Feedforward neural network function represented by morphological transform

This paper is based on a binary discrete signal system. We analyze the feedforward neural network (NN) in light of morphological hit-or-miss transform (HMT), indicate that every first- hidden-layer node (the direct successors of input nodes) corresponds to a certain family of structuring elements pairs (called structuring elements pairs family determined by weights and threshold vector (w1, w2,......wM, (mu) ), and the I-O function of the node can be represented as the union of HMT by the members of the family. The structuring elements pairs family can be found by searching an algorithm of artificial intelligence. On the basis of the above analysis, we further investigate the whole feedforward NN, indicate that any recognition function (on binary discrete signal system) can be fulfilled by 3-layer (including 1 hidden-layer) feedforward NN, and can also be fulfilled by the union of HMT by a family of structuring elements pairs.