shape description and matching using integral invariants on eccentricity transformed images matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision to keep track of changes inside the breast for example it is important for a computer aided detection system to establish correspondences between regions of interest shape transformations computed both with integral invariants ii and with geodesic distance yield signatures that are invariant to isometric deformations such as bending and articulations integral invariants describe the boundaries of planar shapes however they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure conversely eccentricity transforms ecc can match shapes by signatures of geodesic distance histograms based on information from inside the shape but they ignore the boundary information we describe a method that combines the boundary signature of a shape obtained from ii and structural information from the ecc to yield results that improve on them separately

a linear programming approach for the weighted graph matching problem a linear programming lp approach is proposed for the weighted graph matching problem a linear program is obtained by formulating the graph matching problem in l sub 1 norm and then transforming the resulting quadratic optimization problem to a linear one the linear program is solved using a simplex based algorithm then approximate 0 1 integer solutions are obtained by applying the hungarian method on the real solutions of the linear program the complexity of the proposed algorithm is polynomial time and it is o n sup 6 l for matching graphs of size n the developed algorithm is compared to two other algorithms one is based on an eigendecomposition approach and the other on a symmetric polynomial transform experimental results showed that the lp approach is superior in matching graphs than both other methods

symmetry aware graph matching visual symmetry encodes middle to high level geometric information and plays an important role in many computer vision applications not much effort however has been devoted to utilize symmetry information for graph matching in this paper we propose a new framework for symmetry aware graph matching in the context of image matching in the framework we first define symmetry matrices to characterize the geometric symmetry relation among image features and then develop two methods to discover such symmetry after that we design general strategies to boost graph matching algorithms with symmetry constraints and apply these strategies to several state of the art algorithms for evaluation the proposed symmetry aware graph matching algorithms are first applied to two datasets involving clear symmetry patterns a recently proposed architecture image set and a dental panoramic radiograph collection the results clearly demonstrate the benefits of using symmetry information an experiment is also conducted on a dataset where symmetry is less obvious the results show that our strategies still achieve better of similar performance compared with state of the arts highlightsit is the first time symmetry constraints that are introduced into graph matching the symmetry aware graph matching improves the matching performance a new dataset with annotation for evaluating graph matching is constructed

point correspondence by a new third order graph matching algorithm the correspondence between point sets is a fundamental problem in pattern recognition which is often formulated and solved by graph matching in this paper we propose to solve the correspondence problem by a new third order graph matching algorithm compared with some previous hyper graph matching algorithms the proposed one achieves considerable memory reduction and is applicable to both undirected and directed graphs specifically the correspondence is formulated by the matching between adjacency tensors encoding the third order structural information of each graph which is then transformed to be a tractable matrix form two types of gradient based optimization methods the graduated nonconvexity and concavity procedure gnccp and graduated assignment ga algorithm are generalized to solve the problem comparative experiments with state of the art algorithms on both synthetic and real data witness the effectiveness of the proposed method highlightsan adjacency tensor based third order graph matching algorithm is proposed it enjoys a much lower storage complexity than affinity tensor based high order algorithms instead of spectral decomposition based optimization it adopts gradient based optimization experiments on synthetic and real world data witness its state of the art performance

efficient high order matching we present a computational approach to high order matching of data sets in rd those are matchings based on data affinity measures that score the matching of more than two pairs of points at a time high order affinities are represented by tensors and the matching is then given by a rank one approximation of the affinity tensor and a corresponding discretization our approach is rigorously justified by extending zass and shashua s hypergraph matching to high order spectral matching this paves the way for a computationally efficient dual marginalization spectral matching scheme we also show that based on the spectral properties of random matrices affinity tensors can be randomly sparsified while retaining the matching accuracy our contributions are experimentally validated by applying them to synthetic as well as real data sets

learning with jensen tsallis kernels jensen type jensen shannon js and jensen tsallis kernels were first proposed by martins et al 2009 these kernels are based on js divergences that originated in the information theory in this paper we extend the jensen type kernels on probability measures to define positive definite kernels on euclidean space we show that the special cases of these kernels include dot product kernels since jensen type divergences are multidistribution divergences we propose their multipoint variants and study spectral clustering and kernel methods based on these we also provide experimental studies on benchmark image database and gene expression database that show the benefits of the proposed kernels compared with the existing kernels the experiments on clustering also demonstrate the use of constructing multipoint similarities

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

examples of attractors in scalar reaction diffusion equations on considere l equation de reaction diffusion scalaire avec des conditions aux limites de neumann u t e 2 u xx f x u 0 x 1 u x 0 t u x 1 t 0 pour une non linearite f x u u 1 u u a x ou a 0 1 0 1 est une fonction echelon on etudie la caracterisation de l attracteur quand e est petit

