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

rulegraphs for graph matching in pattern recognition abstract in pattern recognition the graph matching problem involves the matching of a sample data graph with the subgraph of a larger model graph where vertices and edges correspond to pattern parts and their relations in this paper we present rulegraphs a new method that combines the graph matching approach with rule based approaches from machine learning this new method reduces the cardinality of the np complete graph matching problem by replacing model part and their relational attribute states by rules which depict attribute bounds and evidence for different classes we show how rulegraphs when combined with techniques for checking feature label compatibilities not only reduce the search space but also improve the uniqueness of the matching process

classification in noisy environments using a distance measure between structural symbolic descriptions a definition of distance measure between structural descriptions that is based on a probabilistic interpretation of the matching predicate is proposed it aims at coping with the problem of classification when noise causes both local and structural deformations the distance measure is defined according to a top down evaluation scheme distance between disjunctions of conjuncts conjunctions and literals at the lowest level the similarity between a feature value in the pattern model g and the corresponding value in the observation ex is defined as the probability of observing a greater distortion the classification problem is approached by means of a multilayered framework in which the cases of single perfect match no perfect match and multiple perfect match are treated differently a plausible solution for the problem of completing the attribute and structure spaces based on the probabilistic approach is also given a comparison with other related works and an application in the domain of layout based document recognition are presented

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 sub graph isomorphism algorithm for matching large graphs we present an algorithm for graph isomorphism and subgraph isomorphism suited for dealing with large graphs a first version of the algorithm has been presented in a previous paper where we examined its performance for the isomorphism of small and medium size graphs the algorithm is improved here to reduce its spatial complexity and to achieve a better performance on large graphs its features are analyzed in detail with special reference to time and memory requirements the results of a testing performed on a publicly available database of synthetically generated graphs and on graphs relative to a real application dealing with technical drawings are presented confirming the effectiveness of the approach especially when working with large graphs

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

bayesian graph edit distance this paper describes a novel framework for comparing and matching corrupted relational graphs the paper develops the idea of edit distance originally introduced for graph matching by sanfeliu and fu 1983 we show how the levenshtein distance 1966 can be used to model the probability distribution for structural errors in the graph matching problem this probability distribution is used to locate matches using map label updates we compare the resulting graph matching algorithm with that recently reported by wilson and hancock the use of edit distance offers an elegant alternative to the exhaustive compilation of label dictionaries moreover the method is polynomial rather than exponential in its worst case complexity we support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem this demonstrates experimentally that the gain in efficiency is not at the expense of quality of match

a new method of feature fusion and its application in image recognition a new method of feature extraction based on feature fusion is proposed in this paper according to the idea of canonical correlation analysis cca at first the theory framework of cca used in pattern recognition and its reasonable description are discussed the process can be explained as follows extract two groups of feature vectors with the same pattern establish the correlation criterion function between the two groups of feature vectors and extract their canonical correlation features to form effective discriminant vector for recognition then the problem of canonical projection vectors is solved when two total scatter matrixes are singular such that it fits for the case of high dimensional space and small sample size in this sense the applicable range of cca is extended at last the inherent essence of this method used in recognition is analyzed further in theory experimental results on concordia university cenparmi database of handwritten arabic numerals and yale face database show that recognition rate is far higher than that of the algorithm adopting single feature or the existing fusion algorithm

