations as an application we obtain a variational formula for the eigenvalues associated with the process killed upon leaving a bounded open set d the variational formula is more user friendly than the classical rayleigh ritz formula we illustrate this by obtaining upper bounds on the eigenvalues in terms of dirichlet eigenvalues of the laplacian on d these results generalize some work of banuelos and kulczycki on the cauchy process along the way we prove an operator inequality for the operators associated with the transition densities of brownian motion and the brownian motion killed upon leaving d

analytic implementations of the cardinalized probability hypothesis density filter the probability hypothesis density phd recursion propagates the posterior intensity of the random finite set rfs of targets in time the cardinalized phd cphd recursion is a generalization of the phd recursion which jointly propagates the posterior intensity and the posterior cardinality distribution in general the cphd recursion is computationally intractable this paper proposes a closed form solution to the cphd recursion under linear gaussian assumptions on the target dynamics and birth process based on this solution an effective multitarget tracking algorithm is developed extensions of the proposed closed form recursion to accommodate nonlinear models are also given using linearization and unscented transform techniques the proposed cphd implementations not only sidestep the need to perform data association found in traditional methods but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard phd filter our implementations only have a cubic complexity but simulations suggest favorable performance compared to the standard joint probabilistic data association jpda filter which has a nonpolynomial complexity

the bin occupancy filter and its connection to the phd filters an algorithm that is capable not only of tracking multiple targets but also of ldquotrack managementrdquo meaning that it does not need to know the number of targets as a user input is of considerable interest in this paper we devise a recursive track managed filter via a quantized state space ldquobinrdquo model in the limit as the discretization implied by the bins becomes as refined as possible infinitesimal bins we find that the filter equations are identical to mahler s probability hypothesis density phd filter a novel track managed filtering scheme that is attracting increasing attention thus one contribution of this paper is an interpretation of if not the phd itself at least what the phd is doing this does offer some intuitive appeal but has some practical use as well with this model it is possible to identify the phd s ldquotarget deathrdquo problem and also the statistical inference structures of the phd filters to obviate the target death problem phd originator mahler developed a new ldquocardinalizedrdquo version of phd cphd the second contribution of this paper is to extend the ldquobin occupancyrdquo model such that the resulting recursive filter is identical to the cardinalized phd filter

a subgraph isomorphism algorithm using resolution abstract an efficient algorithm for subgraph isomorphism is presented it combines tree search with relaxation by using resolution bitwise parallelism which is an important factor in speed is achieved during the resolution process even though a sequential computer is used the algorithm can be easily modified to apply to multi relation labeled graphs attributed graphs and some higher order structures such as arrangements

spectral geometry of singular riemannian spaces on considere la trace du noyau de la chaleur et l application de la methode de l equation de la chaleur au theoreme d indice pour la caracteristique d euler et des complexes signatures

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

on the hot spots conjecture of j rauch rodrigo banuelos research partially supported by nsf grant dms 9400854 krzysztof burdzy s research partially supported by nsf grant dms 9322689

matching invariant to translations rotations and scale changes abstract an optimization approach to invariant matching is proposed in this approach an object or a pattern is invariantly represented by an object centred description called an attributed relational structure ars embedding invariant properties and relations between the primitives of the pattern such as line segments and points noise effect is taken into account such that a scene can consist of noisy sub parts of a model the matching is then to find the optimal mapping between the arss of the scene and the model a gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labelling method experiments are shown to illustrate the matching algorithm and to demonstrate that the approach is truly invariant to arbitrary translations rotations and scale changes under noise

brownian motion in wedges last passage time and the second arc sine law we consider a planar brownian motion starting from o at time t 0 and stopped at t 1 and a set f oii i 1 2 n of n semi infinite straight lines emanating from o denoting by g the last time when f is reached by the brownian motion we compute the probability law of g in particular we show that for a symmetric f and even n values this law can be expressed as a sum of arcsin or arcsin 2 functions the original result of levy is recovered as the special case n 2 a relation with the problem of reaction diffusion of a set of three particles in one dimension is discussed

optimal encoding of graph homomorphism energy using fuzzy information aggregation operators abstract the attributed relational graph matching arg strategy is a well known approach to object pattern recognition in the past for the parallel solution of arg matching problem an overall objective function was constructed using linearly weighted information aggregation function and one set of parameter values was chosen for all models by trial and error for the parameters in the function in this paper the compatibility between every pair of model and scene attributes is interpreted as a fuzzy value and subsequently the nonlinear fuzzy information aggregation operators are used to fuse the information captured in the chosen attributes to learn the parameters in the fuzzy information aggregation operators the learning from samples strategy is used the learning of weight parameters is formulated as an optimisation problem and solved using the gradient projection algorithm based learning procedure the learning procedure implicitly evaluates ambiguity robustness and discriminatory power of the relational attributes chosen for graph matching and assigns weights appropriately to the chosen attributes the learning procedure also enables us to compute a distinct set of optimal parameters for every model to reflect the characteristics of the model so that the homomorphic arg matching problem can be optimally encoded in the energy function for the model experimental results are presented to illustrate effectiveness and necessity of the parameter estimation and learning procedures

invariant representation matching and pose estimation of 3d space curves under similarity transformations this paper presents a system for matching and pose estimation of 3d space curves under the similarity transformation composed of rotation translation and uniform scaling the system makes use of constraints not only on the feature points but also on curve segments a representation called the similarity invariant coordinate system sics is presented for deriving semi local invariants of 3d curves the sics also enables an efficient exploration of constraints on the shape of the entire curve model based curve matching is performed in the principle of maximum a posteriori map probability in which markov random fields mrfs are used to model the prior probability results are given to demonstrate the matching with missing and extra feature points the extensive exploration of the curve shape constraints in both the matching and the pose estimation stages are shown to significantly improve the quality of the recognition and pose estimation