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

multi graph matching via affinity optimization with graduated consistency regularization this paper addresses the problem of matching common node correspondences among multiple graphs referring to an identical or related structure this multi graph matching problem involves two correlated components i the local pairwise matching affinity across pairs of graphs ii the global matching consistency that measures the uniqueness of the pairwise matchings by different composition orders previous studies typically either enforce the matching consistency constraints in the beginning of an iterative optimization which may propagate matching error both over iterations and across graph pairs or separate affinity optimization and consistency enforcement into two steps this paper is motivated by the observation that matching consistency can serve as a regularizer in the affinity objective function especially when the function is biased due to noises or inappropriate modeling we propose composition based multi graph matching methods to incorporate the two aspects by optimizing the affinity score meanwhile gradually infusing the consistency we also propose two mechanisms to elicit the common inliers against outliers compelling results on synthetic and real images show the competency of our algorithms

multi modal clique graph matching for view based 3d model retrieval multi view matching is an important but a challenging task in view based 3d model retrieval to address this challenge we propose an original multi modal clique graph mcg matching method in this paper we systematically present a method for mcg generation that is composed of cliques which consist of neighbor nodes in multi modal feature space and hyper edges that link pairwise cliques moreover we propose an image set based clique edgewise similarity measure to address the issue of the set to set distance measure which is the core problem in mcg matching the proposed mcg provides the following benefits 1 preserves the local and global attributes of a graph with the designed structure 2 eliminates redundant and noisy information by strengthening inliers while suppressing outliers and 3 avoids the difficulty of defining high order attributes and solving hyper graph matching we validate the mcg based 3d model retrieval using three popular single modal data sets and one novel multi modal data set extensive experiments show the superiority of the proposed method through comparisons moreover we contribute a novel real world 3d object data set the multi view rgb d object data set to the best of our knowledge it is the largest real world 3d object data set containing multi modal and multi view information

randomized algorithms for the low rank approximation of matrices we describe two recently proposed randomized algorithms for the construction of low rank approximations to matrices and demonstrate their application inter alia to the evaluation of the singular value decompositions of numerically low rank matrices being probabilistic the schemes described here have a finite probability of failure in most cases this probability is rather negligible 10 17 is a typical value in many situations the new procedures are considerably more efficient and reliable than the classical deterministic ones they also parallelize naturally we present several numerical examples to illustrate the performance of the schemes

l_p norm regularization algorithms for optimization over permutation matrices optimization problems over permutation matrices appear widely in facility layout chip design scheduling pattern recognition computer vision graph matching etc since this problem is np hard due to the combinatorial nature of permutation matrices we relax the variable to be the more tractable doubly stochastic matrices and add an l p norm 0 p 1 regularization term to the objective function the optimal solutions of the l p regularized problem are the same as the original problem if the regularization parameter is sufficiently large a lower bound estimation of the nonzero entries of the stationary points and some connections between the local minimizers and the permutation matrices are further established then we propose an l p regularization algorithm with local refinements the algorithm approximately solves a sequence of l p regularization subproblems by the projected gradient method using a nonmonotone line search with the barzilai borwein step sizes its performance can be fu

fast and scalable approximate spectral graph matching for correspondence problems establishing consistent correspondences between two sets of features is a fundamental problem in computer vision this problem can be well formulated as graph matching in which nodes and edges represent feature points and pairwise relationships between feature points respectively spectral matching 19 is the state of the art eigenvector based method for graph matching the spectral matching algorithm has been used successfully for small data but its heavy memory requirement limited the maximum data sizes and contexts it can be used in this paper we propose fasm a fast and scalable approximate spectral matching algorithm the main ideas are twofold first we exploit the redundancy in the data generation process to approximate the affinity matrix with the linear combination of kronecker products between bases and index matrices the bases and index matrices are highly compressed representation of the approximated affinity matrix requiring much smaller memory than in previous works which store the whole affinity matrix second we compute the eigenvector of the approximated affinity matrix using the small bases and index matrices without explicitly materializing the approximated matrix experimental results show that our proposed method is up to 33x faster requiring up to 645x smaller memory than the exact algorithm with little or no loss of accuracy

modal matching for correspondence and recognition modal matching is a new method for establishing correspondences and computing canonical descriptions the method is based on the idea of describing objects in terms of generalized symmetries as defined by each object s eigenmodes the resulting modal description is used for object recognition and categorization where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects in general modes provide a global to local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison in contrast to previous techniques which required correspondence to be computed with an initial or prototype shape modal matching utilizes a new type of finite element formulation that allows for an object s eigenmodes to be computed directly from available image information this improved formulation provides greater generality and accuracy and is applicable to data of any dimensionality correspondence results with 2d contour and point feature data are shown and recognition experiments with 2d images of hand tools and airplanes are described

