Joint Optimization for Consistent Multiple Graph Matching

Yan, Junchi; Tian, Yu; Zha, Hongyuan; Yang, Xiaokang; Zhang, Ya; Chu, Stephen M.

doi:10.1109/iccv.2013.207

Cited by 60 publications

(83 citation statements)

References 20 publications

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“…Note that for notational simplicity, without loss of generality, here we omit the weight λ ij for each quadratic term in the objective function as used in [47].…”

Section: Graph Matching Formulationsmentioning

confidence: 99%

“…This score definition is widely used in graph matching related work, such as [9,52,43,10,8,47]. By stacking all P ij into one whole matrix, we define the resulting matching configuration matrix 2 as:…”

Section: Notations and Preliminariesmentioning

confidence: 99%

“…However, on one hand, many practical computer vision tasks need matching multiple images or point sets, which is a building block for various applications that involve multi-view registration or matching. On the other hand, it is generally recognized [47,44,40,36] that simultaneously exploring all pairwise affinity information across the whole pool of graphs G = {G 1 , · · · , G N } may improve the matching accuracy. Such an improvement is accomplished through avoiding trapping to local optima, or a false optima away from the semantic true correspondence due to the large deformation, appearing in the pairwise case since only affinity between two local graphs is explored.…”

Section: Introductionmentioning

confidence: 99%

“…Current graph matching methods mostly focused on the two-graph scenario such as [21,38,9,41,52,43,10,8,47]. In particular, there are several research groups focusing on graph matching and related problems over the past years, such as Professor Horst Bunke's group in Bern [3], Professor Edwin R. Hancock's group in York [2], and Professor Francesc Serratosa's group in Tarragona [1], to name a few.…”

Section: Introductionmentioning

confidence: 99%

“…In computer vision, GM has primarily been used to find correspondences among two or more sets of local features extracted from images. Different from conventional matching methods such as RANSAC [15] and Iterative Closest Point (ICP) [4], GM goes beyond the first-order node-wise feature as well as the focus of location information [51], which incorporates more distinctive pairwise [43,47] or higher-order [50,13,28,33] node interactions for matching structural objects. Consequently, GM has attracted considerable research attention [12,17,22,34,16] for decades, yet remains computationally challenging due to its combinatorial nature.…”

Section: Introductionmentioning

confidence: 99%

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Graduated Consistency-Regularized Optimization for Multi-graph Matching

Yan

Liu³

et al. 2014

Computer Vision – ECCV 2014

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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 NP-hard, 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 global-optimal 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.

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“…Note that for notational simplicity, without loss of generality, here we omit the weight λ ij for each quadratic term in the objective function as used in [47].…”

Section: Graph Matching Formulationsmentioning

confidence: 99%

Section: Notations and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Graduated Consistency-Regularized Optimization for Multi-graph Matching

Yan

Liu³

et al. 2014

Computer Vision – ECCV 2014

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Vertex nomination via seeded graph matching

Patsolic

Park

Lyzinski

et al. 2020

Statistical Analysis

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Consider two networks on overlapping, nonidentical vertex sets. Given vertices of interest (VOIs) in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph matching methods can be applied directly to recover the missing correspondences, herein we present a principled methodology appropriate for situations in which the networks are too large/noisy for brute-force graph matching. Our methodology identifies vertices in a local neighborhood of the VOIs in the first network that have verifiable corresponding vertices in the second network. Leveraging these known correspondences, referred to as seeds, we match the induced subgraphs in each network generated by the neighborhoods of these verified seeds, and rank the vertices of the second network in terms of the most likely matches to the original VOIs. We demonstrate the applicability of our methodology through simulations and real data examples. K E Y W O R D Sgraph inference, graph matching, graph mining, seeded graph matching, stochastic block model, vertex nomination Abbreviations: SGM, seeded graph matching; VN, vertex nomination; VOI, vertex of interest.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Incremental Multi-graph Matching via Diversity and Randomness Based Graph Clustering

Yan

Liu

et al. 2018

Computer Vision – ECCV 2018

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Joint Optimization for Consistent Multiple Graph Matching

Cited by 60 publications

References 20 publications

Graduated Consistency-Regularized Optimization for Multi-graph Matching

Graduated Consistency-Regularized Optimization for Multi-graph Matching

Vertex nomination via seeded graph matching

Incremental Multi-graph Matching via Diversity and Randomness Based Graph Clustering

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