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

scale and rotation invariant matching using linearly augmented trees we propose a novel linearly augmented tree method for efficient scale and rotation invariant object matching the proposed method enforces pairwise matching consistency defined on trees and high order constraints on all the sites of a template the pairwise constraints admit arbitrary metrics while the high order constraints use l1 norms and therefore can be linearized such a linearly augmented tree formulation introduces hyperedges and loops into the basic tree structure but different from a general loopy graph its special structure allows us to relax and decompose the optimization into a sequence of tree matching problems that are efficiently solvable by dynamic programming the proposed method also works on continuous scale and rotation parameters we can match with a scale up to any large value with the same efficiency our experiments on ground truth data and a variety of real images and videos show that the proposed method is efficient accurate and reliable

an eigenspace projection clustering method for inexact graph matching in this paper we show how inexact graph matching that is the correspondence between sets of vertices of pairs of graphs can be solved using the renormalization of projections of the vertices as defined in this case by their connectivities into the joint eigenspace of a pair of graphs and a form of relational clustering an important feature of this eigenspace renormalization projection clustering epc method is its ability to match graphs with different number of vertices shock graph based shape matching is used to illustrate the model and a more objective method for evaluating the approach using random graphs is explored with encouraging results

matching by linear programming and successive convexification we present a novel convex programming scheme to solve matching problems focusing on the challenging problem of matching in a large search range and with cluttered background matching is formulated as metric labeling with l1 regularization terms for which we propose a novel linear programming relaxation method and an efficient successive convexification implementation the unique feature of the proposed relaxation scheme is that a much smaller set of basis labels is used to represent the original label space this greatly reduces the size of the searching space a successive convexification scheme solves the labeling problem in a coarse to fine manner importantly the original cost function is reconvexified at each stage in the new focus region only and the focus region is updated so as to refine the searching result this makes the method well suited for large label set matching experiments demonstrate successful applications of the proposed matching scheme in object detection motion estimation and tracking

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

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

matching images with multiple descriptors an unsupervised approach for locally adaptive descriptor selection with the aim to improve the performance of feature matching we present an unsupervised approach for adaptive description selection in the space of homographies inspired by the observation that the homographies of correct feature correspondences vary smoothly along the spatial domain our approach stands on the unsupervised nature of feature matching and can choose a good descriptor locally for matching each feature point instead of using one global descriptor to this end the homography space serves as the domain for selecting various heterogeneous descriptors correspondences obtained by any descriptors are considered as points in the space and their geometric coherence and spatial continuity are measured via computing the geodesic distances in this way mutual verification across different descriptors is allowed and correct correspondences will be highlighted with a high degree of consistency short geodesic distances here it follows that one class svm can be applied to identifying these correct correspondences and achieves adaptive descriptor selection the proposed approach is comprehensively compared with the state of the art approaches and evaluated on five benchmarks of image matching the promising results manifest its effectiveness

saddlepoint approximations for the difference of order statistics and studentized sample quantiles summary for a sample from a given distribution the difference of two order statistics and the studentized quantile are statistics whose distribution is needed to obtain tests and confidence intervals for quantiles and quantile differences this paper gives saddlepoint approximations for densities and saddlepoint approximations of the lugannani rice form for tail probabilities of these statistics the relative errors of the approximations are n i uniformly in a neighbourhood of the parameters and this uniformity is global if the densities are log concave

graph matching with a dual step em algorithm this paper describes a new approach to matching geometric structure in 2d point sets the novel feature is to unify the tasks of estimating transformation geometry and identifying point correspondence matches unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the em algorithm according to our em framework the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters these gating probabilities measure the consistency of the matched neighborhoods in the graphs the recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log likelihood function we evaluate the technique on two real world problems

noncommutative l p spaces without the completely bounded approximation property for any 1 leq p leq infty different from 2 we give examples of non commutative lp spaces without the completely bounded approximation property let f be a non archimedian local field if p 4 or p 4 3 and r geq 3 these examples are the non commutative lp spaces of the von neumann algebra of lattices in sl r f or in sl r r for other values of p the examples are the non commutative lp spaces of the von neumann algebra of lattices in sl r f for r large enough depending on p we also prove that if r geq 3 lattices in sl r f or sl r r do not have the approximation property of haagerup and kraus this provides examples of exact c algebras without the operator space approximation property

a new algorithm for error tolerant subgraph isomorphism detection we propose a new algorithm for error correcting subgraph isomorphism detection from a set of model graphs to an unknown input graph the algorithm is based on a compact representation of the model graphs this representation is derived from the set of model graphs in an off line preprocessing step the main advantage of the proposed representation is that common subgraphs of different model graphs are represented only once therefore at run time given an unknown input graph the computational effort of matching the common subgraphs for each model graph onto the input graph is done only once consequently the new algorithm is only sublinearly dependent on the number of model graphs furthermore the new algorithm can be combined with a future cost estimation method that greatly improves its run time performance

