Generalized morphological components based on interval descriptors and n-ary aggregation functions

Abstract

Morphological perceptrons (MPs) can be characterized as feedforward morphological neural networks (MNNs) with applications in classification and regression. The neuronal aggregation functions of current MP versions are drawn from gray-scale mathematical morphology (MM) that can be described in terms of matrix products in a lattice algebra called minimax algebra. Specifically, MPs have components each of which computes a pair-wise infimum of an erosion and an anti-dilation that can be expressed in terms of products of matrices with entries in a complete l-group extension.In this paper, we use the novel concept of an interval descriptor and an n-ary aggregation function on a bounded poset in order to generalize existing gray-scale and fuzzy morphological components (MCs) of morphological and hybrid morphological/linear perceptrons (HMLPs). In addition, we present several other examples of generalized morphological components (GMCs) that can and will be incorporated as computational units into shallow and deep artificial neural networks.