generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

conditional gauge and potential theory for the schrodinger operator on etend le theoreme de jauge conditionnelle a des operateurs plus generaux et a des domaines moins reguliers on obtient des resultats de theorie du potentiel pour l equation de schrodinger

a limiting result for the structure of collisions between many independent diffusions we study a system of a large number n of independent diffusions undergoing collisions in a roughly constant mean free path regime we derive a propagation of chaos result when n goes to infinity concerning the limit behavior of the trajectory of a particle its first time of collision with all the other particles and the trajectory of the colliding particle

inherent bias and noise in the hough transform considering the hough transformation as a linear imaging process recasts certain well known problems provides a useful vocab ulary and possibly indicates a source of applicable literature on the behavior of the hough transformation in various forms of noise a consideration of the analytic form of peaks in parameter space sets the stage for the idea of using complementary negative votes to cancel off peak positive votes in parameter space thus sharpening peaks and reducing bias

distance statistics in quadrangulations with no multiple edges and the geometry of minbus we present a detailed calculation of the distance dependent two point function for quadrangulations with no multiple edges various discrete observables measuring this two point function are computed and analyzed in the limit of large maps for large distances and in the scaling regime we recover the same universal scaling function as for general quadrangulations we then explore the geometry of lsquo minimal neck baby universes rsquo minbus which are the outgrowths to be removed from a general quadrangulation to transform it into a quadrangulation with no multiple edges the lsquo mother universe rsquo we give a number of distance dependent characterizations of minbus such as the two point function inside a minbu or the law for the distance from a random point to the mother universe

a robust real time ellipse detector abstract in this paper we present an improved ellipse detector that may be used in real time face detection in this algorithm we first extract edges from the image using a robust edge detector which is then followed by a rule based method finally we decompose the parameter space of the hough transform to achieve computational efficiency our extensive experimental results show indeed that the proposed detector is capable of detecting ellipse features with an excellent accuracy under various image conditions at a high speed 10 frames per second on a pentium iii 500 mhz pc

genetic algorithm with competitive image labelling and least square abstract a multi modal genetic algorithm using a dynamic population concept is introduced each image point is assigned a label and for a chromosome to survive it must have at least one image point with its label in this way the genetic algorithm dynamically segments the scene into one or more objects and the background noise a repeated least square technique is applied to enhance the convergence performance the integrated algorithm is tested using a 6 degrees of freedom template matching problem and it is applied to some images that are challenging for genetic algorithm applications

simulation of stopped diffusions in this work we study standard euler updates for simulating stopped diffusions as an immediate application we discuss the computation of first exit times of diffusions from a domain we focus on one dimensional situations and show how the ideas for the simulation of killed diffusions can be adapted to this problem in particular we give a fully implementable algorithm to compute the first exit time from an interval numerically the brownian motion case is treated in detail and extensions to general diffusions are given special emphasis is given to numerical experiments for every ansatz we include numerical experiments confirming the conjectured accuracy of our methods our algorithm is of order one in a weak sense comparisons with other algorithms are shown results that are superior to those obtained with other methods are presented when approximating a first hitting time distribution the results obtained with our algorithm are much better than those achieved with other methods

anomalous diffusion of random walk on random planar maps we prove that the simple random walk on the uniform infinite planar triangulation uipt typically travels graph distance at most n 1 4 o n 1 in n units of time together with the complementary lower bound proven by gwynne and miller 2017 this shows that the typical graph distance displacement of the walk after n steps is n 1 4 o n 1 as conjectured by benjamini and curien geom funct anal 2 2 501 531 2013 arxiv 1202 5454 more generally we show that the simple random walks on a certain family of random planar maps in the gamma liouville quantum gravity lqg universality class for gamma in 0 2 including spanning tree weighted maps bipolar oriented maps and mated crt maps typically travels graph distance n 1 d gamma o n 1 in n units of time where d gamma is the growth exponent for the volume of a metric ball on the map which was shown to exist and depend only on gamma by ding and gwynne commun math phys 374 1877 1934 2018 arxiv 1807 01072 since d gamma 2 this shows that the simple random walk on each of these maps is subdiffusive our proofs are based on an embedding of the random planar maps under consideration into mathbb c wherein graph distance balls can be compared to euclidean balls modulo subpolynomial errors this embedding arises from a coupling of the given random planar map with a mated crt map together with the relationship of the latter map to sle decorated lqg

