Inexact Matching of Large and Sparse Graphs Using Laplacian Eigenvectors

Authors:
David Knossow;Avinash Sharma;Diana Mateus;Radu Horaud
Affiliations:
Perception team, INRIA Grenoble Rhone-Alpes, Saint Ismier Cedex, France 38334;Perception team, INRIA Grenoble Rhone-Alpes, Saint Ismier Cedex, France 38334;Perception team, INRIA Grenoble Rhone-Alpes, Saint Ismier Cedex, France 38334;Perception team, INRIA Grenoble Rhone-Alpes, Saint Ismier Cedex, France 38334
Venue:
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Year:
2009

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Abstract

In this paper we propose an inexact spectral matching algorithm that embeds large graphs on a low-dimensional isometric space spanned by a set of eigenvectors of the graph Laplacian. Given two sets of eigenvectors that correspond to the smallest non-null eigenvalues of the Laplacian matrices of two graphs, we project each graph onto its eigenenvectors. We estimate the histograms of these one-dimensional graph projections (eigenvector histograms) and we show that these histograms are well suited for selecting a subset of significant eigenvectors, for ordering them, for solving the sign-ambiguity of eigenvector computation, and for aligning two embeddings. This results in an inexact graph matching solution that can be improved using a rigid point registration algorithm. We apply the proposed methodology to match surfaces represented by meshes.