On the Computation of the Common Labelling of a Set of Attributed Graphs

Solé-Ribalta, Albert; Serratosa, Francesc

doi:10.1007/978-3-642-10268-4_16

Cited by 13 publications

(23 citation statements)

References 13 publications

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“…The former dataset, created synthetically, is composed by 35 classes. The number of graphs per class is N oe [3,5,7,9,11] and the noise level between graphs is ν oe [10, 20, 40...80]. Therefore, we defined 5 x 7 = 35 different classes: seven classes with four graphs (with different noise levels), seven classes with five graphs (with different noise levels), and so on.…”

Section: Discussionmentioning

confidence: 99%

“…Each class was created as follows. We randomly generate a From each class, we randomly selected N oe [3,5,7,9,11] graphs, to generate the CL.…”

Section: Discussionmentioning

confidence: 99%

“…However, this method is not extensible to N graphs. Another method, which seems to solve both problems, was published in [7]. Nevertheless, its high computational complexity makes its use infeasible with large graphs sets.…”

Section: Introductionmentioning

confidence: 99%

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Graduated Assignment Algorithm for Finding the Common Labelling of a Set of Graphs

Solé-Ribalta

Serratosa

2010

Lecture Notes in Computer Science

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Abstract. In pattern recognition applications, it is useful to represent objects by attributed graphs considering their structural properties. Besides, some graph matching problems need a Common Labelling between vertices of a set of graphs. Computing this Common Labelling is an NP-complete problem. Stateof-the-art algorithms are composed by two steps: in the first, they compute all pairwise labellings among the graphs and in the second, they combine this information to obtain a Common Labelling. The drawback of these methods is that global information is only considered in the second step. To solve this problem, by reducing the Common Labelling problem to the quadratic assignment one, all graphs nodes are labelled to a virtual structure whereby the Common Labeling is generated using global information. We tested the algorithm on both real-world and synthetic data. We show that the algorithm offers better performance than a reference method with same computational cost.

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Section: Discussionmentioning

confidence: 99%

“…Each class was created as follows. We randomly generate a From each class, we randomly selected N oe [3,5,7,9,11] graphs, to generate the CL.…”

Section: Discussionmentioning

confidence: 99%

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Graduated Assignment Algorithm for Finding the Common Labelling of a Set of Graphs

Solé-Ribalta

Serratosa

2010

Lecture Notes in Computer Science

Self Cite

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“…c Matching results using joint matching algorithms based on the second-order consistency constraint. The accuracy and consistency are improved simultaneously additional consistency constraint called cycle-consistency [13][14][15][16][17][18][19][20]. Bonev et al [13] proposed a two-step algorithm to filter out inconsistent matches.…”

Section: Introductionmentioning

confidence: 99%

“…The algorithm finds all possible vertex isomorphisms between whole graph pairs first and then iteratively removes the inconsistent matches that violate the cycle-consistency constraint. Solé-Ribalta and Serratosa [14,16] proposed a more efficient two-step algorithm that uses an N-dimensional probabilistic matrix called a hypercube. In the first step, the algorithm creates a hypercube that describes the joint probability among the multiple isomorphisms.…”

Section: Introductionmentioning

confidence: 99%

Encouraging second-order consistency for multiple graph matching

Park

Yoon

2016

Machine Vision and Applications

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The problems in computer vision of finding the global correspondences across a set of images can be formulated as a multiple graph matching problem consisting of pairwise matching problems. In the multiple graph matching problem, matching consistency is as important as matching accuracy for preventing the contrariety among matched results. Unfortunately, since the majority of conventional pairwise matching methods only approximate the original graph matching problem owing to its computational complexity, a framework that separately matches each graph pair could generate inconsistent results in practical environments. In this paper, we propose a novel multiple graph matching method based on the second-order consistency concept, which simultaneously considers the matching information of all possible graph pairs. We reformulate the multiple graph matching problem to encourage second-order consistency and design an iterative optimization framework. In our experiments, the proposed method outperforms the state-of-the-art methods in terms of both consistency and accuracy.

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The graph association problem: Mathematical models and a lagrangian heuristic

Tauer

Nagi

Sudit

2013

Naval Research Logistics

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Graph association is the problem of merging many graphs that collectively describe a set of possibly repetitive entities and relationships into a single graph that contains unique entities and relationships. As a form of data association, graph association can be used to identify when two sensors are observing the same object so information from both sensors can be combined and analyzed in a meaningful and consistent way. Graph association between two graphs is related to the problem of graph matching, and between multiple graphs it is related to the common labeling of a graph set (also known as multiple graph matching) problem. This article contribution is to formulate graph association as a binary linear program and introduce a heuristic for solving multiple graph association using a Lagrangian relaxation approach to address issues with between-graph transitivity requirements. The algorithms are tested on a representative dataset. The developed model formulation was found to accurately solve the graph association problem. Furthermore, the Lagrangian heuristic was found to solve the developed model within 3% of optimal on many problem instances, and found better solutions to large problems than is possible by directly using CPLEX.

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On the Computation of the Common Labelling of a Set of Attributed Graphs

Cited by 13 publications

References 13 publications

Graduated Assignment Algorithm for Finding the Common Labelling of a Set of Graphs

Graduated Assignment Algorithm for Finding the Common Labelling of a Set of Graphs

Encouraging second-order consistency for multiple graph matching

The graph association problem: Mathematical models and a lagrangian heuristic

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