local registration and deformation of a road cartographic database on a spot satellite image abstract herein we propose a new method to locally register cartographic road networks on spot satellite images this approach is based on markov random fields mrf on graphs since the cartographic and image data are obtained from different sources the noises degrading these data are of different nature cartographers also introduce in the generalization process distortions in the road map in order to emphasize some details of the road this can create important differences between the map data and the ground truth the proposed algorithm aims at correcting the error due to noise and generalization hence increasing the accuracy of the road map the first step of the method is to translate the road network into a graph where the nodes are characteristic points of the roads e g crossroads the random variable or descriptors are defined by the nodes position the edges are defined by the roads joining these points then local registration is performed by defining a model in a bayesian framework the solution is obtained by computing the maximum a posteriori map the posterior probability is assumed to be a product of two probabilities the prior of the network and the likelihood of the map each depending on the image data both are markov random field probabilities the likelihood of the registered map is the probability of a network configuration given the map data it is a measure of a global resemblance between the two we use geometrical measures euclidean distances and angles to build this probability the prior consists of two terms both depending on the image data the dependance exists through the fact that between two connected nodes we compute a best path thanks to a dynamic programing algorithm minimizing a cost function based on image gray levels curvature and gradient information the first term of the prior penalizes configurations for which different roads overlap each other and the second term depends on gray level statistics along these paths we run a simulated annealing algorithm to optimize the proposed model the tests are done on one real image data extracted from spot satellite images and artificially noisy cartographic data translated rotated or randomly deformed network we present some results showing a good global registration but also accurate correction of local distortions

the computation of visible surface representations a computational theory of visible surface representations is developed the visible surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of 1 integrating multiscale constraints on surface depth and orientation from multiple visual sources 2 interpolating dense piecewise smooth surfaces from these constraints 3 detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation and 4 structuring large scale distributed surface representations to achieve computational efficiency visible surface reconstruction is an inverse problem a well posed variational formulation results from the use of a controlled continuity surface model discontinuity detection amounts to the identification of this generic model s distributed parameters from the data finite element shape primitives yield a local discretization of the variational principle the result is an efficient algorithm for visible surface reconstruction

the asymptotic form of the spectral function in sturm liouville problems with a large potential like xc c 2 a new formula is given for the spectral function in singular sturm liouville problems where the potential is like const x c 0

the form of the spectral functions associated with a class of sturm liouville equations with integrable coefficient we consider the second order linear differential equation in the case where roughly q l 1 0 we devise a representation for the spectral function t associated with which is valid for t sufficiently large our results are the best possible

the adaptive hough transform we introduce the adaptive hough transform aht as an efficient way of implementing the hough transform ht method for the detection of 2 d shapes the aht uses a small accumulator array and the idea of a flexible iterative coarse to fine accumulation and search strategy to identify significant peaks in the hough parameter spaces the method is substantially superior to the standard ht implementation in both storage and computational requirements in this correspondence we illustrate the ideas of the aht by tackling the problem of identifying linear and circular segments in images by searching for clusters of evidence in 2 d parameter spaces we show that the method is robust to the addition of extraneous noise and can be used to analyze complex images containing more than one shape

the asymptotic form of the titchmarsh weyl m function associated with a second order differential equation with locally integrable coefficient on deduit un developpement asymptotique pour la m fonction de titchmarsh weyl associee a l equation differentielle lineaire d ordre 2 y qy y sur 0 dans le cas ou la seule restriction sur la fonction a valeur reelle q est q l 1 0 e pour e 0

structural matching by discrete relaxation this paper describes a bayesian framework for performing relational graph matching by discrete relaxation our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching broadly speaking there are two main aspects to this study firstly we focus on the issue of how relational inexactness may be quantified we illustrate that several popular relational distance measures can be recovered as specific limiting cases of the bayesian consistency measure the second aspect of our comparison concerns the way in which structural inexactness is controlled we investigate three different realizations of the matching process which draw on contrasting control models the main conclusion of our study is that the active process of graph editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter

matching three dimensional objects using a relational paradigm abstract a relational model for describing three dimensional objects has been designed and implemented the model which provides a rough description to be used at the top level of a hierarchy for describing objects was designed for initial matching attempts on an unknown object each description is in terms of the set of simple parts of an object simple parts can be sticks long thin parts plates flat wide parts and blobs parts that have three significant dimensions the relations include an attribute value table for global properties of the object the properties of the simple parts binary connection and support relationships ternary connection relationships parallel relationships perpendicular relationships and binary constraints an important use of the model is to characterize the similarity and differences between three dimensional objects toward this end we have defined a measure of relational similarity between three dimensional object models and a measure of feature similarity based only on euclidean distance between attribute value tables in a series of computer tests we compare the results of using the two different similarity measures and conclude that the relational similarity is much more powerful than the feature similarity and should be used when grouping the objects in the database for fast access

