# Deep Morphological Neural Networks

arXiv: https://arxiv.org/abs/1909.01532 · HTML: https://mlsanity.com/paper/1909.01532/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2019.

## Built on by (most cited first, 9 of 9)

- [Going beyond p-convolutions to learn grayscale morphological operators](https://mlsanity.com/paper/2102.10038/) (2021)
- [Binary Morphological Neural Network](https://mlsanity.com/paper/2203.12337/) (2022)
- [Revisiting Tropical Polynomial Division: Theory, Algorithms and Application to Neural Networks](https://mlsanity.com/paper/2306.15157/) (2023)
- [Training Deep Morphological Neural Networks as Universal Approximators](https://mlsanity.com/paper/2505.09710/) (2025)
- [Logarithmic Morphological Neural Nets robust to lighting variations](https://mlsanity.com/paper/2204.09319/) (2022)
- [Binary Multi Channel Morphological Neural Network](https://mlsanity.com/paper/2204.08768/) (2022)
- [HaarNet: Large-scale Linear-Morphological Hybrid Network for RGB-D Semantic Segmentation](https://mlsanity.com/paper/2310.07669/) (2023)
- [A foundation for exact binarized morphological neural networks](https://mlsanity.com/paper/2401.03830/) (2024)
- [Semiring Activation in Neural Networks](https://mlsanity.com/paper/2405.18805/) (2024)

## Abstract (arXiv)

Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome and time-consuming task. In this paper, a morphological neural network is proposed to address this problem. Serving as a nonlinear feature extracting layer in deep learning frameworks, the efficiency of the proposed morphological layer is confirmed analytically and empirically. With a known target, a single-filter morphological layer learns the structuring element correctly, and an adaptive layer can automatically select appropriate morphological operations. For practical applications, the proposed morphological neural networks are tested on several classification datasets related to shape or geometric image features, and the experimental results have confirmed the high computational efficiency and high accuracy.