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Register a new userFusion Moves for Graph Matching
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Added by
Stefan Haller
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We contribute to approximate algorithms for the quadratic assignment problem also known as graph matching. Inspired by the success of the fusion moves technique developed for multilabel discrete Markov random fields, we investigate its applicability to graph matching. In particular, we show how fusion moves can be efficiently combined with the dedicated state-of-the-art dual methods that have recently shown superior results in computer vision and bio-imaging applications. As our empirical evaluation on a wide variety of graph matching datasets suggests, fusion moves significantly improve performance of these methods in terms of speed and quality of the obtained solutions. Our method sets a new state-of-the-art with a notable margin with respect to its competitors.
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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 important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise constraints can be formulated as a quadratic assignment problem (QAP), which is NP-complete and results in intrinsic computational difficulties. In this paper, we present a functional representation for graph matching (FRGM) that aims to provide more geometric insights on the problem and reduce the space and time complexities of corresponding algorithms. To achieve these goals, we represent a graph endowed with edge attributes by a linear function space equipped with a functional such as inner product or metric, that has an explicit geometric meaning. Consequently, the correspondence between graphs can be represented as a linear representation map of that functional. Specifically, we reformulate the linear functional representation map as a new parameterization for Euclidean graph matching, which is associative with geometric parameters for graphs under rigid or nonrigid deformations. This allows us to estimate the correspondence and geometric deformations simultaneously. The use of the representation of edge attributes rather than the affinity matrix enables us to reduce the space complexity by two orders of magnitudes. Furthermore, we propose an efficient optimization strategy with low time complexity to optimize the objective function. The experimental results on both synthetic and real-world datasets demonstrate that the proposed FRGM can achieve state-of-the-art performance.
Image-text matching has received growing interest since it bridges vision and language. The key challenge lies in how to learn correspondence between image and text. Existing works learn coarse correspondence based on object co-occurrence statistics, while failing to learn fine-grained phrase correspondence. In this paper, we present a novel Graph Structured Matching Network (GSMN) to learn fine-grained correspondence. The GSMN explicitly models object, relation and attribute as a structured phrase, which not only allows to learn correspondence of object, relation and attribute separately, but also benefits to learn fine-grained correspondence of structured phrase. This is achieved by node-level matching and structure-level matching. The node-level matching associates each node with its relevant nodes from another modality, where the node can be object, relation or attribute. The associated nodes then jointly infer fine-grained correspondence by fusing neighborhood associations at structure-level matching. Comprehensive experiments show that GSMN outperforms state-of-the-art methods on benchmarks, with relative Recall@1 improvements of nearly 7% and 2% on Flickr30K and MSCOCO, respectively. Code will be released at: https://github.com/CrossmodalGroup/GSMN.
This work addresses the problem of learning compact yet discriminative patch descriptors within a deep learning framework. We observe that features extracted by convolutional layers in the pixel domain are largely complementary to features extracted in a transformed domain. We propose a convolutional network framework for learning binary patch descriptors where pixel domain features are fused with features extracted from the transformed domain. In our framework, while convolutional and transformed features are distinctly extracted, they are fused and provided to a single classifier which thus jointly operates on convolutional and transformed features. We experiment at matching patches from three different datasets, showing that our feature fusion approach outperforms multiple state-of-the-art approaches in terms of accuracy, rate, and complexity.
Graph matching (GM), as a longstanding problem in computer vision and pattern recognition, still suffers from numerous cluttered outliers in practical applications. To address this issue, we present the zero-assignment constraint (ZAC) for approaching the graph matching problem in the presence of outliers. The underlying idea is to suppress the matchings of outliers by assigning zero-valued vectors to the potential outliers in the obtained optimal correspondence matrix. We provide elaborate theoretical analysis to the problem, i.e., GM with ZAC, and figure out that the GM problem with and without outliers are intrinsically different, which enables us to put forward a sufficient condition to construct valid and reasonable objective function. Consequently, we design an efficient outlier-robust algorithm to significantly reduce the incorrect or redundant matchings caused by numerous outliers. Extensive experiments demonstrate that our method can achieve the state-of-the-art performance in terms of accuracy and efficiency, especially in the presence of numerous outliers.
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