matching perspective views of a polyhedron using circuits we present a novel approach for finding corresponding points between two line drawings extracted from perspective views of a moving object whose surface is composed of planar polygons in our approach each circuit of the drawings is encoded with a boundary shape code which we call the rlcc code run length code of convex and concave strings then a clustering technique is used to obtain the matching result recursively a series of measures are taken to make the algorithm tolerate considerable dissimilarities which may exist between the two drawings such as missing lines scale differences rotation perspective shape distortions etc experimental results are presented

a transformation invariant matching algorithm for handwritten chinese character recognition abstract all the chinese characters are composed of some fundamental characters called radicals the algorithms we present here are used to match the radicals stored in the data base with the input chinese character from the radicals in the input chinese character we can know what this input chinese character really is the matching process is equivalent to checking the validity of the relation that the radical is a sub character of the input chinese character the least square error estimation and some properties of the chinese characters are also used here to check whether the relation mentioned above is satisfied and if this relation is satisfied the sub character matched with the radical is extracted this matching algorithm has some superior merits which are 1 transformation scaling rotation and translation invariant and furthermore 2 invulnerable to the inherent defects of the thinning algorithms it overcomes these defects at the expense of more computation time but it can be run in parallel so large computation time is no longer a very serious problem experiments with 114 characters and 62 radicals have been conducted and we find that the success rate of our matching algorithms is above 99 thus we conclude that our algorithms are very reliable

an inverse problem involving the titchmarsh weyl m function let m denote the titchmarsh weyl m function associated with the differential equation with neumann boundary condition at 0 in the case q c m 0 e for some integer m and e 0 we prove the following result theorem 2 1 if for some integer 3 we know that im l 2 m 0 0 on the ray e i then q v 0 0 for all v in the set 0 1 m for which 2 mod

representation and shape matching of 3 d objects a three dimensional scene analysis system for the shape matching of real world 3 d objects is presented various issues related to representation and modeling of 3 d objects are addressed a new method for the approximation of 3 d objects by a set of planar faces is discussed the major advantage of this method is that it is applicable to a complete object and not restricted to single range view which was the limitation of the previous work in 3 d scene analysis the method is a sequential region growing algorithm it is not applied to range images but rather to a set of 3 d points the 3 d model of an object is obtained by combining the object points from a sequence of range data images corresponding to various views of the object applying the necessary transformations and then approximating the surface by polygons a stochastic labeling technique is used to do the shape matching of 3 d objects the technique matches the faces of an unknown view against the faces of the model it explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification it is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels the objective here is to match the individual views of the object taken from any vantage point details of the algorithm are presented and the results are shown on several unknown views of a complicated automobile casting

on the location of the weyl circles the paper deals with explicit estimates concerning certain circles in the complex plane which were associated with sturm liouville problems by h weyl by the use of riccati equations instead of linear integral equations improvements are obtained for results of everitt and halvorsen concerning the behaviour of the titchmarsh weyl m coefficient

structural pattern recognition using genetic algorithms this paper presents a genetic algorithm ga based optimization procedure for the solution of structural pattern recognition problem using the attributed relational graph representation and matching technique in this study candidate solutions are represented by integer strings and the population is randomly initialized the ga is employed to generate a monomorphic mapping as all the mapping constraints are not enforced during the search phase in order to speedup the search an efficient pose clustering algorithm is used to eliminate spurious matches and to determine the presence of the model in the scene the performance of the proposed approach to pattern recognition by subgraph isomorphism is demonstrated using line patterns and silhouette images

