Morphological bidirectional associative memories

The theory of artificial neural networks has been successfully applied to a wide variety of pattern recognition problems. In this theory, the first st ep in computing the next state of a neuron or in performing the next layer neural network computation involves the linear operation of multiplying neu ral values by their synaptic strengths and adding the results. Thresholding usually follows the linear operation in order to provide for nonlinearity of the network. In this paper we discuss a novel class of artificial neural networks, called morphological neural networks ;s in which the operations of multiplication and addition are replaced by addition and maximum (or min imum), respectively. By taking the maximum (or minimum) of sums instead of the sum of products, morphological network computation is nonlinear before thresholding. As a consequence, the properties of morphological neural netw orks are drastically different from those of traditional neural network mod els. The main emphasis of the research presented here is on morphological b idirectional associative memories (MBAMs). In particular, we establish a ma thematical theory for MBAMs and provide conditions that guarantee perfect b idirectional recall for corrupted patterns. Some examples that illustrate p erformance differences between the morphological model and the traditional semilinear model are also given. (C) 1999 Elsevier Science Ltd. All rights reserved.