function theory random paths and covering spaces pour des varietes de riemann connexes m on etudie la relation entre la theorie de fonction harmonique sur m les proprietes statistiques des chemins aleatoires sur m et la structure geometrique globale de m

recognition of handprinted hebrew characters using features selected in the hough transform space abstract automatic identification of handprinted hebrew characters is described in this paper the recognition model devised constitutes a multi stage system in the first stage a coarse classifier allocates the input patterns into one of 17 categories based on the number and the location of end points within predetermined regions in the characters matrix the second stage uses features extracted in the hough transform space to classify characters assigned to each of 16 categories the remaining one category composed of similar square like rotated l shape classes is recognized by structural analysis and a statistical classifier an additional step of postprocessing is added to compensate for the sensitivity of the hough transform to the existence of similar classes within some of the categories experiments were conducted with a multi author 40 writers data base an average recognition rate of 86 9 was observed for the system this compared favorably with the results of two other recognition methods

harmonic functions and exit boundary of superdiffusion abstract all positive harmonic functions in an arbitrary domain of a euclidean space can be described in terms of the so called exit boundary this was established in 1941 by r s martin a probabilistic approach to the martin theory is due to doob and hunt it was extended later to harmonic functions associated with a wide class of markov processes the subject of this paper are harmonic functions associated with a superdiffusion x we call them x harmonic the results of evans and perkins imply the existence and uniqueness of an integral representation of positive x harmonic functions through extreme functions an outstanding problem is to find all extremal functions they are in 1 1 correspondence with the points of the exit boundary an interest in x harmonic functions is motivated in part by the fact that each of them provides a way of conditioning a superprocess path properties of conditioned superprocesses corresponding to various special x harmonic functions were investigated by a number of authors important classes of x harmonic functions are related to positive solutions of semilinear partial differential equations almost nothing is known about their decomposition into extreme elements a progress in this direction may create new tools for investigating solutions of the equations the goal of this paper is to summarize all known facts about x harmonic functions to present the results of various authors in a more general setting in a unified form and to outline a program of further work

subtree prune and regraft a reversible real tree valued markov process we use dirichlet form methods to construct and analyze a reversible markov process the stationary distribution of which is the brownian continuum random tree this process is inspired by the subtree prune and regraft spr markov chains that appear in phylogenetic analysis a key technical ingredient in this work is the use of a novel gromov hausdorff type distance to metrize the space whose elements are compact real trees equipped with a probability measure also the investigation of the dirichlet form hinges on a new path decomposition of the brownian excursion

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

propagation of chaos for a system of annihilating brownian spheres on etudie un systeme de n boules euclidiennes de rayon s n 2 dans r d dont les centres evoluent selon des mouvements browniens independants x i 1 c n initialement distribues comme u 0 dx v x dx v borne qui disparaissent aussitot une collision avec d autres boules on montre que ce systeme de particules presente une propagation de la propriete de chaos

invariance principles for random bipartite planar maps it is conjectured in the physics literature that properly rescaled random planar maps when conditioned to have a large number of faces should converge to a limiting surface whose law does not depend up to scaling factors on details of the class of maps that are sampled previous works on the topic starting with chassaing schaeffer have shown that the radius of a random quadrangulation with n faces converges in distribution once rescaled by n 1 4 to the diameter of the brownian snake up to a scaling constant using a bijection due to bouttier di francesco guitter between bipartite planar maps and a family of labeled trees we show the corresponding invariance principle for a class of random maps that follow a boltzmann distribution the radius of such maps conditioned to have n faces or n vertices and under a criticality assumption converges in distribution once rescaled by n 1 4 to a scaled version of the diameter of the brownian snake convergence results for the so called profile of maps are also provided as well as convergence of rescaled bipartite maps to the brownian map as introduced by marckert mokkadem the proofs of these results rely on a new invariance principle for two type spatial galton watson trees

geometric primitive extraction using a genetic algorithm extracting geometric primitives from geometric sensor data is an important problem in model based vision a minimal subset is the smallest number of points necessary to define a unique instance of a geometric primitive a genetic algorithm based on a minimal subset representation is used to perform primitive extraction it is shown that the genetic approach is an improvement over random search and is capable of extracting more complex primitives than the hough transform