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

robust point pattern matching based on spectral context finding correspondences between two related feature point sets is a basic task in computer vision and pattern recognition in this paper we present a novel method for point pattern matching via spectral graph analysis in particular we aim to render the spectral matching algorithm more robust for positional jitter and outlier a local structural descriptor namely the spectral context is proposed to describe the attribute domain of point sets which is fundamentally different from the previous methods furthermore the approximate distance order is defined and employed as the metric for geometric consistency of neighboring points in this work by combining these two novel ingredients we formulate feature point set matching as an optimization problem with one to one constraints the correspondences are then obtained by maximizing the given objective function via the technique of probabilistic relaxation comparative experiments conducted on both synthetic and real data demonstrate the effectiveness of the proposed method especially in the presence of positional jitter and outliers a novel spectral method is proposed for the problem of point pattern matching we propose a local structural descriptor via spectral graph analysis we define a metric of geometric consistency by using the quantity of order

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

a shooting approach to layers and chaos in a forced duffing equation abstract we study equilibrium solutions for the problem u t e 2 u xx u 3 u cos x u x 0 t u x 1 t 0 using a shooting method we find solutions for all nonzero e for small e we add to the solutions found by previous authors especially angenent mallet paret and peletier and hale and sakamoto and also give new elementary ode proofs of their results among the new results is the existence of internal layer type solutions considering the ode satisfied by equilibria but on an infinite interval we obtain chaos results for 0 3 2 2 3 and 0 1 4 we also consider the problem of bifurcation of solutions as increases

a tensor based algorithm for high order graph matching this paper addresses the problem of establishing correspondences between two sets of visual features using higher order constraints instead of the unary or pairwise ones used in classical methods concretely the corresponding hypergraph matching problem is formulated as the maximization of a multilinear objective function over all permutations of the features this function is defined by a tensor representing the affinity between feature tuples it is maximized using a generalization of spectral techniques where a relaxed problem is first solved by a multidimensional power method and the solution is then projected onto the closest assignment matrix the proposed approach has been implemented and it is compared to state of the art algorithms on both synthetic and real data

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

an efficient globally optimal algorithm for asymmetric point matching although the robust point matching algorithm has been demonstrated to be effective for non rigid registration there are several issues with the adopted deterministic annealing optimization technique first it is not globally optimal and regularization on the spatial transformation is needed for good matching results second it tends to align the mass centers of two point sets to address these issues we propose a globally optimal algorithm for the robust point matching problem in the case that each model point has a counterpart in scene set by eliminating the transformation variables we show that the original matching problem is reduced to a concave quadratic assignment problem where the objective function has a low rank hessian matrix this facilitates the use of large scale global optimization techniques we propose a modified normal rectangular branch and bound algorithm to solve the resulting problem where multiple rectangles are simultaneously subdivided to increase the chance of shrinking the rectangle containing the global optimal solution in addition we present an efficient lower bounding scheme which has a linear assignment formulation and can be efficiently solved extensive experiments on synthetic and real datasets demonstrate the proposed algorithm performs favorably against the state of the art methods in terms of robustness to outliers matching accuracy and run time

competitive graph searches we exemplify an optimization criterion for divide and conquer algorithms with a technique called generic competitive graph search the technique is then applied to solve two problems arising from biocomputing so called common connected components and cograph sandwich the first problem can be defined as follows given two graphs on the same set of n vertices find the coarsest partition of the vertex set into subsets which induce connected subgraphs in both input graphs the second problem is an instance of sandwich problems given a partial subgraph g 1 of g 2 find a partial subgraph g of g 2 that is partial supergraph of g 1 sandwich and that is a cograph for the former problem our generic algorithm not only achieves the current best known performance on arbitrary graphs and forests but also improves by a logn factor when the input is made of planar graphs however our complexity for intervals graphs is slightly lower than a recent result for the latter problem we first study the relationship between the common connected components problem and the cograph sandwich problem then using our competitive graph search paradigm we improve the computation of cograph sandwiches from o n n m down to o n mlog 2n where n is the number of vertices and m of total edges

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

fast computation of low rank matrix approximations given a matrix a it is often desirable to find a good approximation to a that has low rank we introduce a simple technique for accelerating the computation of such approximations when a has strong spectral features that is when the singular values of interest are significantly greater than those of a random matrix with size and entries similar to a our technique amounts to independently sampling and or quantizing the entries of a thus speeding up computation by reducing the number of nonzero entries and or the length of their representation our analysis is based on observing that the acts of sampling and quantization can be viewed as adding a random matrix n to a whose entries are independent random variables with zero mean and bounded variance since with high probability n has very weak spectral features we can prove that the effect of sampling and quantization nearly vanishes when a low rank approximation to a p n is computed we give high probability bounds on the quality of our approximation both in the frobenius and the 2 norm

