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40
Feature Correspondence via Graph Matching: Models and Global Optimization
"... Abstract. In this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from a pair of images containing a human figure in distinct poses. We formulate th ..."
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Cited by 60 (1 self)
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Abstract. In this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from a pair of images containing a human figure in distinct poses. We formulate this matching task as an energy minimization problem by defining a complex objective function of the appearance and the spatial arrangement of the features. Optimization of this energy is an instance of graph matching, which is in general a NPhard problem. We describe a novel graph matching optimization technique, which we refer to as dual decomposition (DD), and demonstrate on a variety of examples that this method outperforms existing graph matching algorithms. In the majority of our examples DD is able to find the global minimum within a minute. The ability to globally optimize the objective allows us to accurately learn the parameters of our matching model from training examples. We show on several matching tasks that our learned model yields results superior to those of stateoftheart methods. 1
A tensorbased algorithm for highorder graph matching
 In CVPR
, 2009
"... Abstract—This paper addresses the problem of establishing correspondences between two sets of visual features using higherorder constraints instead of the unary or pairwise ones used in classical methods. Concretely, the corresponding hypergraph matching problem is formulated as the maximization of ..."
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Cited by 37 (2 self)
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Abstract—This paper addresses the problem of establishing correspondences between two sets of visual features using higherorder 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 stateoftheart algorithms on both synthetic and real data.
Bundle Methods for Regularized Risk Minimization
"... A wide variety of machine learning problems can be described as minimizing a regularized risk functional, with different algorithms using different notions of risk and different regularizers. Examples include linear Support Vector Machines (SVMs), Gaussian Processes, Logistic Regression, Conditional ..."
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Cited by 36 (2 self)
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A wide variety of machine learning problems can be described as minimizing a regularized risk functional, with different algorithms using different notions of risk and different regularizers. Examples include linear Support Vector Machines (SVMs), Gaussian Processes, Logistic Regression, Conditional Random Fields (CRFs), and Lasso amongst others. This paper describes the theory and implementation of a scalable and modular convex solver which solves all these estimation problems. It can be parallelized on a cluster of workstations, allows for datalocality, and can deal with regularizers such as L1 and L2 penalties. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1/ɛ) steps to ɛ precision for general convex problems and in O(log(1/ɛ)) steps for continuously differentiable problems. We demonstrate the performance of our general purpose solver on a variety of publicly available datasets.
Graphical models and point pattern matching
 IEEE Trans. PAMI
, 2006
"... Abstract—This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless c ..."
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Cited by 30 (5 self)
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Abstract—This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes. Index Terms—Point pattern matching, graph matching, graphical models, Markov random fields, junction tree algorithm. 1
A Survey on Shape Correspondence
, 2011
"... We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours, or point sets. This survey is motivated in part by recent developments in spacetime registration, where one seeks a correspondence between nonrigid and timevarying surfaces, an ..."
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Cited by 28 (6 self)
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We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours, or point sets. This survey is motivated in part by recent developments in spacetime registration, where one seeks a correspondence between nonrigid and timevarying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline. Establishing a meaningful correspondence between shapes is often difficult since it generally requires an understanding of the structure of the shapes at both the local and global levels, and sometimes the functionality of the shape parts as well. Despite its inherent complexity, shape correspondence is a recurrent problem and an essential component of numerous geometry processing applications. In this survey, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria arising from the problem definition. The main categories of classification are defined in terms of the input and output representation, objective function, and solution approach. We conclude the survey by discussing open problems and future perspectives.
Dense Nonrigid Surface Registration Using HighOrder Graph Matching
"... In this paper, we propose a highorder graph matching formulation to address nonrigid surface matching. The singleton terms capture the geometric and appearance similarities (e.g., curvature and texture) while the highorder terms model the intrinsic embedding energy. The novelty of this paper incl ..."
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Cited by 24 (5 self)
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In this paper, we propose a highorder graph matching formulation to address nonrigid surface matching. The singleton terms capture the geometric and appearance similarities (e.g., curvature and texture) while the highorder terms model the intrinsic embedding energy. The novelty of this paper includes: 1) casting 3D surface registration into a graph matching problem that combines both geometric and appearance similarities and intrinsic embedding information, 2) the first implementation of highorder graph matching algorithm that solves a nonconvex optimization problem, and 3) an efficient twostage optimization approach to constrain the search space for dense surface registration. Our method is validated through a series of experiments demonstrating its accuracy and efficiency, notably in challenging cases of large and/or nonisometric deformations, or meshes that are partially occluded. 1.
