Nonlinear relaxation labeling as growth transformation

Presents some new results which demonstrate that, despite its heuristic and simple-minded derivation, the familiar nonlinear relaxation labeling algorithm of Rosenfeld et al. (1976) is in fact intimately related with a well-established theory of constraint satisfaction developed by Hummel and Zucker (1983). In particular, it is shown that, when a certain symmetry condition is met, the algorithm possesses a Liapunov function which turns out to be (the negative of) a well-known consistency measure. This follows almost immediately from a powerful result of Baum and Eagon (1967) developed in the context of Markov chain theory. These properties are also shown to naturally generalize to higher-order relaxation schemes. Some applications of the results presented here are finally outlined.