a global solution to sparse correspondence problems we propose a new methodology for reliably solving the correspondence problem between sparse sets of points of two or more images this is a key step inmost problems of computer vision and so far no general method exists to solve it our methodology is able to handle most of the commonly used assumptions in a unique formulation independent of the domain of application and type of features it performs correspondence and outlier rejection in a single step and achieves global optimality with feasible computation feature selection and correspondence are first formulated as an integer optimization problem this is a blunt formulation which considers the whole combinatorial space of possible point selections and correspondences to find its global optimal solution we build a concave objective function and relax the search domain into its convex hull the special structure of this extended problem assures its equivalence to the original one but it can be optimally solved by efficient algorithms that avoid combinatorial search this methodology can use any criterion provided it can be translated into cost functions with continuous second derivatives

bounds on the extreme eigenvalues of positive definite toeplitz matrices easily computable bounds on the extreme eigenvalues of positive semidefinite psd toeplitz matrices are presented the bounds are especially suitable for matrices of relatively small dimension the bounds are derived for the wider class of psd hermitian matrices and interpreted via the levinson durbin algorithm for toeplitz matrices as a by product of this derivation an order recursive algorithm for the eigenvector eigenvalue decomposition is obtained and certain properties of the eigenvalues distribution are revealed

an algorithmic view of gene teams comparative genomics is a growing field in computational biology and one of its typical problem is the identification of sets of orthologous genes that have virtually the same function in several genomes many different bioinformatics approaches have been proposed to define these groups often based on the detection of sets of genes that are not too far in all genomes in this paper we propose a unifying concept called gene teams which can be adapted to various notions of distance we present two algorithms for identifying gene teams formed by n genes placed on m linear chromosomes the first one runs in o mn log2n and uses a divide and conquer approach based on the formal properties of gene teams we next propose an optimization of the original algorithm and in order to better understand the complexity bound of the algorithms we recast the problem in the hopcroft s partition refinement framework this allows us to analyze the complexity of the algorithms with elegant amortized techniques both algorithms require linear space we also discuss extensions to circular chromosomes that achieve the same complexity

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

minimizing nonsubmodular functions with graph cuts a review optimization techniques based on graph cuts have become a standard tool for many vision applications these techniques allow to minimize efficiently certain energy functions corresponding to pairwise markov random fields mrfs currently there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of mrf energies e g submodular functions in this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions in particular nonsubmodular functions while these results are well known in the optimization community to our knowledge they were not used in the context of computer vision and mrf optimization we demonstrate the relevance of these results to vision on the problem of binary texture restoration

linear scale and rotation invariant matching matching visual patterns that appear scaled rotated and deformed with respect to each other is a challenging problem we propose a linear formulation that simultaneously matches feature points and estimates global geometrical transformation in a constrained linear space the linear scheme enables search space reduction based on the lower convex hull property so that the problem size is largely decoupled from the original hard combinatorial problem our method therefore can be used to solve large scale problems that involve a very large number of candidate feature points without using prepruning in the search this method is more robust in dealing with weak features and clutter we apply the proposed method to action detection and image matching our results on a variety of images and videos demonstrate that our method is accurate efficient and robust

fast matching of large point sets under occlusions the problem of isometric point pattern matching can be modeled as inference in small tree width graphical models whose embeddings in the plane are said to be globally rigid although such graphical models lead to efficient and exact solutions they cannot generally handle occlusions as even a single missing point may break the rigidity of the graph in question in addition such models can efficiently handle point sets of only moderate size in this paper we propose a new graphical model that is not only adapted to handle occlusions but is much faster than previous approaches for solving the isometric point pattern matching problem we can match point patterns with thousands of points in a few seconds

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

an eigendecomposition approach to weighted graph matching problems an approximate solution to the weighted graph matching problem is discussed for both undirected and directed graphs the weighted graph matching problem is that of finding the optimum matching between two weighted graphs which are graphs with weights at each arc the proposed method uses an analytic instead of a combinatorial or iterative approach to the optimum matching problem using the eigendecompositions of the adjacency matrices in the case of the undirected graph matching problem or hermitian matrices derived from the adjacency matrices in the case of the directed graph matching problem a matching close to the optimum can be found efficiently when the graphs are sufficiently close to each other simulation results are given to evaluate the performance of the proposed method

