Binary Morphological Neural Network

TL;DR

This paper introduces a morphological neural network tailored for binary images, replacing traditional CNN layers with erosions and dilations, and provides theoretical and experimental validation of its capabilities.

Contribution

It presents a novel neural network architecture that directly models morphological operations for binary images, with theoretical analysis and promising experimental results.

Findings

The network can learn basic binary morphological operators.

Theoretical analysis confirms the network's morphological properties.

Experimental results demonstrate effective learning of binary operators.

Abstract

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.