Relaxation labeling and associative memory

This paper attempts to consolidate the theoretical foundation of the relaxation labeling processes, explore the connections between the relaxation labeling model and the Hopfield associative memory model, and seek for their unification. We start by defining a new labeling assignment space and then formulating relaxation labeling process as a dynamic system of Lyapunov type, which is equipped with a well defined energy function and described by a naturally fitted updating rule. We present consistency condition and show each ω-limit point of the dynamic system gives a consistent labeling. We finally make a peace between the multilabel and one-label relaxation labeling and reveal an interesting result that, for a one-label case, the newly formulated relaxation labeling model reduces to the Hopfield associative memory model