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

an image understanding system using attributed symbolic representation and inexact graph matching this paper presents a powerful image understanding system that utilizes a semantic syntactic or attributed synibolic representation scheme in the form of attributed relational graphs arg s for comprehending the global information contents of images nodes in the arg represent the global image features while the relations between those features are represented by attributed branches between their corresponding nodes the extraction of arg representation from images is achieved by a multilayer graph transducer scheme this scheme is basically a rule based system that uses a combination of model driven and data driven concepts in performing a hierarchical symbolic mapping of the image information content from the spatial domain representation into a global representation further analysis and inter pretation of the imagery data is performed on the extracted arg representation a distance measure between images is defined in terms of the distance between their respective arg representations the distance between two arg s and the inexact matching of their respective components are calculated by an efficient dynamic programming technique the system handles noise distortion and ambiguity in real world images by two means namely through modeling and embedding them into the transducer s mapping rules as well as through the appropriate cost of error transformation for the inexact matching of the arg image representation two illustrative experiments are presented to demonstrate some capabilities of the proposed system experiment i deals with locating objects in multiobject scenes while experiment ii is concerned with target detection in sar images

consistency driven alternating optimization for multigraph matching a unified approach the problem of graph matching gm in general is nondeterministic polynomial complete and many approximate pairwise matching techniques have been proposed for a general setting in real applications it typically requires to find the consistent matching across a batch of graphs sequentially performing pairwise matching is prone to error propagation along the pairwise matching sequence and the sequences generated in different pairwise matching orders can lead to contradictory solutions motivated by devising a robust and consistent multiple gm model we propose a unified alternating optimization framework for multi gm in addition we define and use two metrics related to graphwise and pairwise consistencies the former is used to find an appropriate reference graph which induces a set of basis variables and launches the iteration procedure the latter defines the order in which the considered graphs in the iterations are manipulated we show two embodiments under the proposed framework that can cope with the nonfactorized and factorized affinity matrix respectively our multi gm model has two major characters 1 the affinity information across multiple graphs are explored in each iteration by fixing part of the matching variables via a consistency driven mechanism and 2 the framework is flexible to incorporate various existing pairwise gm solvers in an out of box fashion and also can proceed with the output of other multi gm methods the experimental results on both synthetic data and real images empirically show that the proposed framework performs competitively with the state of the art

mixtures of probabilistic principal component analyzers principal component analysis pca is one of the most popular techniques for processing compressing and visualizing data although its effectiveness is limited by its global linearity while nonlinear variants of pca have been proposed an alternative paradigm is to capture data complexity by a combination of local linear pca projections however conventional pca does not correspond to a probability density and so there is no unique way to combine pca models therefore previous attempts to formulate mixture models for pca have been ad hoc to some extent in this article pca is formulated within a maximum likelihood framework based on a specific form of gaussian latent variable model this leads to a well defined mixture model for probabilistic principal component analyzers whose parameters can be determined using an expectationmaximization algorithm we discuss the advantages of this model in the context of clustering density modeling and local dimensionality reduction and we demonstrate its application to image compression and handwritten digit recognition

image completion by diffusion maps and spectral relaxation we present a framework for image inpainting that utilizes the diffusion framework approach to spectral dimensionality reduction we show that on formulating the inpainting problem in the embedding domain the domain to be inpainted is smoother in general particularly for the textured images thus the textured images can be inpainted through simple exemplar based and variational methods we discuss the properties of the induced smoothness and relate it to the underlying assumptions used in contemporary inpainting schemes as the diffusion embedding is nonlinear and noninvertible we propose a novel computational approach to approximate the inverse mapping from the inpainted embedding space to the image domain we formulate the mapping as a discrete optimization problem solved through spectral relaxation the effectiveness of the presented method is exemplified by inpainting real images where it is shown to compare favorably with contemporary state of the art schemes

correspondence matching with modal clusters the modal correspondence method of shapiro and brady aims to match point sets by comparing the eigenvectors of a pairwise point proximity matrix although elegant by means of its matrix representation the method is notoriously susceptible to differences in the relational structure of the point sets under consideration in this paper we demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach to do this we place the modal matching problem in a probabilistic setting in which the correspondences between pairwise clusters can be used to constrain the individual point correspondences we demonstrate the utility of the method on a number of synthetic and real world point pattern matching problems

an extended path following algorithm for graph matching problem the path following algorithm was proposed recently to approximately solve the matching problems on undirected graph models and exhibited a state of the art performance on matching accuracy in this paper we extend the path following algorithm to the matching problems on directed graph models by proposing a concave relaxation for the problem based on the concave and convex relaxations a series of objective functions are constructed and the frank wolfe algorithm is then utilized to minimize them several experiments on synthetic and real data witness the validity of the extended path following algorithm

an algorithm for finding the most similar given sized subgraphs in two weighted graphs we propose a weighted common subgraph wcs matching algorithm to find the most similar subgraphs in two labeled weighted graphs wcs matching as a natural generalization of equal sized graph matching and subgraph matching has found wide applications in many computer vision and machine learning tasks in this brief wcs matching is first formulated as a combinatorial optimization problem over the set of partial permutation matrices then it is approximately solved by a recently proposed combinatorial optimization framework graduated nonconvexity and concavity procedure experimental comparisons on both synthetic graphs and real world images validate its robustness against noise level problem size outlier number and edge density

