# Binary Morphological Neural Network

arXiv: https://arxiv.org/abs/2203.12337 · HTML: https://mlsanity.com/paper/2203.12337/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 23 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Bitwise Neural Networks](https://mlsanity.com/paper/1601.06071/) (2016)
- [Deep Morphological Neural Networks](https://mlsanity.com/paper/1909.01532/) (2019)
- [Going beyond p-convolutions to learn grayscale morphological operators](https://mlsanity.com/paper/2102.10038/) (2021)

## Built on by (most cited first, 4 of 4)

- [An Algorithm to Train Unrestricted Sequential Discrete Morphological Neural Networks](https://mlsanity.com/paper/2310.04584/) (2023)
- [Binary Multi Channel Morphological Neural Network](https://mlsanity.com/paper/2204.08768/) (2022)
- [A foundation for exact binarized morphological neural networks](https://mlsanity.com/paper/2401.03830/) (2024)
- [Training morphological neural networks with gradient descent: some theoretical insights](https://mlsanity.com/paper/2403.12975/) (2024)

## Abstract (arXiv)

In the last ten years, Convolutional Neural Networks (CNNs) have formed the basis of deep-learning architectures for most computer vision tasks. However, they are not necessarily optimal. For example, mathematical morphology is known to be better suited to deal with binary images. In this work, we create a morphological neural network that handles binary inputs and outputs. We propose their construction inspired by CNNs to formulate layers adapted to such images by replacing convolutions with erosions and dilations. We give explainable theoretical results on whether or not the resulting learned networks are indeed morphological operators. We present promising experimental results designed to learn basic binary operators, and we have made our code publicly available online.