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

matching delaunay graphs this paper describes a bayesian framework for matching delaunay triangulations relational structures of this sort are ubiquitous in intermediate level computer vision being used to represent both voronoi tessellations of the image plane and volumetric surface data our matching process is realised in terms of probabilistic relaxation the novelty of our method stems from its use of a support function specified in terms of face units of the graphs under match in this way we draw on more expressive constraints than is possible at the level of edge units alone in order to apply this new relaxation process to the matching of realistic imagery requires a model of the compatibility between faces of the data and model graphs we present a particularly simple compatibility model that is entirely devoid of free parameters it requires only knowledge of the numbers of nodes edges and faces in the model graph the resulting matching scheme is evaluated on radar images and compared with its edge based counterpart we establish the operational limits and noise sensitivity on the matching of random dot patterns

fuzzy clustering and switching regression models using ambiguity and distance rejects abstract this paper examines how reject options can be used in performing fuzzy clustering and switching regression models we define an objective function in which reject options are introduced to optimization of certain clustering models this approach can be directly applied to any clustering model which can be represented as a functional dependent upon a set of cluster centers the approach can be further generalized for models that require parameters other than the cluster centers two types of reject have been included 1 the ambiguity reject which concerns patterns lying near the cluster boundaries or in the case of switching regression problems the data points which fit several models equally well 2 the distance or error reject dealing with patterns that are far away from all the clusters clustering and fuzzy c regression algorithms such as fcm fuzzy c means and fcrm fuzzy c regression models which use calculus based optimization methods suffer from several drawbacks they are very sensitive to the presence of noise moreover the memberships are relative numbers the membership of a point in a cluster depends on the membership of the point in all other clusters so the cluster centers or estimates for the parameters are poor this can be a serious problem in situations where one wishes to generate membership functions from training data this paper provides answers to these problems to avoid the memberships to be spread across the clusters and to allow the distinction between equally likely and unknown we define partial ambiguity rejects which introduce a discounting process between the classical fcm or fcrm membership functions to improve the performance of our algorithm in the presence of noise we use an amorphous noise cluster defined in demko et al actes des sixiemes rencontres del la societe francophone de classification montpellier france september 1998 to compute these rejects we propose an extension of fcrm algorithm hathaway and bezdek ieee trans fuzzy systems 1 3 1993 195 203 this algorithm is called the fuzzy c 2 regression model fc 2rm preliminary computational experiences on the developed algorithm are encouraging and compare favorably with results from other methods as fcrm and afc algorithms on the same data sets

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

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

a return to the hardy littlewood integral inequality this paper is concerned with the extension and generalization of a classic integral inequality first considered by hardy and littlewood in 1932 the integral inequality is big int b a p f 2 q f 2 big 2 leqslant k int b a w f 2 int b a w w 1 pf qf 2 f in delta where k is a positive number the coefficients p q and w are real valued and w 0 on the interval a b infty a b leqslant infty and p 1 q w in l loc a b delta is the maximal linear manifold of functions f for which the two integrals on the right hand side are both finite the hardy littlewood inequality is the special case a 0 b infty p w 1 and q 0 on 0 infty here k 4 and all the cases of equality can be identified in this paper the results of everitt in 1971 connecting the above inequality with the titchmarsh weyl m coefficient of the associated differential equation py qy lambda wy on a b are restated in an improved form and are shown to hold under the above minimal conditions on the coefficients p q and w it is proved that the best possible value for the number k satisfies 1 k leqslant infty and that within these bounds all values of k can be realized in the course of establishing these results new information of independent interest is obtained about the behaviour of the m coefficient near the real axis examples are given to exhibit the wide range of possibilities for the integral inequality recent results on the asymptotic form of the m coefficient and on the transformation theory of the associated differential equation are shown to have applications for the general properties of the inequality all recent contributions to this general integral inequality are listed in the references and their content is surveyed during the course of the paper