Kernelized sorting
 in Advances in Neural Information Processing Systems
, 2009
"... Abstract—Object matching is a fundamental operation in data analysis. It typically requires the definition of a similarity measure between the classes of objects to be matched. Instead, we develop an approach which is able to perform matching by requiring a similarity measure only within each of the ..."
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Cited by 16 (3 self)
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Abstract—Object matching is a fundamental operation in data analysis. It typically requires the definition of a similarity measure between the classes of objects to be matched. Instead, we develop an approach which is able to perform matching by requiring a similarity measure only within each of the classes. This is achieved by maximizing the dependency between matched pairs of observations by means of the Hilbert Schmidt Independence Criterion. This problem can be cast as one of maximizing a quadratic assignment problem with special structure and we present a simple algorithm for finding a locally optimal solution.
Unsupervised Learning for Graph Matching
 Computer Vision and Pattern Recognition
"... Graph matching is an important problem in computer vision. It is used in 2D and 3D object matching and recognition. Despite its importance, there is little literature on learning the parameters that control the graph matching problem, even though learning is important for improving the matching rate ..."
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Cited by 15 (3 self)
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Graph matching is an important problem in computer vision. It is used in 2D and 3D object matching and recognition. Despite its importance, there is little literature on learning the parameters that control the graph matching problem, even though learning is important for improving the matching rate, as shown by this and other work. In this paper we show for the first time how to perform parameter learning in an unsupervised fashion, that is when no correct correspondences between graphs are given during training. We show empirically that unsupervised learning is comparable in efficiency and quality with the supervised one, while avoiding the tedious manual labeling of ground truth correspondences. We also verify experimentally that this learning method can improve the performance of several stateofthe art graph matching algorithms. 1.
Covering Trees and Lowerbounds on Quadratic Assignment
"... Many computer vision problems involving feature correspondence among images can be formulated as an assignment problem with a quadratic cost function. Such problems are computationally infeasible in general but recent advances in discrete optimization such as treereweighted belief propagation (TRW) ..."
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Cited by 9 (3 self)
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Many computer vision problems involving feature correspondence among images can be formulated as an assignment problem with a quadratic cost function. Such problems are computationally infeasible in general but recent advances in discrete optimization such as treereweighted belief propagation (TRW) often provide highquality solutions. In this paper, we improve upon these algorithms in two ways. First, we introduce covering trees, a variant of TRW which provide the same bounds on the MAP energy as TRW with far fewer variational parameters. Optimization of these parameters can be carried out efficiently using either fixed–point iterations (as in TRW) or subgradient based techniques. Second, we introduce a new technique that utilizes bipartite matching applied to the minmarginals produced with covering trees in order to compute a tighter lowerbound for the quadratic assignment problem. We apply this machinery to the problem of finding correspondences with pairwise energy functions, and demonstrate the resulting hybrid method outperforms TRW alone and a recent related subproblem decomposition algorithm on benchmark image correspondence problems. 1.
Stochastic blockcoordinate frankwolfe optimization for structural svms. arXiv preprint:1207.4747
, 2012
"... We propose a randomized blockcoordinate variant of the classic FrankWolfe algorithm for convex optimization with blockseparable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality gap as the full FrankWolfe algorithm. We also show that, w ..."
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Cited by 9 (2 self)
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We propose a randomized blockcoordinate variant of the classic FrankWolfe algorithm for convex optimization with blockseparable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality gap as the full FrankWolfe algorithm. We also show that, when applied to the dual structural support vector machine (SVM) objective, this yields an online algorithm that has the same low iteration complexity as primal stochastic subgradient methods. However, unlike stochastic subgradient methods, the blockcoordinate FrankWolfe algorithm allows us to compute the optimal stepsize and yields a computable duality gap guarantee. Our experiments indicate that this simple algorithm outperforms competing structural SVM solvers. 1.