# An Algorithm to Train Unrestricted Sequential Discrete Morphological Neural Networks

arXiv: https://arxiv.org/abs/2310.04584 · HTML: https://mlsanity.com/paper/2310.04584/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 6 Oct 2023.

## Builds on (most cited first, 7 of 7)

- [Morphological Network: How Far Can We Go with Morphological Neurons?](https://mlsanity.com/paper/1901.00109/) (2019)
- [Learning Deep Morphological Networks with Neural Architecture Search](https://mlsanity.com/paper/2106.07714/) (2021)
- [Binary Morphological Neural Network](https://mlsanity.com/paper/2203.12337/) (2022)
- [Morphological Networks for Image De-raining](https://mlsanity.com/paper/1901.02411/) (2019)
- [MorphPool: Efficient Non-linear Pooling & Unpooling in CNNs](https://mlsanity.com/paper/2211.14037/) (2022)
- [Discrete Morphological Neural Networks](https://mlsanity.com/paper/2309.00588/) (2023)
- [Image operator learning coupled with CNN classification and its application to staff line removal](https://mlsanity.com/paper/1709.06476/) (2017)

## Built on by (most cited first, 2 of 2)

- [The Lattice Overparametrization Paradigm for the Machine Learning of Lattice Operators](https://mlsanity.com/paper/2310.06639/) (2023)
- [On the representation of stack operators by mathematical morphology](https://mlsanity.com/paper/2504.09766/) (2025)

## Abstract (arXiv)

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.