a distributed hierarchical genetic algorithm for efficient optimization and pattern matching in this paper we propose a new approach in genetic algorithm called distributed hierarchical genetic algorithm dhga for optimization and pattern matching it is eventually a hybrid technique combining the advantages of both distributed and hierarchical processes in exploring the search space the search is initially distributed over the space and then in each subspace the algorithm works in a hierarchical way the entire space is essentially partitioned into a number of subspaces depending on the dimensionality of the space this is done in order to spread the search process more evenly over the whole space in each subspace the genetic algorithm is employed for searching and the search process advances from one hypercube to a neighboring hypercube hierarchically depending on the convergence status of the population and the solution obtained so far the dimension of the hypercube and the resolution of the search space are altered with iterations thus the search process passes through variable resolution coarse to fine search space both analytical and empirical studies have been carried out to evaluate the performance between dhga and distributed conventional ga dcga for different function optimization problems further the performance of the algorithms is demonstrated on problems like pattern matching and object matching with edge map

local extinction versus local exponential growth for spatial branching processes let x be either the branching diffusion corresponding to the operator lu u2 u on d rd where x 0 and 0 is bounded from above or the superprocess corresponding to the operator lu u u2 on d rd with 0 and is bounded from above but no restriction on its sign let c denote the generalized principal eigenvalue for the operator l on d we prove the following dichotomy either c 0 and x exhibits local extinction or c 0 and there is exponential growth of mass on compacts of d with rate c for superdiffusions this completes the local extinction criterion obtained by pinsky ann probab 24 1996 237 267 and a recent result on the local growth of mass under a spectral assumption given by englander and turaev ann probab 30 2002 683 722 the proofs in the above two papers are based on pde techniques however the proofs we offer are probabilistically conceptual for the most part they are based on spine decompositions or immortal particle representations along with martingale convergence and the law of large numbers further they are generic in the sense that they work for both types of processes

the multiple window parameter transform the multiwindow transform an extension of parameter transform techniques that increase performance and scope by exploiting the long range correlated information contained in multiple portions of an image is presented multiple window transforms allow the extraction of high dimensional features with improvement in accuracy over conventional techniques while keeping linear to low order polynomial computational and space requirements with respect to image size and dimensionality of the features using correlated information provides a direct link between extracted features and supporting regions in the image this coupled with evidence integration techniques is used to suppress noisy or nonexistent feature hypotheses parameter spaces are implemented as constraint satisfaction networks where feature hypotheses with overlapping support in the image compete after an iterative relaxation phase surviving hypotheses have disjoint support forming a segmentation of the image examples show the performance and provide insight about the behavior

spines skeletons and the strong law of large numbers for superdiffusions consider a supercritical superdiffusion x t t 0 on a domain d r d with branching mechanism x z x z x z 2 0 e zy 1 zy x dy the skeleton decomposition provides a pathwise description of the process in terms of immigration along a branching particle diffusion we use this decomposition to derive the strong law of large numbers slln for a wide class of superdiffusions from the corresponding result for branching particle diffusions that is we show that for suitable test functions f and starting measures f x t p f x t w p almost surely as t where w is a finite non deterministic random variable characterized as a martingale limit our method is based on skeleton and spine techniques and offers structural insights into the driving force behind the slln for superdiffusions the result covers many of the key examples of interest and in particular proves a conjecture by fleischmann and swart stochastic process appl 106 2003 141 165 for the super wright fisher diffusion

gradient estimates on manifolds using coupling we use a coupling method to give gradient estimates for solutions to 12 z u 0 on a manifold the size of the gradient depends on a lower bound on the ricci curvature of the manifold and bounds on the vector field z

lower order circle and ellipse hough transform in this work we present two new algorithms for the detection of circles and ellipses which use the fht algorithm as a basis fast circle hough transform fcht and fast ellipse hough transform feht the first stage of these two algorithms devoted to obtaining the centers of the figures is computationally the most costly with the objective of improving the execution times of this stage it has been implemented using a new focusing algorithm instead of the typical polling process in a parameter space this new algorithm uses a new strategy that manages to reduce the execution times especially in the case where multiple figures appear in the image or when they are of very different sizes we also perform a labeling of the image points that permits discriminating which of these belong to each figure saving computations in subsequent stages