partitioning a graph in o a log2 v abstract we present an o a log 2 v algorithm to partition a graph where v is the set of vertices and a the set of arcs extending hopcroft s fast partitioning algorithm

factorized graph matching graph matching gm is a fundamental problem in computer science and it plays a central role to solve correspondence problems in computer vision gm problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem qap although widely used solving the correspondence problem through gm has two main limitations 1 the qap is np hard and difficult to approximate 2 gm algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems to address aforementioned problems this paper proposes factorized graph matching fgm fgm factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges four are the benefits that follow from this factorization 1 there is no need to compute the costly in space and time pairwise affinity matrix 2 the factorization allows the use of a path following optimization algorithm that leads to improved optimization strategies and matching performance 3 given the factorization it becomes straight forward to incorporate geometric transformations rigid and non rigid to the gm problem 4 using a matrix formulation for the gm problem and the factorization it is easy to reveal commonalities and differences between different gm methods the factorization also provides a clean connection with other matching algorithms such as iterative closest point experimental results on synthetic and real databases illustrate how fgm outperforms state of the art algorithms for gm the code is available at http humansensing cs cmu edu fgm

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

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

the fiedler vector of a laplacian tensor for hypergraph partitioning based on recent advances in spectral hypergraph theory l qi and z luo tensor anaysis spectral theory and special tensors siam philadelphia 2017 we explore the fiedler vector of an even uniform hypergraph which is the z eigenvector associated with the second smallest z eigenvalue of a normalized laplacian tensor arising from the hypergraph then we develop a novel tensor based spectral method for partitioning vertices of the hypergraph for this purpose we extend the normalized laplacian matrix of a simple graph to the normalized laplacian tensor of an even uniform hypergraph the corresponding fiedler vector is related to the cheeger constant of the hypergraph then we establish a feasible optimization algorithm to compute the fiedler vector according to the normalized laplacian tensor the convergence of the proposed algorithm and the probability of obtaining the fiedler vector of the hypergraph are analyzed theoretically finally preliminary numerical experiments illustrate that the new a

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

correspondence matching using kernel principal components analysis and label consistency constraints this paper investigates spectral approaches to the problem of point pattern matching we make two contributions first we consider rigid point set alignment here we show how kernel principal components analysis kernel pca can be effectively used for solving the rigid point correspondence matching problem when the point sets are subject to outliers and random position jitter specifically we show how the point proximity matrix can be kernelised and spectral correspondence matching transformed into one of kernel pca second we turn our attention to the matching of articulated point sets here we show label consistency constraints can be incorporated into definition of the point proximity matrix the new methods are compared to those of shapiro and brady and scott and longuet higgins together with multidimensional scaling we provide experiments on both synthetic data and real world data

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

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

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

robust point matching for nonrigid shapes by preserving local neighborhood structures in previous work on point matching a set of points is often treated as an instance of a joint distribution to exploit global relationships in the point set for nonrigid shapes however the local relationship among neighboring points is stronger and more stable than the global one in this paper we introduce the notion of a neighborhood structure for the general point matching problem we formulate point matching as an optimization problem to preserve local neighborhood structures during matching our approach has a simple graph matching interpretation where each point is a node in the graph and two nodes are connected by an edge if they are neighbors the optimal match between two graphs is the one that maximizes the number of matched edges existing techniques are leveraged to search for an optimal solution with the shape context distance used to initialize the graph matching followed by relaxation labeling updates for refinement extensive experiments show the robustness of our approach under deformation noise in point locations outliers occlusion and rotation it outperforms the shape context and tps rpm algorithms on most scenarios

a path following algorithm for the graph matching problem we propose a convex concave programming approach for the labeled weighted graph matching problem the convex concave programming formulation is obtained by rewriting the weighted graph matching problem as a least square problem on the set of permutation matrices and relaxing it to two different optimization problems a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices the concave relaxation has the same global minimum as the initial graph matching problem but the search for its global minimum is also a hard combinatorial problem we therefore construct an approximation of the concave problem solution by following a solution path of a convex concave problem obtained by linear interpolation of the convex and concave formulations starting from the convex relaxation this method allows to easily integrate the information on graph label similarities into the optimization problem and therefore perform labeled weighted graph matching the algorithm is compared with some of the best performing graph matching methods on four data sets simulated graphs qaplib retina vessel images and handwritten chinese characters in all cases the results are competitive with the state of the art

