A unification of 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 their unification. We start by defining a new labeling assignment space and then formulate the 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 a consistency condition and show that each ω-limit point of the dynamic system gives a consistent labeling. We finally make a peace between the multi-label 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