Going beyond p-convolutions to learn grayscale morphological operators

TL;DR

This paper introduces two new morphological layers that extend p-convolutions, enabling more effective integration of morphological operations into deep neural networks without the drawbacks of previous methods.

Contribution

The authors propose two novel morphological layers that improve upon p-convolutions, facilitating differentiable morphological operations in deep learning architectures.

Findings

New layers outperform previous p-convolution methods.

Demonstrated potential for integration into deep neural networks.

Showed effectiveness in morphological tasks.

Abstract

Integrating mathematical morphology operations within deep neural networks has been subject to increasing attention lately. However, replacing standard convolution layers with erosions or dilations is particularly challenging because the min and max operations are not differentiable. Relying on the asymptotic behavior of the counter-harmonic mean, p-convolutional layers were proposed as a possible workaround to this issue since they can perform pseudo-dilation or pseudo-erosion operations (depending on the value of their inner parameter p), and very promising results were reported. In this work, we present two new morphological layers based on the same principle as the p-convolutional layer while circumventing its principal drawbacks, and demonstrate their potential interest in further implementations within deep convolutional neural network architectures.