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

robust point sets matching by fusing feature and spatial information using nonuniform gaussian mixture models most of the traditional methods that handle the point sets matching between two images are based on local feature descriptors and the succedent mismatch eliminating strategies which usually suffers from the sparsity of the initial match set because some correct ambiguous associations are easily filtered out by the ratio test of sift matching due to their second ranking in feature similarity in this paper we propose a nonuniform gaussian mixture model ngmm for point sets matching between a pair of images which combines feature with position information of the local feature points extracted from the image pair to achieve point sets matching in a gmm framework the proposed point set matching using an ngmm is able to change the correspondence assignments throughout the matching process and has the potential to match up even ambiguous matches correctly the proposed ngmm framework can be either used to directly find matches between two point sets obtained from two images or applied to remove outliers in a match set when finding matches ngmm tries to learn a nonrigid transformation between the two point sets and provide a probability for every found match to measure the reliability of the match then a probability threshold can be used to get the final robust match set when removing outliers ngmm requires that the vector field formed by the correct matches to be coherent and the matches contradicting the coherent vector field will be regarded as mismatches to be removed a number of comparison and evaluation experiments reveal the good performance of the proposed ngmm framework in both finding matches and discarding mismatches

fast and scalable approximate spectral matching for higher order graph matching this paper presents a fast and efficient computational approach to higher order spectral graph matching exploiting the redundancy in a tensor representing the affinity between feature points we approximate the affinity tensor with the linear combination of kronecker products between bases and index tensors the bases and index tensors are highly compressed representations of the approximated affinity tensor requiring much smaller memory than in previous methods which store the full affinity tensor we compute the principal eigenvector of the approximated affinity tensor using the small bases and index tensors without explicitly storing the approximated tensor to compensate for the loss of matching accuracy by the approximation we also adopt and incorporate a marginalization scheme that maps a higher order tensor to matrix as well as a one to one mapping constraint into the eigenvector computation process the experimental results show that the proposed method is faster and requires smaller memory than the existing methods with little or no loss of accuracy

stability of stationary solutions of a one dimensional parabolic equation with homogeneous neumann boundary conditions for some x in 0 rr the guiding idea of this paper is to observe the changes in the stability behavior of the solutions if we perturb the autonomous problem intro ducing a forcing term g in 8 it was shown that iff and g are related by a boundedness condi tion see condition in theorem 3 1 then there exists a stable solution of 1 1 close to each stable solution of 1 2 we want to call these stable solutions of 1 1

gnccp graduated nonconvexityand concavity procedure in this paper we propose the graduated nonconvexity and concavity procedure gnccp as a general optimization framework to approximately solve the combinatorial optimization problems defined on the set of partial permutation matrices gnccp comprises two sub procedures graduated nonconvexity which realizes a convex relaxation and graduated concavity which realizes a concave relaxation it is proved that gnccp realizes exactly a type of convex concave relaxation procedure ccrp but with a much simpler formulation without needing convex or concave relaxation in an explicit way actually gnccp involves only the gradient of the objective function and is therefore very easy to use in practical applications two typical related np hard problems partial graph matching and quadratic assignment problem qap are employed to demonstrate its simplicity and state of the art performance

an efficient multilinear optimization framework for hypergraph matching hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows the use of higher order geometric information hypergraph matching can be formulated as a third order optimization problem subject to assignment constraints which turns out to be np hard in recent work we have proposed an algorithm for hypergraph matching which first lifts the third order problem to a fourth order problem and then solves the fourth order problem via optimization of the corresponding multilinear form this leads to a tensor block coordinate ascent scheme which has the guarantee of providing monotonic ascent in the original matching score function and leads to state of the art performance both in terms of achieved matching score and accuracy in this paper we show that the lifting step to a fourth order problem can be avoided yielding a third order scheme with the same guarantees and performance but being two times faster moreover we introduce a homotopy type method which further improves the performance

a probabilistic approach to spectral graph matching spectral matching sm is a computationally efficient approach to approximate the solution of pairwise matching problems that are np hard in this paper we present a probabilistic interpretation of spectral matching schemes and derive a novel probabilistic matching pm scheme that is shown to outperform previous approaches we show that spectral matching can be interpreted as a maximum likelihood ml estimate of the assignment probabilities and that the graduated assignment ga algorithm can be cast as a maximum a posteriori map estimator based on this analysis we derive a ranking scheme for spectral matchings based on their reliability and propose a novel iterative probabilistic matching algorithm that relaxes some of the implicit assumptions used in prior works we experimentally show our approaches to outperform previous schemes when applied to exhaustive synthetic tests as well as the analysis of real image sequences

