Binary Multi Channel Morphological Neural Network

TL;DR

This paper introduces Binary Morphological Neural Networks (BiMoNNs), a new architecture combining neural networks with mathematical morphology, offering explainability and effective learning of morphological operators for binary data, demonstrated on medical imaging.

Contribution

The paper presents a novel BiMoNN architecture that integrates morphological operators into neural networks, enabling explainability and binarization of networks for binary input-output tasks.

Findings

BiMoNNs can learn classical morphological operators

BiMoNNs are equivalent to morphological operators

Promising results on medical imaging tasks

Abstract

Neural networks and particularly Deep learning have been comparatively little studied from the theoretical point of view. Conversely, Mathematical Morphology is a discipline with solid theoretical foundations. We combine these domains to propose a new type of neural architecture that is theoretically more explainable. We introduce a Binary Morphological Neural Network (BiMoNN) built upon the convolutional neural network. We design it for learning morphological networks with binary inputs and outputs. We demonstrate an equivalence between BiMoNNs and morphological operators that we can use to binarize entire networks. These can learn classical morphological operators and show promising results on a medical imaging application.