Efficient Alignment and Correspondence Using Edit Distance

This paper presents work aimed at rendering the dual-step EM algorithm of Cross and Hancock more efficient. The original algorithm integrates the processes of point-set alignment and correspondence. The consistency of the pattern of correspondence matches on the Delaunay triangulation of the points is used to gate contributions to the expected log-likelihood function for point-set alignment parameters. However, in its original form the algorithm uses a dictionary of structure-preserving mappings to asses the consistency of match. This proves to be a serious computational bottleneck. In this paper, we show how graph edit-distance can be used to compute the correspondence probabilities more efficiently. In a sensitivity analysis, we show that the edit distance method is not only more efficient, it is also more accurate than the dictionary-based method.