An Algorithm to Train Unrestricted Sequential Discrete Morphological Neural Networks

TL;DR

This paper introduces a new algorithm for training unrestricted sequential Discrete Morphological Neural Networks (DMNN), enabling more flexible modeling of morphological operators and improving their application in binary image processing.

Contribution

It presents a novel training algorithm for unrestricted sequential DMNN, extending previous work on canonical DMNN and enabling the representation of general W-operators.

Findings

The algorithm successfully trains unrestricted DMNN in practical scenarios.

Unrestricted DMNN can represent a broader class of morphological operators.

The approach improves the modeling capacity of morphological neural networks.

Abstract

There have been attempts to insert mathematical morphology (MM) operators into convolutional neural networks (CNN), and the most successful endeavor to date has been the morphological neural networks (MNN). Although MNN have performed better than CNN in solving some problems, they inherit their black-box nature. Furthermore, in the case of binary images, they are approximations that loose the Boolean lattice structure of MM operators and, thus, it is not possible to represent a specific class of W-operators with desired properties. In a recent work, we proposed the Discrete Morphological Neural Networks (DMNN) for binary image transformation to represent specific classes of W-operators and estimate them via machine learning. We also proposed a stochastic lattice descent algorithm (SLDA) to learn the parameters of Canonical Discrete Morphological Neural Networks (CDMNN), whose architecture is composed only of operators that can be decomposed as the supremum, infimum, and complement of erosions and dilations. In this paper, we propose an algorithm to learn unrestricted sequential DMNN, whose architecture is given by the composition of general W-operators. We illustrate the algorithm in a practical example.