dense subgraph partition of positive hypergraphs in this paper we present a novel partition framework called dense subgraph partition dsp to automatically precisely and efficiently decompose a positive hypergraph into dense subgraphs a positive hypergraph is a graph or hypergraph whose edges except self loops have positive weights we first define the concepts of core subgraph conditional core subgraph and disjoint partition of a conditional core subgraph then define dsp based on them the result of dsp is an ordered list of dense subgraphs with decreasing densities which uncovers all underlying clusters as well as outliers a divide and conquer algorithm called min partition evolution is proposed to efficiently compute the partition dsp has many appealing properties first it is a nonparametric partition and it reveals all meaningful clusters in a bottom up way second it has an exact and efficient solution called min partition evolution algorithm the min partition evolution algorithm is a divide and conquer algorithm thus time efficient and memory friendly and suitable for parallel processing third it is a unified partition framework for a broad range of graphs and hypergraphs we also establish its relationship with the densest k subgraph problem d k s an np hard but fundamental problem in graph theory and prove that dsp gives precise solutions to d k s for all k in a graph dependent set called critical k set to our best knowledge this is a strong result which has not been reported before moreover as our experimental results show for sparse graphs especially web graphs the size of critical k set is close to the number of vertices in the graph we test the proposed partition framework on various tasks and the experimental results clearly illustrate its advantages

on the minimax misclassification ratio of hypergraph community detection community detection in hypergraphs is explored under a generative hypergraph model called d wise hypergraph stochastic block model d mathtt hsbm which naturally extends the stochastic block model mathtt sbm from graphs to d uniform hypergraphs the fundamental limit of the misclassification ratio the loss function in the community detection problem is studied for the converse part a lower bound of the minimax risk that is the minimax expected misclassification ratio is derived asymptotically it decays exponentially fast to zero as the number of nodes tends to infinity and the rate function is a weighted combination of several divergence terms each of which is the renyi divergence of order 1 2 between two bernoulli distributions the bernoulli distributions involved in the characterization of the rate function are those governing the random instantiation of hyperedges in d mathtt hsbm for the achievability part we propose a two step polynomial time algorithm which with high probability has a misclassification ratio with a decaying exponent that is asymptotically greater than or equal to that of our proposed lower bound the first step of the algorithm is a hypergraph spectral clustering method which achieves partial recovery to a certain precision level the second step is a local refinement method which leverages the underlying probabilistic model along with parameter estimation from the outcome of the first step to characterize the asymptotic performance of the proposed algorithm we first derive a sufficient condition for attaining weak consistency in the hypergraph spectral clustering step then under the guarantee of weak consistency in the first step we upper bound the loss with high probability attained in the local refinement step by an exponentially decaying function of the size of the hypergraph and characterize the decaying rate compared to existing works in mathtt sbm the main technical challenge lies in the complex structure of error events since community relations become much more complicated the experimental results on both the synthetic data and real world datasets validate our theoretical finding that the refinement step is critical in achieving the optimal statistical limit for the special case d 3 it is further shown by analyzing the performance of mle that the proposed lower bound of the minimax risk is tight and hence the exponential decaying rate of the asymptotic minimax risk is characterized we conjecture that this continues to hold for general d as well

graph matching by simplified convex concave relaxation procedure the convex and concave relaxation procedure ccrp was recently proposed and exhibited state of the art performance on the graph matching problem however ccrp involves explicitly both convex and concave relaxations which typically are difficult to find and thus greatly limit its practical applications in this paper we propose a simplified ccrp scheme which can be proved to realize exactly ccrp but with a much simpler formulation without needing the concave relaxation in an explicit way thus significantly simplifying the process of developing ccrp algorithms the simplified ccrp can be generally applied to any optimizations over the partial permutation matrix as long as the convex relaxation can be found based on two convex relaxations we obtain two graph matching algorithms defined on adjacency matrix and affinity matrix respectively extensive experimental results witness the simplicity as well as state of the art performance of the two simplified ccrp graph matching algorithms

ridge network detection in crumpled paper via graph density maximization crumpled sheets of paper tend to exhibit a specific and complex structure which is described by physicists as ridge networks existing literature shows that the automation of ridge network detection in crumpled paper is very challenging because of its complex structure and measuring distortion in this paper we propose to model the ridge network as a weighted graph and formulate the ridge network detection as an optimization problem in terms of the graph density first we detect a set of graph nodes and then determine the edge weight between each pair of nodes to construct a complete graph next we define a graph density criterion and formulate the detection problem to determine a subgraph with maximal graph density further we also propose to refine the graph density by including a pairwise connectivity into the criterion to improve the connectivity of the detected ridge network our experimental results show that with the density criterion our proposed method effectively automates the ridge network detection

discrete particle swarm optimization for high order graph matching high order graph matching aims at establishing correspondences between two sets of feature points using high order constraints it is usually formulated as an np hard problem of maximizing an objective function this paper introduces a discrete particle swarm optimization algorithm for resolving high order graph matching problems which incorporates several re defined operations a problem specific initialization method based on heuristic information and a problem specific local search procedure the proposed algorithm is evaluated on both synthetic and real world datasets its outstanding performance is validated in comparison with three state of the art approaches

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