# Consensus of Two Graph Correspondences Through a Generalisation of the Bipartite Graph Matching

• Carlos Francisco Moreno-García
• Francesc Serratosa
• Xavier Cortés
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9069)

## Abstract

One of the most important processes related to structural pattern recognition is to compare the involved objects through representing them as attributed graphs and using error-tolerant graph matching methods. To do so, it is needed a first step to extract the graphs given the original objects and deduct the whole attribute values of nodes and edges. Depending on the application, there are several methods to obtain these graphs and so, the object at hand can be represented by several graphs, not only with different nodes and edges but also with different attribute domains. In the case that we have several graphs to represent the same object, we can deduct several correspondences between graphs. In this work, we want to solve the problem of having these correspondences by exploding this diversity to announce a final correspondence in which the incongruences introduced in the graph extraction and also the graph matching could be reduced. We present a consensus method which, given two correspondences between two pairs of attributed graphs generated by separate entities and with different attribute domains, enounces a final correspondence consensus considering the existence of outliers. Our method is based on a generalisation of the Bipartite graph matching algorithm that minimises the Edit cost of the consensus correspondence while forcing (to the most) to be the mean correspondence of the two original correspondences.

## Keywords

Bipartite graph matching Graph correspondence Consensus correspondence

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© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• Carlos Francisco Moreno-García
• 1
Email author
• Francesc Serratosa
• 1
• Xavier Cortés
• 1
1. 1.Universitat Rovira i VirgiliTarragonaSpain