conditioned super brownian motion we investigate classes of conditioned super brownian motions namely h transformsp h with non negative finitely based space time harmonic functionsh t we prove thath h is the unique solution of a martingale problem with interaction and is a weak limit of a sequence of rescaled interacting branching brownian motions we identify the limit behaviour of h transforms with functionsh t h t 1 depending only on the total mass 1 using the palm measures of the super brownian motion we describe for an additive spacetime harmonic functionh t h t x dx theh transformp h as a conditioned super brownian motion in which an immortal particle moves like an h transform of brownian motion

sur la saucisse de wiener et les points multiples du mouvement brownien on considere b t t 0 un mouvement brownien a valeurs dans l espace euclidien a d dimensions r d d 2 issu de o on s interesse a la probabilite que b penetre avant un instant donne t dans une petite boule de l espace

face contour extraction from front view images abstract facial feature detection is crucial for visual recognition of human faces this paper reports on a study in detecting face contours from front view id type pictures based on the eye and mouth positions which can be detected by the algorithms proposed in ref 1 g chow and x li pattern recognition 26 1739 1755 1993 a simplified adaptive hough transform aht technique is used to identify straight cheek lines which are approximately vertical from the edge image independently parabolas forming the chin are detected by another aht procedure the location and curvature of the chin line together with the cheek lines characterize the shape of the face this method was tested on over 70 different face images and is shown to produce results with a high degree of accuracy we discuss in detail the specific issues involved in the detections such as the definition of relevant subimage parameter ranges resolution of the accumulator array peak cells and end point determination

local convergence of large random triangulations coupled with an ising model we prove the existence of the local weak limit of the measure obtained by sampling random triangulations of size n decorated by an ising configuration with a weight proportional to the energy of this configuration to do so we establish the algebraicity and the asymptotic behaviour of the partition functions of triangulations with spins for any boundary condition in particular we show that these partition functions all have the same phase transition at the same critical temperature some properties of the limiting object called the infinite ising planar triangulation are derived including the recurrence of the simple random walk at the critical temperature

stochastic de giorgi iteration and regularity of stochastic partial differential equations under general conditions we devise a stochastic version of de giorgi iteration scheme for semilinear stochastic parabolic partial differential equation of the form tu div a u f t x u gi t x u w ti with progressively measurable diffusion coefficients we use the scheme to show that the solution of the equation is almost surely holder continuous in both space and time variables

the radial part of brownian motion ii its life and times on the cut locus this paper is a sequel to kendall 1987 which explained how the ito formula for the radial part of brownian motionx on a riemannian manifold can be extended to hold for all time including those times a whichx visits the cut locus this extension consists of the subtraction of a correction term a continuous predictable non decreasing processl which changes only whenx visits the cut locus in this paper we derive a representation onl in terms of measures of local time ofx on the cut locus in analytic terms we compute an expression for the singular part of the laplacian of the riemannian distance function the work uses a relationship of the riemannian distance function to convexity first described by wu 1979 and applied to radial parts of martingales in kendall 1993

the scaling limit of random simple triangulations and random simple quadrangulations let mnmn be a simple triangulation of the sphere s2s2 drawn uniformly at random from all such triangulations with nn vertices endow mnmn with the uniform probability measure on its vertices after rescaling graph distance by 3 4n 1 4 3 4n 1 4 the resulting random measured metric space converges in distribution in the gromov hausdorff prokhorov sense to the brownian map in proving the preceding fact we introduce a labelling function for the vertices of mnmn under this labelling distances to a distinguished point are essentially given by vertex labels with an error given by the winding number of an associated closed loop in the map we establish similar results for simple quadrangulations

coupled brownian motions and partial domain monotonicity for the neumann heat kernel abstract let d and be two convex domains with smooth boundary and with corresponding neumann heat kernels d x y t and gw x y t chavel has conjectured that if x y d then the following monotonicity result holds for all t d x y t x y t he has proved this in the special case when is a ball centred at either x or y by exploiting the connection of the neumann kernel to reflecting brownian motion it is possible to prove the result when is general and d is a ball centred at either x or y the proof depends on a careful coupling construction of the reflecting brownian motions for d and using the same probability space for both processes

