Results 1  10
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21
Robust Point Matching via Vector Field Consensus
, 2013
"... Abstract — In this paper, we propose an efficient algorithm, called vector field consensus, for establishing robust point correspondences between two sets of points. Our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences, or ..."
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Abstract — In this paper, we propose an efficient algorithm, called vector field consensus, for establishing robust point correspondences between two sets of points. Our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences, or outliers, in addition to a limited number of true correspondences (inliers). Next, we solve for correspondence by interpolating a vector field between the two point sets, which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint. We formulate this a maximum a posteriori (MAP) estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. We impose nonparametric geometrical constraints on the correspondence, as a prior distribution, using Tikhonov regularizers in a reproducing kernel Hilbert space. MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We illustrate this method on data sets in 2D and 3D and demonstrate that it is robust to a very large number of outliers (even up to 90%). We also show that in the special case where there is an underlying parametric geometrical model (e.g., the epipolar line constraint) that we obtain better results than standard alternatives like RANSAC if a large number of outliers are present. This suggests a twostage strategy, where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters. Our algorithm is computationally efficient and we provide code for others to use it. In addition, our approach is general and can be applied to other problems, such as learning with a badly corrupted training data set. Index Terms — Point correspondence, outlier removal, matching, regularization.
Graph Matching via Sequential Monte Carlo
"... Abstract. Graph matching is a powerful tool for computer vision and machine learning. In this paper, a novel approach to graph matching is developed based on the sequential Monte Carlo framework. By constructing a sequence of intermediate target distributions, the proposed algorithm sequentially per ..."
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Cited by 6 (1 self)
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Abstract. Graph matching is a powerful tool for computer vision and machine learning. In this paper, a novel approach to graph matching is developed based on the sequential Monte Carlo framework. By constructing a sequence of intermediate target distributions, the proposed algorithm sequentially performs a sampling and importance resampling to maximize the graph matching objective. Through the sequential sampling procedure, the algorithm effectively collects potential matches under onetoone matching constraints to avoid the adverse effect of outliers and deformation. Experimental evaluations on synthetic graphs and real images demonstrate its higher robustness to deformation and outliers. Key words: graph matching, sequential Monte Carlo, feature correspondence, image matching, object recognition 1
Robust Feature Matching with Alternate Hough and Inverted Hough Transforms
"... We present an algorithm that carries out alternate Hough transform and inverted Hough transform to establish feature correspondences, and enhances the quality of matching in both precision and recall. Inspired by the fact that nearby features on the same object share coherent homographies in matchin ..."
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We present an algorithm that carries out alternate Hough transform and inverted Hough transform to establish feature correspondences, and enhances the quality of matching in both precision and recall. Inspired by the fact that nearby features on the same object share coherent homographies in matching, we cast the task of feature matching as a density estimation problem in the Hough space spanned by the hypotheses of homographies. Specifically, we project all the correspondences into the Hough space, and determine the correctness of the correspondences by their respective densities. In this way, mutual verification of relevant correspondences is activated, and the precision of matching is boosted. On the other hand, we infer the concerted homographies propagated from the locally grouped features, and enrich the correspondence candidates for each feature. The recall is hence increased. The two processes are tightly coupled. Through iterative optimization, plausible enrichments are gradually revealed while more correct correspondences are detected. Promising experimental results on three benchmark datasets manifest the effectiveness of the proposed approach. 1.
Graduated ConsistencyRegularized Optimization for Multigraph Matching
"... Abstract. Graph matching has a wide spectrum of computer vision applications such as finding feature point correspondences across images. The problem of graph matching is generally NPhard, so most existing work pursues suboptimal solutions between two graphs. This paper investigates a more genera ..."
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Abstract. Graph matching has a wide spectrum of computer vision applications such as finding feature point correspondences across images. The problem of graph matching is generally NPhard, so most existing work pursues suboptimal solutions between two graphs. This paper investigates a more general problem of matching N attributed graphs to each other, i.e. labeling their common node correspondences such that a certain compatibility/affinity objective is optimized. This multigraph matching problem involves two key ingredients affecting the overall accuracy: a) the pairwise affinity matching score between two local graphs, and b) global matching consistency that measures the uniqueness and consistency of the pairwise matching results by different sequential matching orders. Previous work typically either enforces the matching consistency constraints in the beginning of iterative optimization, which may propagate matching error both over iterations and across different graph pairs; or separates score optimizing and consistency synchronization in two steps. This paper is motivated by the observation that affinity score and consistency are mutually affected and shall be tackled jointly to capture their correlation behavior. As such, we propose a novel multigraph matching algorithm to incorporate the two aspects by iteratively approximating the globaloptimal affinity score, meanwhile gradually infusing the consistency as a regularizer, which improves the performance of the initial solutions obtained by existing pairwise graph matching solvers. The proposed algorithm with a theoretically proven convergence shows notable efficacy on both synthetic and public image datasets. 1
Efficient Geometric Graph Matching Using Vertex Embedding
 In SIGSPATIAL
, 2013
"... For many applications such as road network analysis and image processing, it is critical to study spatial properties of objects in addition to object relationships. Geometric graphs provide a suitable modeling framework for such applications, where vertices are located in some 2D space. For applica ..."
