Spectral Multiplicity Tolerant Inexact Graph Matching

A graph can be exactly specified by the spectrum and corresponding eigenvectors of its adjacency matrix. This provides a solid foundation for spectrum based graph matching. However, most previous methods ignore the spectral multiplicity, which may significantly affect the matching accuracy. In this paper, we address the problem of minimizing the matching error when graph spectral multiplicity is involved. We first model spectral multiplicity by the sub-eigenspace rotation matrix R, and integrate R into the spectrum based graph matching model. We then focus on the exact graph matching problem, and show how to establish the vertex-to-vertex correspondence by iteratively optimizing the sub-eigenspace rotation matrix R and the permutation matrix P. A reliable matching initialization method is proposed to make this process converge rapidly. Finally, we extend the approach to the inexact graph matching problem by optimally warping two graphs to the same size. The proposed approach is robust and efficient. We support our approach with numerical experiments and demonstrate its effectiveness in the practical application of uncalibrated stereo matching.