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.