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For many applications such as road network analysis and image processing, it is critical to study spatial properties of objects in addition to object relationships. Geometric graphs provide a suitable modeling framework for such applications, where vertices are located in some 2D space. For applications where the similarity between the structures of different graphs plays an important role, typically, inexact graph matching algorithms are employed. However, graph matching algorithms face many problems such as scalability with respect to graph size and less tolerance to changes in graph structure or labels. In this paper, we propose a solution to the problem of inexact graph matching for geometric graphs in the 2D space. Our approach allows to effectively answer subgraph and common subgraph queries for geometric graphs that differ in structure, spatial properties, and labels. Initially, a spatial feature is extracted from each vertex, and string edit distance is used to find the distance between pairs of vertices. To speed up graph matching, we propose vertex embedding into the Euclidean space. Based on this, the distance between two vertices can be computed using the Euclidean distance in constant time. To answer subgraph and common subgraph queries, we introduce an iterative matching algorithm that matches two graphs using their similarity in the Euclidean space. Such an algorithm merges highly similar vertices to create similar connected subgraphs. Using representative geometric graphs extracted from road networks, we show that our approach outperforms existing graph matching approaches in terms of matching quality and runtime.
Spectral Clustering for DivideandConquer Graph Matching
, 2014
"... We present a bijective parallelizable seeded graph matching algorithm designed to match very large graphs. Our algorithm combines spectral graph embedding with existing stateoftheart seeded graph matching procedures. We theoretically justify our approach by proving that modestly correlated, large ..."
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Cited by 2 (1 self)
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We present a bijective parallelizable seeded graph matching algorithm designed to match very large graphs. Our algorithm combines spectral graph embedding with existing stateoftheart seeded graph matching procedures. We theoretically justify our approach by proving that modestly correlated, large stochastic block model random graphs are correctly matched utilizing very few seeds through our divideandconquer procedure. Lastly, we demonstrate the effectiveness of our approach in matching very large graphs in simulated and real data examples.
Graph matching by simplified convexconcave relaxation procedure
 INT’L J. COMPUTER VISION
, 2014
"... The convex and concave relaxation procedure (CCRP) was recently proposed and exhibited stateoftheart 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 appl ..."
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Cited by 2 (1 self)
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The convex and concave relaxation procedure (CCRP) was recently proposed and exhibited stateoftheart 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.
Improving graph matching via density maximization
 in Proc. Int’ Conf. Computer Vision
, 2013
"... Graph matching has been widely used in various applications in computer vision due to its powerful performance. However, it poses three challenges to image sparse feature matching: (1) The combinatorial nature limits the size of the possible matches; (2) It is sensitive to outliers because the obj ..."
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Cited by 1 (0 self)
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Graph matching has been widely used in various applications in computer vision due to its powerful performance. However, it poses three challenges to image sparse feature matching: (1) The combinatorial nature limits the size of the possible matches; (2) It is sensitive to outliers because the objective function prefers more matches; (3) It works poorly when handling manytomany object correspondences, due to its assumption of one single cluster for each graph. In this paper, we address these problems with a unified framework—Density Maximization. We propose a graph density local estimator (
Fast and Scalable Approximate Spectral Matching for HigherOrder Graph Matching
, 2014
"... This paper presents a fast and efficient computational approach to higherorder 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 ind ..."
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This paper presents a fast and efficient computational approach to higherorder 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 representation 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. In order to compensate for the loss of matching accuracy by the approximation, we also adopt and incorporate a marginalization scheme that maps a higherorder tensor to matrix as well as a onetoone mapping constraint into the eigenvector computation process. The experimental results show that the proposed method is faster and requiring smaller memory than the existing methods with little or no loss of accuracy.
Learning Graph Matching: oriented to Category Modeling from Cluttered Scenes
"... Although graph matching is a fundamental problem in pattern recognition, and has drawn broad interest from many fields, the problem of learning graph matching has not received much attention. In this paper, we redefine the learning of graph matching as a model learning problem. In addition to conven ..."
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Although graph matching is a fundamental problem in pattern recognition, and has drawn broad interest from many fields, the problem of learning graph matching has not received much attention. In this paper, we redefine the learning of graph matching as a model learning problem. In addition to conventional training of matching parameters, our approach modifies the graph structure and attributes to generate a graphical model. In this way, the model learning is oriented toward both matching and recognition performance, and can proceed in an unsupervised1 fashion. Experiments demonstrate that our approach outperforms conventional methods for learning graph matching. 1.