a property of the asymptotic series for a class of titchmarsh weyl m functions in an earlier paper 6 we showed that if q c n 0 e for some e 0 then the titchmarsh weyl m function associated with the second order linear differential equation has the asymptotic expansion as a in a sector of the form 0 we show that if the real valued function q admits the expansion in a neighbourhood of 0 then

discrete time calogero moser system and lagrangian 1 form structure we study the lagrange formalism of the rational calogero moser cm system both in discrete time and continuous time as a first example of a lagrangian 1 form structure in the sense of the recent paper lobb and nijhoff 2009 j phys a math theor 42 454013 the discrete time model of the cm system was established some time ago arising as a pole reduction of a semi discrete version of the kadomtsev petviashvili kp equation and was shown to lead to an exactly integrable correspondence multivalued map in this paper we present the full kp solution based on the commutativity of the discrete time flows in the two discrete kp variables the compatibility of the corresponding lax matrices is shown to lead directly to the relevant closure relation on the level of the lagrangians performing successive continuum limits on both the level of the kp equation and the level of the cm system we establish the proper lagrangian 1 form structure for the continuum case of the cm model we use the example of the three particle case to elucidate the implementation of the novel least action principle which was presented in lobb and nijhoff 2009 for the simpler case of lagrangian 1 forms

symbol recognition by error tolerant subgraph matching between region adjacency graphs we propose an error tolerant subgraph isomorphism algorithm formulated in terms of region adjacency graphs rag a set of edit operations to transform one rag into another one are defined as regions are represented by polylines and string matching techniques are used to measure their similarity the algorithm follows a branch and bound approach driven by the rag edit operations this formulation allows matching computing under distorted inputs and also reaching a solution in a near polynomial time the algorithm has been used for recognizing symbols in hand drawn diagrams

a super integrable discretization of the calogero model a time discretization that preserves the super integrability of the calogero model is obtained by application of the integrable time discretization of the harmonic oscillator to the projection method for the calogero model with continuous time in particular the difference equations of motion which provide an explicit scheme for time integration are explicitly presented for the two body case numerical results exhibit that the scheme conserves all the 3 conserved quantities of the two body calogero model with a precision of the machine epsilon times the number of iterations

inexact graph matching for model based recognition evaluation and comparison of optimization algorithms a method for segmentation and recognition of image structures based on graph homomorphisms is presented in this paper it is a model based recognition method where the input image is over segmented and the obtained regions are represented by an attributed relational graph arg this graph is then matched against a model graph thus accomplishing the model based recognition task this type of problem calls for inexact graph matching through a homomorphism between the graphs since no bijective correspondence can be expected because of the over segmentation of the image with respect to the model the search for the best homomorphism is carried out by optimizing an objective function based on similarities between object and relational attributes defined on the graphs the following optimization procedures are compared and discussed deterministic tree search for which new algorithms are detailed genetic algorithms and estimation of distribution algorithms in order to assess the performance of these algorithms using real data experimental results on supervised classification of facial features using face images from public databases are presented

optimization in model matching and perceptual organization we introduce an optimization approach for solving problems in computer vision that involve multiple levels of abstraction our objective functions include compositional and specialization hierarchies we cast vision problems as inexact graph matching problems formulate graph matching in terms of constrained optimization and use analog neural networks to perform the optimization the method is applicable to perceptual grouping and model matching preliminary experimental results are shown

indexing hierarchical structures using graph spectra hierarchical image structures are abundant in computer vision and have been used to encode part structure scale spaces and a variety of multiresolution features in this paper we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph dag into a low dimensional vector space based on a novel spectral characterization of a dag this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearest neighbor search we establish the insensitivity of the signature to minor perturbation of graph structure due to noise occlusion or node split merge to accommodate large scale occlusion the dag rooted at each nonleaf node of the query votes for model objects that share that part effectively accumulating local evidence in a model dag s topological subspaces we demonstrate the approach with a series of indexing experiments in the domain of view based 3d object recognition using shock graphs

