Bayesian graph edit distance

This paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of edit-distance originally introduced for graph-matching by Sanfeliu and Fu (1983). We show how the Levenshtein distance (1966) can be used to model the probability distribution for structural errors in the graph-matching problem. This probability distribution is used to locate matches using MAP label updates. We compare the resulting graph-matching algorithm with that recently reported by Wilson and Hancock. The use of edit-distance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worst-case complexity. We support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem. This demonstrates experimentally that the gain in efficiency is not at the expense of quality of match.