Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of the node-wise and structure-wise affinity across graphs and the resulting objective, to guide the matching procedure effectively finding the true matching against noises. To this end, this paper devises an end-to-end differentiable deep network pipeline to learn the affinity for graph matching. It involves a supervised permutation loss regarding with node correspondence to capture the combinatorial nature for graph matching. Meanwhile deep graph embedding models are adopted to parameterize both intra-graph and cross-graph affinity functions, instead of the traditional shallow and simple parametric forms e.g. a Gaussian kernel. The embedding can also effectively capture the higher-order structure beyond second-order edges. The permutation loss model is agnostic to the number of nodes, and the embedding model is shared among nodes such that the network allows for varying numbers of nodes in graphs for training and inference. Moreover, our network is class-agnostic with some generalization capability across different categories. All these features are welcomed for real-world applications. Experiments show its superiority against state-of-the-art graph matching learning methods.
Previous graph matching affinity learning methods are mostly based on simple and shallow parametric models, which use popular distances (typically weighted Euclid distance) in the node and edge feature space plus a similarity kernel function (e.g. Gaussian kernel) to derive the final affinity score. In particular, a unified (shallow) parametric graph structure learning model is devised between two graphs in a vector form @math @cite_30 . The authors in @cite_30 observe that the above simple model can incorporate most previous shallow learning models, including @cite_43 @cite_16 @cite_12 . Therefore, this method will be compared in our experiment.
@cite_30 @cite_43 @cite_16 @cite_12
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Many tasks in computer vision are formulated as graph matching problems. Despite the NP-hard nature of the problem, fast and accurate approximations have led to significant progress in a wide range of applications. Learning graph models from observed data, however, still remains a challenging issue. This paper presents an effective scheme to parameterize a graph model, and learn its structural attributes for visual object matching. For this, we propose a graph representation with histogram-based attributes, and optimize them to increase the matching accuracy. Experimental evaluations on synthetic and real image datasets demonstrate the effectiveness of our approach, and show significant improvement in matching accuracy over graphs with pre-defined structures. As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm. Graph matching is an essential problem in computer vision that has been successfully applied to 2D and 3D feature matching and object recognition. Despite its importance, little has been published on learning the parameters that control graph matching, even though learning has been shown to be vital for improving the matching rate. In this paper we show how to perform parameter learning in an unsupervised fashion, that is when no correct correspondences between graphs are given during training. Our experiments reveal that unsupervised learning compares favorably to the supervised case, both in terms of efficiency and quality, while avoiding the tedious manual labeling of ground truth correspondences. We verify experimentally that our learning method can improve the performance of several state-of-the art graph matching algorithms. We also show that a similar method can be successfully applied to parameter learning for graphical models and demonstrate its effectiveness empirically. In this paper we present a new approach for establishing correspondences between sparse image features related by an unknown non-rigid 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 NP-hard 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 state-of-the-art methods.