an energy function and continuous edit process for graph matching the contributions of this article are twofold first we develop a new nonquadratic energy function for graph matching the starting point is a recently reported mixture model that gauges relational consistency using a series of exponential functions of the hamming distances between graph neighborhoods we compute the effective neighborhood potentials associated with the mixture model by identifying the single probability function of zero kullback divergence this new energy function is simply a weighted sum of graph hamming distances the second contribution is to locate matches by graduated assignment rather than solving the meanfield saddle point equations which are intractable for our nonquadratic energy function we apply the soft assign ansatz to the derivatives of our energy function here we introduce a novel departure from the standard graduated assignment formulation of graph matching by allowing the connection strengths of the data graph to update themselves the aim is to provide a means by

a metric for comparing relational descriptions relational models are frequently used in high level computer vision finding a correspondence between a relational model and an image description is an important operation in the analysis of scenes in this paper the process of finding the correspondence is formalized by defining a general relational distance measure that computes a numeric distance between any two relational descriptions a model and an image description two models or two image descriptions the distance measure is proved to be a metric and is illustrated with examples of distance between object models a variant measure used in our past studies is shown not to be a metric

statistical physics algorithms that converge in recent years there has been significant interest in adapting techniques from statistical physics in particular mean field theory to provide deterministic heuristic algorithms for obtaining app

a comparison of approaches to high level image interpretation abstract a critical comparison of methods of high level interpretation of segmented images is presented and illustrated by examples drawn from two dimensional image analysis the methods discussed include boundary correlation generalized hough transformation relational distance measures graph matching heuristic search and relaxation labelling each technique is considered in terms of its reliability in interpreting noisy and cluttered scenes and in terms of the dynamic complexity of the algorithm as a function of the input data although 2 d analysis of linearly segmented scenes is used as a mechanism for comparison many of the arguments are applicable to three dimensional image interpretation based on surface modelling for example

geometric graph comparison from an alignment viewpoint in this paper we propose a new approach for the comparison and retrieval of geometric graphs formulated from an alignment perspective the algorithm presented here is quite general in nature and applies to geometric graphs of any dimension the method involves two major steps firstly graph alignment is effected making use of an optimisation approach whose target function arises from a diffusion process over the graphs under study this provides from the theoretical viewpoint a link between stochastic processes on graphs and the heat kernel the second step involves using a probabilistic approach to recover the transformation parameters that map the graph vertices to one another so as to permit the computation of a similarity measure based on the goodness of fit between the two graphs under study here we view the transformation parameters as random variables and aim at minimising the kullback liebler divergence between the two graphical structures under study we provide a sensitivity analysis on synthetic data and illustrate the utility of the method for purposes of comparison and retrieval of cad objects and binary shape categorisation we also compare our results to those yielded by alternatives elsewhere in the literature

inexact graph matching using genetic search this paper describes a framework for performing relational graph matching using genetic search there are three novel ingredients to the work firstly we cast the optimisation process into a bayesian framework by exploiting the recently reported global consistency measure of wilson and hancock as a fitness measure the second novel idea is to realise the crossover process at the level of subgraphs rather than employing string based or random crossover finally we accelerate convergence by employing a deterministic hill climbing process prior to selection since we adopt the bayesian consistency measure as a fitness function the basic measure of relational distance underpinning the technique is hamming distance our standpoint is that genetic search provides a more attractive means of performing stochastic discrete optimisation on the global consistency measure than alternatives such as simulated annealing moreover the action of the optimisation process is easily understood in terms of its action in the hamming distance domain we demonstrate empirically not only that the method possesses polynomial convergence time but also that the convergence rate is more rapid than simulated annealing we provide some experimental evaluation of the method in the matching of aerial stereograms and evaluate its sensitivity on synthetically generated graphs