etude asymptotique par des mesures de 135 1135 1135 1de saucisses de wiener localisees let b t t 0 be a brownian motion in 3 we denote its wiener sausage byw t 1 n w t 1 n left m in mathbb r 3 exists s leqq t parallel b s m parallel leqq frac 1 n right spitzer has proved in 64 that lim n vol w t 1 n 2 t

path processes and historical superprocesses a superprocessx over a markov process can be obtained by a passage to the limit from a branching particle system for which describes the motion of individual particles the historical process hat xi for is the process whose state at timet is the path of over time interval 0 t the superprocess hat x over hat xi the historical superprocess over reflects not only the particle distribution at any fixed time but also the structure of family trees the principal property of a historical process hat xi is that hat xi s is a function of hat xi t for alls t every process with this property is calleda path process we develop a theory of superprocesses over path processes whose core is the integration with respect to measure functionals by applying this theory to historical superprocesses we construct the first hitting distributions and prove a special markov property for superprocesses

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

circle detection using electro magnetism optimization nature inspired computing has yielded remarkable applications of collective intelligence which considers simple elements for solving complex tasks by common interaction on the other hand automatic circle detection in digital images has been considered an important and complex task for the computer vision community that has devoted a tremendous amount of research seeking for an optimal circle detector this paper presents an algorithm for the automatic detection of circular shapes embedded into cluttered and noisy images without considering conventional hough transform techniques the approach is based on a nature inspired technique known as the electro magnetism optimization emo it follows the electro magnetism principle regarding a collective attraction repulsion mechanism which manages particles towards an optimal solution each particle represents a solution by holding a charge which is related to the objective function to be optimized the algorithm uses the encoding of three non collinear points embedded into an edge only image as candidate circles guided by the values of the objective function the set of encoded candidate circles charged particles are evolved using an emo algorithm so that they can fit into actual circular shapes over the edge only map of the image experimental evidence from several tests on synthetic and natural images which provide a varying range of complexity validates the efficiency of our approach regarding accuracy speed and robustness

compact brownian surfaces i brownian disks we show that under certain natural assumptions large random plane bipartite maps with a boundary converge after rescaling to a one parameter family mathrm bd l 0 l infty of random metric spaces homeomorphic to the closed unit disk of mathbb r 2 the space mathrm bd l being called the brownian disk of perimeter l and unit area these results can be seen as an extension of the convergence of uniform plane quadrangulations to the brownian map which intuitively corresponds to the limit case where l 0 similar results are obtained for maps following a boltzmann distribution in which the perimeter is fixed but the area is random

connecting brownian paths on considere deux processus l un etant le mouvement brownien conditionne de doob z et l autre ayant une distribution absolument continue relativement a celle de z

the topological structure of scaling limits of large planar maps we discuss scaling limits of large bipartite planar maps if p 2 is a fixed integer we consider for every integer n 2 a random planar map mn which is uniformly distributed over the set of all rooted 2p angulations with n faces then at least along a suitable subsequence the metric space consisting of the set of vertices of mn equipped with the graph distance rescaled by the factor n 1 4 converges in distribution as n towards a limiting random compact metric space in the sense of the gromov hausdorff distance we prove that the topology of the limiting space is uniquely determined independently of p and of the subsequence and that this space can be obtained as the quotient of the continuum random tree for an equivalence relation which is defined from brownian labels attached to the vertices we also verify that the hausdorff dimension of the limit is almost surely equal to 4

limit of normalized quadrangulations the brownian map consider qn a random pointed quadrangulation chosen equally likely among the pointed quadrangulations with n faces in this paper we show that when n goes to qn suitably normalized converges weakly in a certain sense to a random limit object which is continuous and compact and that we name the brownian map the same result is shown for a model of rooted quadrangulations and for some models of rooted quadrangulations with random edge lengths a metric space of rooted resp pointed abstract maps that contains the model of discrete rooted resp pointed quadrangulations and the model of the brownian map is defined the weak convergences hold in these metric spaces