feature matching with affine function transformation models feature matching is an important problem and has extensive uses in computer vision however existing feature matching methods support either a specific or a small set of transformation models in this paper we propose a unified feature matching framework which supports a large family of transformation models we call the family of transformation models the affine function family in which all transformations can be expressed by affine functions with convex constraints in this framework the goal is to recover transformation parameters for every feature point in a template point set to calculate their optimal matching positions in an input image given pairwise feature dissimilarity values between all points in the template set and the input image we create a convex dissimilarity function for each template point composition of such convex functions with any transformation model in the affine function family is shown to have an equivalent convex optimization form that can be optimized efficiently four example transformation models in the affine function family are introduced to show the flexibility of our proposed framework our framework achieves 0 0 percent matching errors for both cmu house and hotel sequences following the experimental setup in 6

saddlepoint approximations for the difference of order statistics summary saddlepoint approximations for the distribution of the difference of order statistics from a continuous distribution are presented the approximations are illustrated for the case of the exponential distribution where we can find the exact probability density function of the difference of order statistics and for the case of the noncentral chi squared distribution which has application to the problem of testing a time series for linearity in both cases we show that the saddlepoint approximation is much better than the normal approximation especially for realistic sample sizes

general saddlepoint approximations with applications to l statistics abstract saddlepoint approximations are extended to general statistics the technique is applied to derive approximations to the density of linear combinations of order statistics including trimmed means a comparison with exact results shows the accuracy of these approximations even in very small sample sizes

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

gaussian field consensus a robust nonparametric matching method for outlier rejection abstract in this paper we propose a robust method called gaussian field consensus gfc for outlier rejection from given putative point set matching correspondences finding correct correspondences inliers is a key component in many computer vision and pattern recognition tasks and the goal of outlier mismatch rejection is to fit the transformation function that maps one feature point set to another our gfc starts by inputting a putative correspondence set which is contaminated by many outliers and the main task of our gfc is to identify the underlying true correspondences from outliers then we formulate this challenging problem by gaussian field nonparametric matching model which bases on the exponential distance loss and kernel method in a reproducing kernel hilbert space next we introduce a local linear constraint based on the regularization theory to preserve the topological structure of the feature points moreover the sparse approximation is used to reduce the search space in this way we can handle a large number of points easily finally we test the gfc method on several real image datasets in the presence of outliers where the experimental results show that our proposed method outperforms current state of the art methods in most test scenarios

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

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

a rkhs interpolator based graph matching algorithm we present an algorithm for performing attributed graph matching this algorithm is derived from a generalized framework for describing functionally expanded interpolators which is based on the theory of reproducing kernel hilbert spaces rkhs the algorithm incorporates a general approach to a wide class of graph matching problems based on attributed graphs allowing the structure of the graphs to be based on multiple sets of attributes no assumption is made about the adjacency structure of the graphs to be matched

generalized laguerre expansions of multivariate probability densities with moments we generalize the well known laguerre series approach to approximate multivariate probability density functions pdfs using multidimensional laguerre polynomials the generalized laguerre series which is defined around a gamma pdf is suited for simulating high complex natural phenomena that deviate from gaussianity combining the multivariate laguerre approximation and bayes theorem an approximation to the conditional pdfs is derived numerical results first showed the superiority of the gamma expansion over other numerical methods the ability of the gamma expansion to fit mixtures of gaussian ans super gaussian pdfs univariate and multivariate lognormal pdfs and complex geologic media is shown through different examples

object matching using a locally affine invariant and linear programming techniques in this paper we introduce a new matching method based on a novel locally affine invariant geometric constraint and linear programming techniques to model and solve the matching problem in a linear programming formulation all geometric constraints should be able to be exactly or approximately reformulated into a linear form this is a major difficulty for this kind of matching algorithm we propose a novel locally affine invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming based methods do the key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points whose weights can be solved easily by least squares errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points the resulting overall objective function can be solved efficiently by linear programming techniques our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

spectral correspondence for point pattern matching this paper investigates the correspondence matching of point sets using spectral graph analysis in particular we are interested in the problem of how the modal analysis of point sets can be rendered robust to contamination and drop out we make three contributions first we show how the modal structure of point sets can be embedded within the framework of the em algorithm second we present several methods for computing the probabilities of point correspondences from the modes of the point proximity matrix third we consider alternatives to the gaussian proximity matrix we evaluate the new method on both synthetic and real world data here we show that the method can be used to compute useful correspondences even when the level of point contamination is as large as 50 we also provide some examples on deformed point set tracking