ricci flow embedding for rectifying non euclidean dissimilarity data pairwise dissimilarity representations are frequently used as an alternative to feature vectors in pattern recognition one of the problems encountered in the analysis of such data is that the dissimilarities are rarely euclidean while statistical learning algorithms often rely on euclidean dissimilarities such non euclidean dissimilarities are often corrected or a consistent euclidean geometry is imposed on them via embedding this paper commences by reviewing the available algorithms for analysing non euclidean dissimilarity data the novel contribution is to show how the ricci flow can be used to embed and rectify non euclidean dissimilarity data according to our representation the data is distributed over a manifold consisting of patches each patch has a locally uniform curvature and this curvature is iteratively modified by the ricci flow the raw dissimilarities are the geodesic distances on the manifold rectified euclidean dissimilarities are obtained using the ricci flow to flatten the curved manifold by modifying the individual patch curvatures we use two algorithmic components to implement this idea firstly we apply the ricci flow independently to a set of surface patches that cover the manifold second we use curvature regularisation to impose consistency on the curvatures of the arrangement of different surface patches we perform experiments on three real world datasets and use these to determine the importance of the different algorithmic components i e ricci flow and curvature regularisation we conclude that curvature regularisation is an essential step needed to control the stability of the piecewise arrangement of patches under the ricci flow

graph matching based on spectral embedding with missing value this paper proposes an efficient algorithm for inexact graph matching based on spectral embedding with missing value we commence by building an association graph model based on initial matching algorithm then by dot product representation of graph with missing value a new embedding method co embedding where the correspondences between unmatched nodes are treated as missing data in an association graph is presented at last a new graph matching algorithm which alternates between the co embedding and point pattern matching is proposed convictive experimental results on both synthetic and real world data demonstrate the effectiveness of the proposed graph matching algorithm

structural graph matching using the em algorithm and singular value decomposition this paper describes an efficient algorithm for inexact graph matching the method is purely structural that is it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes we make two contributions 1 commencing from a probability distribution for matching errors we show how the problem of graph matching can be posed as maximum likelihood estimation using the apparatus of the em algorithm and 2 we cast the recovery of correspondence matches between the graph nodes in a matrix framework this allows one to efficiently recover correspondence matches using the singular value decomposition we experiment with the method on both real world and synthetic data here we demonstrate that the method offers comparable performance to more computationally demanding methods

deterministic search for relational graph matching abstract this paper describes a comparative study of various deterministic discrete search strategies for graph matching the framework for our study is provided by the bayesian consistency measure recently reported by wilson and hancock ieee pami 19 1997 634 648 pattern recognition 17 1996 263 276 and wilson et al comput vision image understanding 72 1998 20 38 we investigate two classes of update process the first of these aims to exploit discrete gradient ascent methods we investigate the effect of searching in the direction of both the local and global gradient maximum an experimental study demonstrates that although more computationally intensive the global gradient method offers significant performance advantages in terms of accuracy of match our second search strategy is based on tabu search in order to develop this method we introduce memory into the search procedure by defining context dependant search paths we illustrate that although it is more efficient than the global gradient method tabu search delivers almost comparable performance

integrable time discretisation of the ruijsenaars schneider model an exactly integrable symplectic correspondence is derived which in a continuum limit leads to the equations of motion of the relativistic generalization of the calogero moser system that was introduced for the first time by ruijsenaars and schneider for the discrete time model the equations of motion take the form of bethe ansatz equations for the inhomogeneous spin 1 2 xyz heisenberg magnet we present a lax pair the sympletic structure and prove the involutivity of the invariants exact solutions are investigated in the rational and hyperbolic trigonometric limits of the system that is given in terms of elliptic functions these solutions are connected with discrete soliton equations the results obtained allow us to consider the bethe ansatz equations as ones giving an integrable symplectic correspondence mixing the parameters of the quantum integrable system and the parameters of the corresponding bethe wavefunction