weak limits of stopped diffusions on considere le probleme d homogeneisation suivant soit le mouvement brownien dans r d d 3 tue sur la surface de plusieurs petits corps absorbants on etudie la limite lorsque le nombre de corps approche l infini et que la dimension des corps approche 0

stability of geodesics in the brownian map the brownian map is a random geodesic metric space arising as the scaling limit of random planar maps we strengthen the so called confluence of geodesics phenomenon observed at the root of the map and with this reveal several properties of its rich geodesic structure our main result is the continuity of the cut locus at typical points a small shift from such a point results in a small local modification to the cut locus moreover the cut locus is uniformly stable in the sense that any two cut loci coincide outside a closed nowhere dense set of zero measure we obtain similar stability results for the set of points inside geodesics to a fixed point furthermore we show that the set of points inside geodesics of the map is of first baire category hence most points in the brownian map are endpoints finally we classify the types of geodesic networks which are dense for each k 1 2 3 4 6 9 k 1 2 3 4 6 9 there is a dense set of pairs of points which are joined by networks of exactly kk geodesics and of a specific topological form we find the hausdorff dimension of the set of pairs joined by each type of network all other geodesic networks are nowhere dense

toward global solution to map image restoration and segmentation using common structure of local minima abstract in this paper an iterative optimization algorithm called the comb algorithm is presented for approximating the global solution to map image restoration and segmentation the comb derives new initial configurations based on the best local minimum found so far and leads a local search towards the global minimum experimental comparisons show that the comb produces solutions of quality comparable to simulated annealing

a probabilistic approach to martin boundaries for manifolds with ends we use martingale methods and coupling arguments to prove results of li and tam 1987 and donnelly 1986 characterizing positive and bounded harmonic functions respectively on certain manifolds with ends

lifschitz tail on hyperbolic space neumann conditions on considere un espace hyperbolique h de dimension n et l operateur laplacien hyperbolique h etant donne une distribution aleatoire de points a l aide d un processus ponctuel de poisson tel que chaque point se situe dans une boule hyperbolique de rayons on etudie la question suivante si est un petit nombre reel combien y a t il de valeurs propres inferieures a pour l operateur 1 2 h dans une boule b de centre o avec des conditions de neumann sur la frontiere et avec des conditions aux limites de dirichlet sur les boules aleatoires formant des intersections avec b si le rayon de b est suffisamment grand

sur la mesure de sortie du super mouvement brownien we study some properties of the exit measure of super brownian motion from a smooth domaind inr d in particular we give precise estimates for the probability that the exit measure gives a positive mass to a small ball on the boundary as an application we compute the hausdorff dimension of the support of the exit measure in dimension 2 we prove that the exit measure is absolutely continuous with respect to the lebesgue measure on the boundary in connection with dynkin s work our results give some information on the behavior of solutions of u u 2 ind and are related to the characterization of removable singularities at the boundary as a consequence of our estimates we give a sufficient condition for the uniqueness of the positive solution of u u 2 ind that tends to on an open subseto of d and to 0 on the complement in d of the closure ofo our proofs use the path valued process studied in l2 l3

uniqueness and universality of the brownian map we consider a random planar map mn which is uniformly distributed over the class of all rooted q angulations with n faces we let mn be the vertex set of mn which is equipped with the graph distance dgr both when q 4 is an even integer and when q 3 there exists a positive constant cq such that the rescaled metric spaces mn cqn 1 4dgr converge in distribution in the gromov hausdorff sense toward a universal limit called the brownian map the particular case of triangulations solves a question of schramm

solutions of nonlinear differential equations on a riemannian manifold and their trace on the martin boundary let l be a second order elliptic differential operator on a riemannian manifold e with no zero order terms we say that a function h is l harmonic if lh 0 every positive l harmonic function has a unique representation

a probabilistic approach to one class of nonlinear differential equations we establish connections between positive solutions of one class of nonlinear partial differential equations and hitting probabilities and additive functionals of superdiffusion processes as an application we improve results on superprocesses by using the recent progress in the theory of removable singularities for differential equations

