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.
This research is supported by the Spanish CICYT project DPI2013-42458-P, by project TIN2013-47245-C2-2-R and by Consejo Nacional de Ciencia y Tecnologías (CONACyT Mexico)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Moreno-García, C.F., Serratosa, F.: Weighted Mean Assignment of a Pair of Correspondences Using Optimisation Functions. In: Fränti, P., Brown, G., Loog, M., Escolano, F., Pelillo, M. (eds.) S+SSPR 2014. LNCS, vol. 8621, pp. 301–311. Springer, Heidelberg (2014)
Franek, F., Jiang, X., He, C.: Weighted Mean of a Pair of Clusterings. Pattern Analysis Applications (2012)
Sanromà, G., Alquézar, R., Serratosa, F., Herrera, B.: Smooth Point-set Registration using Neighbouring Constraints. Pattern Recognition Letters 33, 2029–2037 (2012)
Sanromà, G., Alquézar, R., Serratosa, F.: A New Graph Matching Method for Point-Set Correspondence using the EM Algorithm and Softassign. Computer Vision and Image Understanding 116(2), 292–304 (2012)
Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. Pattern Analysis and Machine Intelligence 18(4), 377–388 (1996)
Serratosa, F.: Speeding up Fast Bipartite Graph Matching through a New Cost Matrix. International Journal of Pattern Recognition & Artificial Intelligence 29(2) (2015)
Serratosa, F.: Fast Computation of Bipartite Graph Matching. Pattern Recognition Letters 45, 244–250 (2014)
Riesen, K., Bunke, H.: Approximate Graph Edit Distance Computation by Means of Bipartite Graph Matching. Image Vision Comput. 27(7), 950–959 (2009)
Serratosa, F., Cortés, X.: Interactive Graph-Matching using Active Query Strategies. Pattern Recognition 48, 1360–1369 (2015)
Cortés, X., Serratosa, F.: An Interactive Method for the Image Alignment problem based on Partially Supervised Correspondence. Expert Systems With Applications 42(1), 179–192 (2015)
Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover Publications (1998)
Kuhn, H.W.: The Hungarian Method for the Assignment Problem Export. Naval Research Logistics Quarterly 2(1-2), 83–97 (1955)
Jonker, R., Volgenant, T.: Improving the Hungarian Assignment Algorithm. Operations Research Letters 5(4), 171–175 (1986)
Timofte, R., Van Gool, L.: Adaptive and Weighted Collaborative Representations for Image Classification. Pattern Recognition Letters (Available Online 2014)
Saha, S., Ekbal, A.: Combining Multiple Classifiers using Vote Based Classifier Ensemble Technique for Named Entity Recognition. Data & Knowledge Engineering 85, 15–39 (2013)
Serratosa, F., Cortés, X., Solé, A.: Component Retrieval Based on a Database of Graphs for Hand-Written Electronic-Scheme Digitalisation. Expert Systems with Applications 40, 2493–2502 (2013)
Riesen, K., Bunke, H., Fischer, A.: Improving Graph Edit Distance Approximation by Centrality Measures. In: International Conference on Pattern Recognition (2014)
Cortés, X., Serratosa, F.: Learning Graph-Matching Edit-Costs based on the Optimality of the Oracle’s Node Correspondences. Pattern Recognition Letters (2015)
Sanfeliu, A., Fu, K.S.: A Distance Measure between Attributed Relational Graphs for Pattern Recognition. IEEE Transactions on Systems, Man, and Cybernetics 13(3), 353–362 (1983)
Gao, X., Xiao, B., Tao, D., Li, X.: A Survey of Graph Edit Distance. Pattern Analysis and Applications 13(1), 113–129 (2010)
Solé, A., Serratosa, F., Sanfeliu, A.: On the Graph Edit Distance Cost: Properties and Applications. Intern. Journal of Pattern Recognition and Artificial Intell. 26(5) (2012)
Ferrer, M., Valveny, E., Serratosa, F.: Median Graph: A New Exact Algorithm using a Distance Based on the Maximum Common Subgraph. Pattern Recognition Letters 30(5), 579–588 (2009)
Moreno-García, C.F., Serratosa, F., Cortés, X.: Iterative Versus Voting Method to Reach Consensus Given Multiple Correspondences of Two Sets. In: IbPRIA 2015 (2015)
Franek, L., Jiang, X.: Ensemble Clustering by means of Clustering Embedding in Vector Space. Pattern Recognition 47(2), 833–842 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Moreno-García, C.F., Serratosa, F., Cortés, X. (2015). Consensus of Two Graph Correspondences Through a Generalisation of the Bipartite Graph Matching. In: Liu, CL., Luo, B., Kropatsch, W., Cheng, J. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2015. Lecture Notes in Computer Science(), vol 9069. Springer, Cham. https://doi.org/10.1007/978-3-319-18224-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-18224-7_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18223-0
Online ISBN: 978-3-319-18224-7
eBook Packages: Computer ScienceComputer Science (R0)