an median graphs properties algorithms and applications in object prototype learning and similar tasks median computation is an important technique for capturing the essential information of a given set of patterns we extend the median concept to the domain of graphs in terms of graph distance we introduce the novel concepts of set median and generalized median of a set of graphs we study properties of both types of median graphs for the more complex task of computing generalized median graphs a genetic search algorithm is developed experiments conducted on randomly generated graphs demonstrate the advantage of generalized median graphs compared to set median graphs and the ability of our genetic algorithm to find approximate generalized median graphs in reasonable time application examples with both synthetic and nonsynthetic data are shown to illustrate the practical usefulness of the concept of median graphs

fuzzy morphisms between graphs a generic definition of fuzzy morphism between graphs gfm is introduced that includes classical graph related problem definitions as sub cases such as graph and subgraph isomorphism the gfm uses a pair of fuzzy relations one on the vertices and one on the edges each relation is a mapping between the elements of two graphs these two fuzzy relations are linked with constraints derived from the graph structure and the notion of association graph the theory extends the properties of fuzzy relation to the problem of generic graph correspondence we introduce two complementary interpretations of gfm from which we derive several interesting properties the first interpretation is the generalization of the notion of association compatibility the second is the new notion of edge morphism one immediate application is the introduction of several composition laws each property has a theoretical and a practical interpretation in the problem of graph correspondence that is explained throughout the paper special attention is paid to the formulation of a non algorithmical theory in order to propose a first step towards a unified theoretic framework for graph morphisms

a long trip in the charming world of graphs for pattern recognition this paper is a historical overview of graph based methodologies in pattern recognition in the last 40 years history is interpreted with the aim of recognizing the rationale inspiring the papers published in these years so as to roughly classify them despite the extent of scientific production in this field it is possible to identify three historical periods each having its own connotation common to most of the corresponding papers which are called here as the pure the impure and extreme periods highlightsthe paper is a historical survey of graph based methodologies in pattern recognition the scientific evolution of graph based methods over their history is discussed the paper analyses the trend of reusing vector space methods for graphs three distinctive periods are recognized wrt how the vector graph gap is filled reserve a ticket for a historical trip in this charming world and discover it soon

constrained nets for graph matching and other quadratic assignment problems some time ago durbin and willshaw proposed an interesting parallel algorithm the elastic net for approximately solving some geometric optimization problems such as the traveling salesman problem recently it has been shown that their algorithm is related to neural networks of hopfield and tank and that they both can be understood as the semiclassical approximation to statistical mechanics of related physical models the main point of the elastic net algorithm is seen to be in the way one deals with the constraints when evaluating the effective cost function free energy in the thermodynamic analogy and not in its geometric foundation emphasized originally by durbin and willshaw as a consequence the elastic net algorithm is a special case of the more general physically based computations and can be generalized to a large class of nongeometric problems in this paper we further elaborate on this observation and generalize the elastic net to the quadratic assignment problem we work out in detail its special case the graph matching problem because it is an important problem with many applications in computational vision and neural modeling simulation results on random graphs and on structured hand designed graphs of moderate size 20 100 nodes are discussed

the asymptotic form of the spectral functions associated with a class of sturm liouville equations on utilise une forme modifiee de la formule d inversion de stieltjes avec des resultats recents sur la forme asymptotique des m fonctions de titchmarch weyl pour obtenir une expression asymptotique pour les fonctions spectrales t associees a l equation differentielle y q x y y o x b

convergence of a hill climbing genetic algorithm for graph matching abstract this paper presents a convergence analysis for the problem of consistent labelling using genetic search the work builds on a recent empirical study of graph matching where we showed that a bayesian consistency measure could be efficiently optimised using a hybrid genetic search procedure which incorporated a hill climbing step in the present study we return to the algorithm and provide some theoretical justification for its observed convergence behaviour the novelty of the analysis is to demonstrate analytically that the hill climbing step significantly accelerates convergence and that the convergence rate is polynomial in the size of the node set of the graphs being matched