robust clustering with applications in computer vision a clustering algorithm based on the minimum volume ellipsoid mve robust estimator is proposed the mve estimator identifies the least volume region containing h percent of the data points the clustering algorithm iteratively partitions the space into clusters without prior information about their number at each iteration the mve estimator is applied several times with values of h decreasing from 0 5 a cluster is hypothesized for each ellipsoid the shapes of these clusters are compared with shapes corresponding to a known unimodal distribution by the kolmogorov smirnov test the best fitting cluster is then removed from the space and a new iteration starts constrained random sampling keeps the computation low the clustering algorithm was successfully applied to several computer vision problems formulated in the feature space paradigm multithresholding of gray level images analysis of the hough space and range image segmentation

the brownian map is the scaling limit of uniform random plane quadrangulations we prove that uniform random quadrangulations of the sphere with n faces endowed with the usual graph distance and renormalized by n 1 4 converge as n in distribution for the gromov hausdorff topology to a limiting metric space we validate a conjecture by le gall by showing that the limit is up to a scale constant the so called brownian map which was introduced by marckert mokkadem and le gall as the most natural candidate for the scaling limit of many models of random plane maps the proof relies strongly on the concept of geodesic stars in the map which are configurations made of several geodesics that only share a common endpoint and do not meet elsewhere

random planar lattices and integrated superbrownian excursion in this paper a surprising connection is described between a specific brand of random lattices namely planar quadrangulations and aldous integrated superbrownian excursion ise as a consequence the radius r n of a random quadrangulation with n faces is shown to converge up to scaling to the width r r l of the support of the one dimensional ise or precisely more generally the distribution of distances to a random vertex in a random quadrangulation is described in its scaled limit by the random measure ise shifted to set the minimum of its support in zero the first combinatorial ingredient is an encoding of quadrangulations by trees embedded in the positive half line reminiscent of cori and vauquelin s well labelled trees the second step relates these trees to embedded discrete trees in the sense of aldous via the conjugation of tree principle an analogue for trees of vervaat s construction of the brownian excursion from the bridge from probability theory we need a new result of independent interest the weak convergence of the encoding of a random embedded plane tree by two contour walks to the brownian snake description of ise our results suggest the existence of a continuum random map describing in term of ise the scaled limit of the dynamical triangulations considered in two dimensional pure quantum gravity

on the conditioned exit measures of super brownian motion in this paper we present a martingale related to the exit measures of super brownian motion by changing measure with this martingale in the canonical way we have a new process associated with the conditioned exit measure this measure is shown to be identical to a measure generated by a non homogeneous branching particle system with immigration of mass an application is given to the problem of conditioning the exit measure to hit a number of specified points on the boundary of a domain the results are similar in flavor to the immortal particle picture of conditioned super brownian motion but more general as the change of measure is given by a martingale which need not arise from a single harmonic function

the radial part of brownian motion on a manifold a semimartingale property on montre que la discrepance entre les deux membres de la formule de ito forme un processus aleatoire monotone

equations de type de boltzmann spatialement homogenes we study the construction of a nonhomogeneous n valued markov process whose laws at fixed times evolve according to a boltzmann type equation spatially homogeneous we then consider the problem of the asymptotic propagation of chaos for a system of a large number of interacting particles

lifschitz tail and wiener sausage ii the present paper is a continuation of 23 we present here two examples of situations where the method developed in 23 applies the first example is that of a periodic diffusion z in r n 1 with generator l isia dj where a is a c2 z periodic elliptic matrix we consider the wiener sausage w u0 c u i z c where c is a nonpolar compact subset of r for instance a closed ball or disc in r if a denotes the constant matrix of homogenized coefficients of the periodic diffusion see 1 i we show that

on using directional information for parameter space decomposition in ellipse detection in this paper we use the parametric polar representation to extend the application of edge directional information from circle to ellipse extraction as a result we obtain a mapping which decomposes the parameter space required for ellipse extraction into two independent sub spaces and one final histogram accumulator the mapping includes the tangent of the angle of the first and second directional derivatives these tangents are computed by considering edge direction at two border points we show that the use of gradient information for parameter space decomposition avoids the intensive point labelling imposed by geometric constraints used by other approaches

