Graph matching with a dual-step EM algorithm

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 20; no. 11; pp. 1236 - 1253
• Main Authors: Cross, A.D.J., Hancock, E.R.
• Format: Journal Article
• Language: English
• Published: IEEE 01.11.1998
• Subjects: Bipartite graph; Computational geometry; Computer vision; Image sampling; Information geometry; Matrix decomposition; Maximum likelihood estimation; Pattern matching; Robot sensing systems
• ISSN: 0162-8828
• DOI: 10.1109/34.730557

This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. We evaluate the technique on two real-world problems.