Going beyond p-convolutions to learn grayscale morphological operators
This work addresses a specific problem in computer vision and image processing for researchers and practitioners seeking to enhance neural networks with mathematical morphology, but it appears incremental as it builds on prior p-convolution methods.
The authors tackled the challenge of integrating non-differentiable morphological operations like erosion and dilation into deep neural networks by proposing two new morphological layers that improve upon existing p-convolutional layers, demonstrating their potential for use in deep convolutional architectures.
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.