New results on binary auto- and heteroassociative morphological memories

In morphological neural networks, the operations erosion or dilation of mathematical morphology are performed at each node. Alternatively, the total input effect on a morphological neuron can be expressed in terms of lattice induced matrix operations in the mathematical theory of minimax algebra. Morphological associative memories employ a recording strategy that resembles the widely known correlation strategy. The binary autoassociative morphological memory (AMM) can be viewed as the minimax algebra counterpart of the correlation-recorded discrete Hopfield net. In contrast to the Hopfield net, AMM´s are not limited to the storage and retrieval of binary or bipolar patterns and exhibit attractive properties such as one-step convergence and an optimal absolute storage capacity. Heteroassociative morphological memories (HMMs) have yet to be studied extensively and only a few theorems on HMM´s have been proven. This paper proves a number of theorems that yield an exact characterization of the recall phases of binary AMM´s as well as binary HMM´s.