the first exit time of a two dimensional symmetric stable process from a wedge let t be the first exit time of a symmetric stable process with parameter 0 2 from a wedge of angle 2 0 0 such that for starting points x in the wedge e x t p p we characterize p and obtain upper and lower bounds

the expected time to end the tug of war in a wedge using a solution of a nonhomogeneous partial differential equation involving the p laplacian we study the finiteness of the expected time to end the tug of war in a wedge

a capture problem in brownian motion and eigenvalues of spherical domains we resolve a question of bramson and griffeath by showing that the expected capture time of four predators pursuing a single prey all moving by standard brownian motion on a line is finite our main tool is an eigenvalue estimate for a particular spherical domain which we obtain by a coning construction and domain perturbation

on the occupation times of cones by brownian motion we study some features concerning the occupation timeat of a d dimensional conec by brownian motion in particular in the case wherec is convex we investigate the asymptotic behaviour ofp a1 u asu 0 when the brownian motion starts at the vertex ofc we also give the precise integral test which decides whether a s lim inft at tf t 0 or for a decreasing functionf

nonintersecting paths pfaffians and plane partitions gessel and viennot have developed a powerful technique for enumerating various classes of plane partitions the purpose of this article is to show by similar means that one may use pfaffiants to enumerate configurations of nonintersecting paths in which the initial and or terminal vertices of the paths are allowed to vary over specified regions of the digraph this leads to the possibility of enumerating classes of plane partitions in which the shape is allowed to vary whereas the previous applications of gessel and viennot were largely confined to plane partitions of a given shape

matching hierarchical structures using association graphs it is well known that the problem of matching two relational structures can be posed as an equivalent problem of finding a maximal clique in a derived association graph however it is not clear how to apply this approach to computer vision problems where the graphs are hierarchically organized i e are trees since maximal cliques are not constrained to preserve the partial order we provide a solution to the problem of matching two trees by constructing the association graph using the graph theoretic concept of connectivity we prove that in the new formulation there is a one to one correspondence between maximal cliques and maximal subtree isomorphisms this allows us to cast the tree matching problem as an indefinite quadratic program using the motzkin straus theorem and we use replicator dynamical systems developed in theoretical biology to solve it such continuous solutions to discrete problems are attractive because they can motivate analog and biological implementations the framework is also extended to the matching of attributed trees by using weighted association graphs we illustrate the power of the approach by matching articulated and deformed shapes described by shock trees

eccentric behaviors of the brownian sheet along lines keywords brownian sheet level sets points of increase reference prob article 2002 001view record in web of science record created on 2008 12 01 modified on 2017 05 12

non extinction of a fleming viot particle model we consider a branching particle model in which particles move inside a euclidean domain according to the following rules the particles move as independent brownian motions until one of them hits the boundary this particle is killed but another randomly chosen particle branches into two particles to keep the population size constant we prove that the particle population does not approach the boundary simultaneously in a finite time in some lipschitz domains this is used to prove a limit theorem for the empirical distribution of the particle family

structural matching in computer vision using probabilistic relaxation in this paper we develop the theory of probabilistic relaxation for matching features extracted from 2d images derive as limiting cases the various heuristic formulae used by researchers in matching problems and state the conditions under which they apply we successfully apply our theory to the problem of matching and recognizing aerial road network images based on road network models and to the problem of edge matching in a stereo pair for this purpose each line network is represented by an attributed relational graph where each node is a straight line segment characterized by certain attributes and related with every other node via a set of binary relations

the first exit time of planar brownian motion from the interior of a parabola let d be the interior of a parabola in mathbb r 2 and tau d the first exit time of brownian motion from d we show log p tau d t behaves like t 1 3 as t to infty

the exact asymptotic of the collision time tail distribution for independent brownian particles with different drifts in this note we consider the time of the collision for n independent brownian motions x1t xtn with drifts a1 an each starting from x x1 xn where x1 t ch bf x t alpha rm e gamma t 1 o 1 as t and identify c h x in terms of the drifts

exit times from cones in ℝ n of brownian motion for a fairly general class of cones inn dimensions n 3 we determine the corresponding distributions of brownian first exit times asymptotic results may then be read off

the gaussian mixture probability hypothesis density filter a new recursive algorithm is proposed for jointly estimating the time varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty detection uncertainty noise and false alarms the approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density phd recursion to propagate the posterior intensity which is a first order statistic of the random finite set of targets in time at present there is no closed form solution to the phd recursion this paper shows that under linear gaussian assumptions on the target dynamics and birth process the posterior intensity at any time step is a gaussian mixture more importantly closed form recursions for propagating the means covariances and weights of the constituent gaussian components of the posterior intensity are derived the proposed algorithm combines these recursions with a strategy for managing the number of gaussian components to increase efficiency this algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented kalman filters

remark on exit times from cones in mathbb r n of brownian motion our purpose is to show how the asymptotics in corollary 1 3 of 2 can be obtained under much weaker hypotheses it turns out the problem essentially reduces to showing that if r s is a bessel process u 0 and 0 then p left mathop f limits 0 1 r s 2 ds leqq u right o t alpha as t we provide a simple proof of this fact

the multiple model cphd tracker the probability hypothesis density phd is a practical approximation to the full bayesian multi target filter the cardinalized phd cphd filter was proposed to deal with the target death problem of the phd filter a multiple model phd exists in this work a multiple model version of the considerably more complex cphd filter is derived it is implemented using gaussian mixtures and a track management for display and scoring strategy is developed