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Graph Matching With a Dual-Step EM Algorithm
November 1998 (vol. 20 no. 11)
pp. 1236-1253

Abstract—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. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data.

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Index Terms:
EM Algorithm, graph-matching, affine geometry, perspective geometry, relational constraints, Delaunay graph, discrete relaxation.
Citation:
Andrew D.J. Cross, Edwin R. Hancock, "Graph Matching With a Dual-Step EM Algorithm," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 11, pp. 1236-1253, Nov. 1998, doi:10.1109/34.730557
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