estimation of planar curves surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation the author addresses the problem of parametric representation and estimation of complex planar curves in 2 d surfaces in 3 d and nonplanar space curves in 3 d curves and surfaces can be defined either parametrically or implicitly with the latter representation used here a planar curve is the set of zeros of a smooth function of two variables x y a surface is the set of zeros of a smooth function of three variables x y z and a space curve is the intersection of two surfaces which are the set of zeros of two linearly independent smooth functions of three variables x y z for example the surface of a complex object in 3 d can be represented as a subset of a single implicit surface with similar results for planar and space curves it is shown how this unified representation can be used for object recognition object position estimation and segmentation of objects into meaningful subobjects that is the detection of interest regions that are more complex than high curvature regions and hence more useful as features for object recognition

multiple ellipses detection in noisy environments a hierarchical approach detection of multiple ellipses in noisy environments is a basic yet challenging task in many vision related problems the key area of difficulty is on distinguishing the pixels pertaining to each target in the presence of noise to tackle with the issue we propose a hierarchical approach which is motivated by the fact that any segment of an ellipse can identify itself in ellipse reconstruction first we find all the neat edges without any branches followed by an ellipse fitting on each of them second some target candidates are estimated based on the neat edges by a proposed grouping strategy finally the targets are detected based on the candidates by a proposed selective competitive algorithm to distinguish the true pixels of each target a real application of the proposed method is illustrated in addition to some other demonstrative experiments

two representations of a conditioned superprocess we consider a class of measure valued markov processes constructed by taking a superprocess over some underlying markov process and conditioning it to stay alive forever we obtain two representations of such a process the first representation is in terms of an immortal particle that moves around according to the underlying markov process and throws off pieces of mass which then proceed to evolve in the same way that mass evolves for the unconditioned superprocess as a consequence of this representation we show that the tail field of the conditioned superprocess is trivial if the tail field of the underlying process is trivial the second representation is analogous to one obtained by legall in the unconditioned case it represents the conditioned superprocess in terms of a certain process taking values in the path space of the underlying process this representation is useful for studying the transience and recurrence properties of the closed support process

on seeing spaghetti self adjusting piecewise toroidal recognition of flexible extruded objects we present a model for flexible extruded objects such as wires tubes or grommets and demonstrate a novel self adjusting seven dimensional hough transform that derives their diameter and three space curved axes from position and surface normal information the method is purely local and is inexpensive to compute the model considers such objects as piecewise toroidal and decomposes the seven parameters of a torus into three nested subspaces the structures of which counteract the errors implicit in the analysis of objects of great size and or small curvature we believe it is the first example of a parameter space structure designed to cluster ill conditioned hypotheses together so that they can be easily detected and ignored this work complements existing shape from contour approaches for analyzing tori it uses no edge information and it does not require the solution of high degree nonlinear equations by iterative techniques

subordination of trees and the brownian map we discuss subordination of random compact mathbb r trees we focus on the case of the brownian tree where the subordination function is given by the past maximum process of brownian motion indexed by the tree in that particular case the subordinate tree is identified as a stable levy tree with index 3 2 as a more precise alternative formulation we show that the maximum process of the brownian snake is a time change of the height process coding the levy tree we then apply our results to properties of the brownian map in particular we recover in a more precise form a recent result of miller and sheffield identifying the metric net associated with the brownian map

geodesics in large planar maps and in the brownian map we study geodesics in the random metric space called the brownian map which appears as the scaling limit of large planar maps in particular we completely describe geodesics starting from the distinguished point called the root and we characterize the set s of all points that are connected to the root by more than one geodesic the set s is dense in the brownian map and homeomorphic to a non compact real tree furthermore for every x in s the number of distinct geodesics from x to the root is equal to the number of connected components of s x in particular points of the brownian map can be connected to the root by at most three distinct geodesics our results have applications to the behavior of geodesics in large planar maps

on the sensitivity of the hough transform for object recognition object recognition from sensory data involves in part determining the pose of a model with respect to a scene a common method for finding an object s pose is the generalized hough transform which accumulates evidence for possible coordinate transformations in a parameter space whose axes are the quantized transformation parameters large clusters of similar transformations in that space are taken as evidence of a correct match a theoretical analysis of the behavior of such methods is presented the authors derive bounds on the set of transformations consistent with each pairing of data and model features in the presence of noise and occlusion in the image bounds are provided on the likelihood of false peaks in the parameter space as a function of noise occlusion and tessellation effects it is argued that haphazardly applying such methods to complex recognition tasks is risky as the probability of false positives can be very high