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.
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